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NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS
PUBLISHING FOR ONE WORLD
New Delhi · Bangalore · Chennai · Cochin · Guwahati · Hyderabad
Jalandhar · Kolkata · Lucknow · Mumbai · Ranchi
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En
All rights reserved.
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Copyright © 2006, 2004, 1990, New Age International (P) Ltd., Publishers
Published by New Age International (P) Ltd., Publishers
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No part of this ebook may be reproduced in any form, by photostat, microfilm,
xerography, or any other means, or incorporated into any information retrieval
system, electronic or mechanical, without the written permission of the
publisher. All inquiries should be emailed to rights@newagepublishers.com
w.
ISBN (10) : 81-224-2322-1
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ISBN (13) : 978-81-224-2322-8
PUBLISHING FOR ONE WORLD
NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS
4835/24, Ansari Road, Daryaganj, New Delhi - 110002
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Preface to the Fifth Edition
eri
ng
.i n
The data given in the previous edition has been thoroughly checked. Errors occurring in some
pages have been corrected.
This little book has been the companion volume of the author’s book—Fundamentals of Compressible Flow. They together will continue to serve the needs of students, scientists and engineers
in areas of aerospace, mechanical, chemical and gas engineering.
En
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It is hoped that the new format of this edition will be more convenient to use.
S.M. YAHYA
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New Delhi
July, 2006
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Preface to the First Edition
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ng
.i n
There was a long-felt need for gas tables to support the courses in Gas Dynamics, Turbomachinery
and Aerodynamics taught at different levels.
These tables have been prepared for compressible fluids of common use. Long and detailed
tables in a wide range covering a number of values of γ = cp /cv besides being expensive are not
fully used by a majority of students.
Various formulas which form the basis of the tables are also included which will be useful for
ready reference.
With numerical work of this magnitude it is highly probable that some errors may have crept
in; reference to these errors and suggestions for improvement will be highly appreciated.
The ranges of various tables have been chosen according to their importance and frequency
in use.
S.M. YAHYA
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New Delhi
July, 1978
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Contents
v
Preface to the First Edition
vii
eri
ng
.i n
Preface to the Fifth Edition
Notation
Introduction
1.1
1.2
1.3
1.4
1.5
Air
Hydrogen
Carbon Dioxide
Steam
Freon–21
Properties of Standard Atmosphere
3.
Isentropic Flow of Perfect Gases
3.1 γ = 1.3
3.2 γ = 1.4
3.3 γ = 1.67
21
28
40
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Oblique Shocks in Perfect Gases
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62
71
Flow of Perfect Gases with Friction (Fanno Flow)
6.1 γ = 1.3
6.2 γ = 1.4
6.3 γ = 1.67
7.
19
47
52
57
5.1 Wave Angles for Given Deflections, γ = 1.4
5.2 Upstream and Downstream Mach Numbers and Deflections from
Normal Shock Relations, γ = 1.4
6.
14
15
16
17
18
Normal Shocks in Perfect Gases
4.1 γ = 1.3
4.2 γ = 1.4
4.3 γ = 1.67
5.
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2.
4.
2
Gas Dynamic Properties of Some Gases and Vapours
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1.
1
75
81
87
Isothermal Flow of Perfect Gases with Friction
7.1 γ = 1.3
7.2 γ = 1.4
93
99
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Contents
x
Flow of Perfect Gases with Heat Transfer (Rayleigh Flow)
8.1
8.2
8.3
8.4
9.
γ = 1.3
γ = 1.4
γ = 1.67
Maximum Heat Transfer in Perfect Gases
Prandtl-Meyer Function with Mach Angles
9.1 α and ω (M) as functions of M
9.2 M and α as functions of ω (M)
10.
105
111
117
123
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.i n
8.
125
130
Approximate Velocities and Mach Numbers of Air
Corresponding to Dynamic Heads, and Pressure Ratios
135
136
Manometer Inclinations Required for the Desired Magnification
of the Deflection
138
12.
Static Pressure Drop in Gas Pipe Lines
139
13.
Isentropic Compressor Power
141
14.
Pumping Power for Fans and Blowers
143
15.
S.I, Metric and British Units
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134
147
148
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15.1 Principal dimensions and units
15.2 Conversion of Units
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11.
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10.1 Air velocities and Mach numbers as functions of
dynamic heads in mm W.G.
10.2 Air velocities and Mach numbers as functions of
dynamic heads in mm Hg.
10.3 Mach Numbers as functions of pressure ratios (γ = 1.4)
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Introduction
1
Notation
Velocity of sound
fluid velocity
specific heat at constant pressure
specific heat at constant volume
A
area of cross-section
D
hydraulic mean diameter
f
h
L
1
Lmax
mean coefficient of friction
F
impulse function
enthalpy, actual deflection
k
constant
length of the pipe line
magnified value of manometer deflection
maximum pipe length required for choking conditions
m
P
∆p
Qmax
R
t
v
Z
α
γ
δ
ρ
η
mass flow rate
power
pressure rise or drop
maximum heat transfer
Gas constant
temperature in °C
specific volume
altitude
Mach angle, manometer inclination
= cp /cv
deflection or half wedge angle
density
efficiency
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En
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.i n
a
c
cp
cv
M
p
pr
Q
s
T
w
∆s
Mach number
pressure
pressure ratio
volume flow rate
entropy
temperature in K
mass flow rate
change of entropy
w.
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σ
wave angle
µ
coefficient of viscosity
ω(M) Prandtl-Meyer function
Subscripts
o
Stagnation state
y
downstream of normal shock
2
downstream of oblique shock
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x
l
s
upstream of normal shock
upstream of oblique shock
isentropic
Superscript
*
corresponding to choking conditions (M = 1)
*t
corresponding to M =
1
γ
(isothermal flow)
1
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Gas Tables for Compressible Flow Calculations
2
Introduction
This section is designed to help the user to make the best use of the data given in the tables.
Detailed explanation of the various theories behind the formulae mentioned in this section are not
included; the user is expected to be aware of these while using the tables. However, some explanatory notes and figures have been included.
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.i n
1. Gas dynamic properties of some vapours and gases
It is well known that the specific heats (cp and cv) of gases and vapours vary with temperature.
Therefore, the values of the ratio of specific heats, Gas constant and the maximum mass flow
parameter also vary with temperature. These have been tabulated for a range of temperatures at
given values of pressure.
Only some of the commonly used gases and vapours have been chosen for these tables.
γ = cp cv
R = cp − cv
a = γRT
A * P0
Lγ F 2 I
=M G
MN R H γ + 1JK
γ +1
γ −1
OP
PQ
...(1.1)
...(1.2)
...(1.3)
12
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Formulae
...(1.4)
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2. Properties of the standard atmosphere
Values of temperature, velocity of sound, pressure, density and dynamic viscosity of air are tabulated against altitude in the range of 0 to 20,000 meters.
The lapse rate in temperature is 0.65°C for each 100 meters of altitude upto an altitude of
11000 metres.
Kinematic viscosity (µ/ρ) can be determined with the help of the last two columns.
3. Isentropic flow of perfect gases
Subsonic and supersonic isentropic flows in nozzles and diffusers are shown in figures 1 and 2
respectively. Pressures corresponding to the choking and stagnation states in both the cases are
also shown.
Assumptions
(a) One dimensional isentropic flow
(b) Perfect gas with constant specific heats and molecular weight.
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Introduction
3
h
p0
eri
ng
.i n
M=0
p
p*
M<1
M = M* = 1
En
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p
M>1
S
Fig. 1. Isentropic Accelerating Flow
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h
p0
M=0
p
M<1
p*
M = M* = 1
p
M>1
S
Fig. 2. Isentropic Decelerating Flow
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Gas Tables for Compressible Flow Calculations
4
Formulas
T0 = T0* = constant
...(3.1)
T
=
T0
...(3.2)
FG IJ
H K
γ
γ −1
F γ − 1 M IJ
= G1 +
H 2 K
FG IJ
H K
1
γ −1
F γ − 1 M IJ
= G1 +
H 2 K
p
T
=
p0
T0
ρ
T
=
ρ0
T0
γ
1
−
γ
2
1
2 1− γ
En
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e
γ +1 2
M
2
M* = * =
γ −1 2
c
1+
M
2
c
1
=
*
M
A
F
2
A
M
×
F γ − 1 M IJ
2 b γ + 1g G1 +
H 2 K
p
=
p0
ww
A
*
g
1 + γM 2
=
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F*
γ +1
2 γ −1
LMF 2 I FG1 + γ − 1 M IJ OP b
NGH γ + 1JK H 2 K Q
arn
A
eri
ng
.i n
1
γ −1 2
1+
M
2
FG 2 IJ
H γ + 1K
M1+
...(3.3)
...(3.4)
...(3.5)
...(3.6)
...(3.7)
2
γ +1
2 γ −1
b g
...(3.8)
γ −1 2
M
2
4. Normal shocks in perfect gases
A normal shock from state X to state Y is shown in figure 3.
Assumptions
(a)
(b)
(c)
(d)
One dimensional flow with normal shocks
Constant area duct
Perfect gas with constant specific heats and molecular weight
Adiabatic flow
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Introduction
5
Formulas
T0 x = T0 y
...(4.1)
LM 2 + M OP
γ −1
=M
MM 2 γ M − 1PPP
Q
N γ −1
12
2
x
py
px
...(4.2)
2
x
=
1 + γM 2x
1+
γM 2y
=
γ −1
2γ
M 2x −
γ +1
γ +1
FG
H
eri
ng
.i n
My
IJ FG
KH
b g
b g
IJ
K
γ −1 2
2γ
γ −1 2
Mx
M 2x − 1
1+
M
x
Ty
−
γ
2
1
2
=
=
2
γ −1 2
Tx
γ +1
My
1+
M 2x
2
2 γ −1
ax
ρy
ρx
FT I
=G J
HT K
12
y
x
=
p y Tx
p x Ty
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ay
En
gin
e
1+
IJ
K
γ
1− γ
F γ − 1 M IJ
= G1 +
H 2 K
γ
γ −1
FG
H
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px
γ −1 2
Mx
= 1+
p0x
2
p0y
ww
py
2
y
p0y
p0x
=
p0y p y p x
p y p x p0x
p
∆s
= ln 0 x
R
p0y
p0y
px
=
...(4.3)
...(4.4)
...(4.5)
...(4.6)
...(4.7)
...(4.8)
...(4.9)
...(4.10)
p0y p y
py px
...(4.11)
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Gas Tables for Compressible Flow Calculations
6
h
M = 1/ g
py
Y
Fanno line
M<1
p*
M<1
eri
ng
.i n
M=1
Norma
l shock
p*
M=1
p = constant
Rayleigh line
M>1
M>1
px
En
gin
e
X
s
Fig. 3. Normal Shock, Fanno and Rayleigh Lines
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5. Oblique shocks in perfect gases
An oblique shock wave is inclined at an angle to the direction of upstream flow. Figure 4 shows an
oblique shock wave at the corner of a wall. Supersonic flow passing through an oblique shock
(wave angle = σ) is deflected through an angle (δ). The same picture is obtained when a supersonic
flow is deflected through an angle (δ) either over a wedge or a wall corner.
Oblique
shock
My
M1 = c1/a1
M2 = c2 /a2
Mx
s
d
Fig. 4. Flow Through Oblique Shock Wave
Figure 4 shows the upstream and downstream Mach numbers corresponding to a normal shock.
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Introduction
7
Assumptions
(a)
(b)
(c)
(d)
Perfect gas, with constant specific heats and molecular weight,
adiabatic flow,
absence of body forces,
absence of external work.
tan δ =
eri
ng
.i n
Formulas
M12 sin 2 σ − 2 cot σ
b
2 + M12 γ + cos 2 σ
M x = M1 sin σ
b
M y = M 2 sin σ − δ
g
g
...(5.1)
...(5.2)
...(5.3)
En
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e
Table 5.1 is used to determine the wave angle for given values of upstream Mach numbers and
deflection.
Table 5.2 enables calculations of properties downstream of the oblique shock through normal
shock tables. The gas property ratios corresponding to Mach number Mx can be found from Table
4.2.
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6. Flow of perfect gases with friction (Fanno Flow)
A Fanno line is shown on h-s co-ordinates in figure 3.
Friction in the passage leads to increase in entropy and takes the process towards the choking
conditions (M = M* = 1).
Assumptions
One dimensional flow with friction,
Constant area duct,
perfect gas with constant specific heats and molecular weight,
adiabatic flow.
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(a)
(b)
(c)
(d)
Formulas
ww
T0 = T0* = constant
p
*
p
c
c
*
=
=
1
M
γ +1
γ −1 2
2 1+
M
2
FG
H
ρ*
=M
ρ
...(6.1)
IJ
K
γ +1
γ −1 2
2 1+
M
2
FG
H
...(6.2)
IJ
K
...(6.3)
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Gas Tables for Compressible Flow Calculations
8
T
*
=
γ +1
γ −1 2
2 1+
M
2
FG
H
IJ
K
...(6.4)
γ +1
2 γ −1
LM 2 FG1 + γ − 1 M IJ OP b
H 2 KP
1
= M
MM
MN bγ + 1g PPQ
2
p *0
F
F*
4f
1 + γM 2
=
LM b g FG
H
N
M 2 γ +1 1 +
γ −1 2
M
2
IJ OP
KQ
L max 1 − M 2 γ + 1
=
+
ln
2γ
D
γM 2
FG
H
...(6.5)
12
En
gin
e
p0
g
eri
ng
.i n
T
bγ + 1g M
2 1+
...(6.6)
2
γ −1 2
M
2
IJ
K
...(6.7)
γ+1
s − s*
γ +1
⎡
⎤ 2γ
= ln M2 ⎢
γ −1 2 ⎞⎥
cp
⎛
⎢ 2 M2 ⎜ 1 +
M ⎟⎥
2
⎝
⎠ ⎦⎥
⎣⎢
arn
...(6.8)
w.
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7. Isothermal flow of perfect gases with friction
The combined effect of friction and heat transfer in long ducts can be considered to produce an
isothermal flow model.
e
j
*t
*t
*t
*t
*t
Here the reference values of the properties p , ρ , c , T0 , p 0 and L max are taken at the
ww
Mach number
M*t =
1
γ
Assumptions
(a)
(b)
(c)
(d)
One dimensional flow with friction and heat transfer,
Constant area duct,
Perfect gas with constant specific heats and molecular weight,
Isothermal flow.
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Introduction
9
Formulas
c
c *t
T0
T0* t
p0
p *0t
4f
1
=
M
...(7.1)
γ
=
ρ*t M
= γ
ρ
=
2γ
γ −1 2
M
1+
3γ − 1
2
=
...(7.2)
FG
H
1
M
γ
IJ
K
LM 2 γ FG1 + γ − 1 M IJ OP
N 3γ − 1 H 2 K Q
2
L max 1 − γM 2
=
+ ln γM 2
D
γM 2
e j
γ
γ −1
En
gin
e
p
*t
eri
ng
.i n
p
...(7.3)
...(7.4)
...(7.5)
arn
8. Flow of perfect gases with heat transfer (Rayleigh flow)
A Rayleight line is shown in figure 3. Heat addition increases the entropy and takes the process
towards the choking conditions, (M = M* = 1). This behaviour imposes a limit to heat addition;
therefore for a given initial Mach Number there is a fixed value of the maximum possible heat
transfer (Qmax). This has been tabulated in Table 8.4.
Assumptions
Formulas
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(a) One dimensional flow with heat transfer,
(b) Constant area frictionless duct,
(c) Perfect gas with constant specific heats and molecular weight.
=
1+ γ
ww
p
p
*
...(8.1)
1 + γM 2
γ
⎡ ⎛
γ − 1 2 ⎞ ⎤ γ−1
2 ⎜1 +
M ⎟⎥
⎢
p0
1+ γ
2
⎝
⎠⎥
⎢
=
*
2
γ +1
p0 1 + γM ⎣⎢
⎦⎥
T
T
*
=
F 1+ γ I
GH 1 + γM JK
2
...(8.2)
2
M2
...(8.3)
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Gas Tables for Compressible Flow Calculations
10
T0*
ρ
ρ*
=
=
2
2
c*
1 + γM 2
=
c
1 + γ M2
b g
F
GH
s − s*
1+ γ
= ln M 2
cp
1 + γM 2
I
JK
γ +1
γ
F = F * = constant
e j
b g
...(8.4)
2
2
...(8.6)
...(8.7)
En
gin
e
M2 − 1
Q max
=
cpT 2 γ + 1 M2
...(8.5)
eri
ng
.i n
T0
b g FGH γ 2− 1 M IJK
e1 + γM j
2 1 + γ M2 1 +
...(8.8)
ww
w.
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arn
9. Prandtl-Meyer functions with Mach angles
Supersonic flow of a gas along a wall turning in the clock-wise direction is shown in figure 5.
Mach wave and the Mach angle (α) are also shown.
Mach wave
M>1
a
M
+d
M
Wall
Fig. 5. Prandtl-Meyer Expansion
Assumptions
(a) Perfect gas with constant specific heats and molecular weight,
(b) Isentropic flow.
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Introduction
11
Formulas
1
M
b g
...(9.1)
γ +1
γ −1 2
M − 1 − tan −1 M 2 − 1
tan −1
γ −1
γ +1
e
ω M =
j
...(9.2)
eri
ng
.i n
sin α =
10. Approximate velocities and Mach numbers of air
At low velocities (M < 0.30) correct values of the velocity of a gas can be determined by measur-
FG
H
IJ
K
b
2
RT p 0 − p
ρ
c=
M=
g
c
bγRTg
12
En
gin
e
1 2
ρc . Conversely the value of the dynamic head required for
2
obtaining a given velocity can also be determined.
Knowledge of the temperature of the gas along with the dynamic head gives the value of Mach
Number.
ing the dynamic head p 0 − p =
...(10.1)
...(10.2)
w.
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arn
For lower velocities dynamic head is measured in millimetres of water (mmW.G) on a vertical
or inclined tube manometer. At higher velocities dynamic head is more conveniently measured in
millimeters of mercury (mm Hg).
Tables 10.1 and 10.2 give approximate velocities and Mach numbers at the prescribed values
of pressure and temperature; the approximation is less realistic at higher Mach numbers on account of increasing deviation of the actual flow from incompressible flow conditions. Therefore,
at higher Mach numbers Table 10.2 gives only rough estimates of the velocity and Mach number.
On account of this discrepancy the use of Table 10.3 is recommended at higher Mach numbers.
ww
11. Measurement of low pressures on inclined manometers.
Low pressures and velocities of gases can be measured by magnifying the actual manometer
deflection (h) many times. This is done by inclining the manometer tube/tubes by angles shown in
table 11.
Actual (h) and magnified (A) values of the deflection are shown in figure 6.
Plane of the manometer tubes
l
h
a
Horizontal plane
Fig. 6. Actual (h) & Magnified (A) Values of Deflections in Inclined Tube Manometer
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Gas Tables for Compressible Flow Calculations
12
12. Static pressure drop (pr = outlet pressure/inlet pressure) in gas pipe lines
Compressors are required to raise the pressure of gases to compensate for the pressure drop in long
pipe lines. In these tables values of static pressure drop in the pipe lines have been tabulated with
the assumption of isothermal flow. The flow has been further assumed to start with a low Mach
number of M1 = 0.02. Pressure drop has been expressed as pressure ratio
p r = p 2 p1 .
p r = φ M1 , γ , f , L D
p r = 0.02 2500 − 4 γ f L D
eri
ng
.i n
Following relations have been used to compute the values of the pressure ratio:
...(12.1)
...(12.2)
Following values of the parameters have been covered:
γ = 1.3, 1, 4
En
gin
e
f = 0.002, 0.0025, 0.0030, 0.0035, 0.0040, 0.0050
L D = 10 − 2 × 105
These values of the pressure drop can be employed to obtain the magnitudes of the compressor
power.
13. Isentropic compressor power
The ideal power required to drive a compressor is given by:
arn
c
h
c ′p T2 s − T1′ = Isentropic power
P′ = m
b γ −1g γ − 1
c ′p T1′ p r
P′ = m
w.
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...(13.1)
The pressure ratio is given by
b
p r = exit pressure entry pressure p 2 p1 = T2 s T1
g
b g
γ γ −1
...(13.2)
ww
For the sake of generality following values have been used in the calculations:
c ′p = 1.0 kJ kg K
T1′ = 300 K
The actual power (for a given pressure ratio) can be calculated by multiplying the values in the
table by the factor k given by:
k = c p × T1 η0 T1′ = c p × T1 300 η0
...(13.3)
where T1 = actual temperature of the gas at entry
η0 = overall efficiency of the compressor and motor (prime mover) together.
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Introduction
13
ν
Q=m
P = Q ⋅ ∆p η 0
Overall all efficiency η0 = 0.65 (assumed)
eri
ng
.i n
14. Approximate values of pumping power for fans and blowers
Fans and blower of various sizes are required to raise the pressure of a gas from a few millimetres
of W.G. to large values. Table 14 presents approximate values of the power requirement of fans
and blowers in a wide range.
Power requirement for a specific application corresponding to values of Q and ∆p which do
not appear in the tables can also be found with the help of available data.
Following formulas have been used:
P = Q ⋅ ∆p 66.261 kW
Q is in
m3/s
; ∆p is in mm W.G.
...(14.1)
...(14.2)
...(14.3)
ww
w.
Le
arn
En
gin
e
15. Dimensions and units
Principal dimensions and units occurring in gas dynamics are given in Table 15.1. Table 15.2 gives
the conversion of some units.
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Gas Tables for Compressible Flow Calculations
14
TABLE 1.1
Gas dynamic properties of air at various temperatures
cv
K
kJ/kg K
kJ/kg K
273
373
473
573
673
1.004
1.010
1.025
1.045
1.069
0.716
0.723
0.737
0.758
0.782
1.402
1.397
1.390
1.379
1.367
773
873
973
1073
1173
1.092
1.115
1.136
1.154
1.170
0.806
0.828
0.849
0.867
0.884
1.355
1.347
1.338
1.331
1.324
1273
1373
1473
1573
1673
1.185
1.197
1.208
1.218
1.227
0.898
0.910
0.920
0.930
0.940
1.320
1.315
1.313
1.309
1.305
w T0 A∗ p0
R
a
kJ/kg K
m/s
0.288
0.288
0.288
0.287
0.287
332.0
387.4
435.3
476.2
513.8
0.0404
0.0403
0.0402
0.0400
0.0400
0.286
0.287
0.287
0.287
0.286
547.3
580.9
611.3
640.2
666.3
0.0400
0.0398
0.0396
0.0396
0.0397
0.287
0.287
0.288
0.288
0.287
694.3
719.9
746.3
770.3
791.7
0.0395
0.0395
0.0394
0.0393
0.0394
ww
w.
Le
arn
En
gin
e
cp
eri
ng
.i n
γ
T
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Gas Dynamic Properties of Some Gases and Vapours
15
TABLE 1.2
Gas dynamic properties of hydrogen at various temperatures
γ
cv
K
kJ/kg K
kJ/kg K
273
373
473
573
14.195
14.448
14.503
14.534
10.071
10.324
10.380
10.409
673
773
873
973
14.581
14.663
14.779
14.930
1073
1173
1273
1373
15.115
15.313
15.518
15.736
1473
1573
1673
1773
15.950
16.166
16.370
16.565
w T0 A∗ p0
R
a
kJ/kg K
m/s
1.409
1.399
1.397
1.396
4.124
4.124
4.123
4.125
1260.0
1467.2
1650.7
1816.7
0.01068
0.01066
0.1065
0.01065
10.456
10.538
10.654
10.805
1.395
1.391
1.387
1.381
4.125
4.125
4.125
4.125
1967.9
2106.4
2235.0
2355.0
0.01065
0.01064
0.01059
0.0106
10.991
11.188
11.393
11.611
1.375
1.368
1.362
1.355
4.124
4.125
4.125
4.125
2466.8
2573.4
2674.4
2770.5
0.01059
0.01058
0.01055
0.01053
1.349
1.342
1.337
1.331
4.125
4.126
4.125
4.125
2862.8
2952.0
3037.4
3120.7
0.01052
0.0105
0.0105
0.01047
eri
ng
.i n
cp
arn
En
gin
e
T
ww
w.
Le
11.825
12.040
12.245
12.440
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Gas Tables for Compressible Flow Calculations
16
TABLE 1.3
Gas dynamic properties of carbon dioxide at various temperatures
γ
cv
K
kJ/kg K
kJ/kg K
273
373
473
573
0.815
0.914
0.993
1.057
0.626
0.725
0.804
0.868
673
773
873
973
1.110
1.155
1.192
1.223
1073
1173
1273
1373
1.249
1.272
1.290
1.306
1473
1573
1673
1773
1.319
1.332
1.342
1.350
1873
1973
2073
2173
1.357
1.364
1.369
1.374
a
kJ/kg K
m/s
1.302
1.261
1.237
1.218
0.189
0.189
0.189
0.189
259.2
298.1
332.6
363.1
0.0485
0.0481
0.0476
0.0473
0.921
0.966
1.003
1.034
1.205
1.195
1.188
1.182
0.189
0.189
0.189
0.189
391.5
417.9
442.8
466.4
0.0472
0.0470
0.0469
0.0469
1.060
1.082
1.101
1.117
1.178
1.176
1.172
1.169
0.189
0.190
0.189
0.189
488.8
511.8
530.9
550.8
0.0467
0.0466
0.0467
0.0466
1.130
1.142
1.152
1.161
1.167
1.166
1.164
1.162
0.189
0.190
0.190
0.189
570.1
590.4
608.5
624.2
0.0466
0.0465
0.0465
0.0465
1.168
1.175
1.181
1.185
1.162
1.161
1.159
1.159
0.189
0.189
0.188
0.189
641.3
657.9
672.1
690.0
0.0465
0.0466
0.0465
0.0464
arn
w.
Le
ww
w T0 A∗ p0
R
eri
ng
.i n
cp
En
gin
e
T
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Gas Dynamic Properties of Some Gases and Vapours
17
TABLE 1.4
Gas dynamic properties of superheated steam at p = 0.981 bar
γ
cv
K
kJ/kg K
kJ/kg K
413
433
453
473
493
1.997
1.985
1.975
1.980
1.985
1.482
1.485
1.490
1.500
1.505
513
533
553
573
593
1.990
1.997
2.000
2.013
2.025
613
633
653
673
693
2.040
2.045
2.050
2.071
2.085
a
kJ/kg K
m/s
1.347
1.336
1.325
1.320
1.318
0.515
0.500
0.485
0.480
0.480
535.0
537.8
539.6
547.4
558.5
0.0297
0.0300
0.0305
0.0306
0.0306
1.515
1.525
1.536
1.548
1.556
1.313
1.310
1.302
1.300
1.300
0.475
0.472
0.464
0.465
0.469
565.6
574.0
578.0
588.6
601.6
0.0307
‘0.0308
0.0311
0.0310
0.0308
1.571
1.584
1.594
1.607
1.619
1.298
1.291
1.286
1.288
1.287
0.469
0.461
0.456
0.464
0.466
611.0
613.8
618.8
634.4
644.9
0.0308
0.0310
0.0311
0.0308
0.0308
1.738
1.658
1.624
1.616
1.620
1.438
1.374
1.348
1.332
1.320
0.762
0.620
0.566
0.536
0.519
704.6
648.0
637.8
639.5
648.1
0.0250
0.0273
0.0283
0.0291
0.0294
2.135
2.144
2.156
2.173
2.194
1.633
1.650
1.671
1.691
1.717
1.307
1.299
1.290
1.285
1.278
0.502
0.494
0.485
0.482
0.477
654.6
667.0
677.2
691.9
703.9
0.0298
0.0299
0.0302
0.0302
0.0303
2.215
2.240
2.265
1.742
1.767
1.792
1.271
1.267
1.264
0.473
0.473
0.473
716.3
731.7
746.8
0.0304
0.0304
0.0304
853
893
933
w.
Le
ww
653
693
733
773
813
2.500
2.278
2.190
2.152
2.139
arn
At p = 9.81 bar
453
493
533
573
613
w T0 A∗ p0
R
eri
ng
.i n
cp
En
gin
e
T
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Gas Tables for Compressible Flow Calculations
18
TABLE 1.5
Gas dynamic properties of superheated Freon-21 at various temperatures
γ
T
cp
cv
K
kJ/kg K
kJ/kg K
R
a
kJ/kg K
m/s
w T0 A∗ p0
0.447
0.496
0.540
0.579
0.615
1.187
1.165
1.152
1.142
1.130
0.084
0.082
0.082
0.082
0.080
155.7
164.4
174.7
184.3
190.9
0.0705
0.0713
0.0733
0.0698
0.0705
At p = 1.0 bar
293
0.616
313
0.630
333
0.646
353
0.662
373
0.678
0.521
0.539
0.557
0.575
0.593
1.182
1.168
1.159
1.151
1.143
0.095
0.091
0.089
0.087
0.085
181.4
182.5
185.4
188.0
190.4
0.0662
0.0673
0.0679
0.0685
0.0691
At p = 10.0 bar
333
0.812
383
0.799
393
0.792
403
0.786
413
0.783
423
0.782
433
0.782
443
0.782
453
0.783
463
0.785
473
0.786
0.644
0.645
0.647
0.651
0.655
0.658
0.663
0.667
0.672
0.676
0.681
1.261
1.239
1.224
1.207
1.195
1.188
1.179
1.172
1.165
1.161
1.154
0.168
0.154
0.145
0.135
0.128
0.124
0.119
0.115
0.111
0.109
0.105
265.6
270.3
264.1
256.3
251.4
249.7
246.5
244.4
242.1
242.1
239.4
0.0508
0.0527
0.0541
0.0558
0.0566
0.0580
0.0590
0.0599
0.0608
0.0614
0.0624
0.703
0.697
0.696
0.699
0.701
1.396
1.304
1.252
1.219
1.207
0.281
0.212
0.176
0.153
0.145
397.6
342.0
312.5
293.8
287.7
0.0408
0.0458
0.0459
0.0527
0.0538
arn
En
gin
e
0.531
0.578
0.622
0.661
0.695
ww
w.
Le
243
283
323
363
403
eri
ng
.i n
At p = 0.10 bar
At p = 20.0 bar
403
0.984
423
0.909
443
0.872
463
0.852
473
0.846
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Properties of Standard Atmosphere
19
TABLE 2
Properties of standard atmosphere
Z
t
T
a
p
ρ
m
°C
K
m/s
bar
kg/m3
µ
Ns
15.00
14.35
13.70
13.05
12.40
11.75
288.15
287.50
286.85
286.20
285.55
284.90
600
700
800
900
1000
11.10
10.45
9.80
9.15
8.50
284.25
283.60
282.95
282.30
281.65
1100
1200
1300
1400
1500
7.85
7.20
6.55
5.90
5.25
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
× 10 6
1.0133
1.000
0.989
0.978
0.966
0.955
1.225
1.213
1.202
1.190
1.178
1.167
17.93
17.90
17.88
17.84
17.80
17.77
338.0
337.6
337.3
337.0
336.6
0.943
0.932
0.921
0.909
0.898
1.156
1.145
1.134
1.123
1.111
17.74
17.70
17.66
17.64
17.61
281.00
280.35
279.70
279.05
278.40
336.1
335.7
335.4
335.0
334.5
0.888
0.877
0.866
0.856
0.845
1.100
1.090
1.079
1.070
1.058
17.58
17.55
17.50
17.48
17.45
4.60
3.95
3.30
2.65
2.00
277.75
277.10
276.45
275.80
275.15
334.1
333.7
333.4
333.0
332.6
0.835
0.825
0.815
0.805
0.795
1.048
1.037
1.027
1.017
1.006
17.40
17.38
17.35
17.31
17.28
1.35
0.70
0.05
−0.60
−1.25
274.50
273.85
273.20
272.55
271.90
332.2
332.0
331.5
331.0
330.6
0.785
0.775
0.766
0.756
0.747
0.996
0.986
0.976
0.967
0.957
17.25
17.22
17.17
17.14
17.12
arn
w.
Le
ww
340.5
340.0
339.7
339.5
338.9
338.5
En
gin
e
0
100
200
300
400
500
eri
ng
.i n
m
2
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Gas Tables for Compressible Flow Calculations
20
TABLE 2
Properties of standard atmosphere
Z
t
T
a
p
ρ
m
°C
K
m/s
bar
kg/m3
µ
Ns
eri
ng
.i n
m
2
× 10 6
-1.90
-2.55
-3.20
-3.85
-4.50
271.25
270.60
269.95
269.30
268.65
330.2
329.7
329.4
329.0
328.7
0.737
0.727
0.719
0.710
0.701
0.948
0.938
0.929
0.920
0.909
17.09
17.05
17.01
16.98
16.95
3500
4000
4500
5000
-7.75
-11.00
-14.25
-17.50
265.40
262.15
258.90
255.65
326.7
324.7
322.7
320.7
0.657
0.616
0.577
0.540
0.863
0.819
0.777
0.736
16.80
16.62
16.45
16.27
5500
6000
6500
7000
-20.75
-24.00
-27.25
-30.50
252.40
249.15
245.90
242.65
318.7
316.5
314.5
312.4
0.505
0.472
0.440
0.411
0.697
0.660
0.624
0.589
16.10
15.94
15.76
15.60
7500
8000
8500
9000
-33.75
-37.00
-40.25
-43.50
239.40
236.15
232.90
229.65
310.03
308.2
306.0
304.0
0.383
0.356
0.331
0.307
0.557
0.525
0.495
0.466
15.42
15.24
15.06
14.89
9500
10000
11000
12000
-46.75
-50.00
-56.50
-56.50
226.40
223.15
216.65
216.65
301.8
299.6
295.2
295.2
0.285
0.264
0.226
0.193
0.439
0.413
0.364
0.311
14.72
14.54
14.17
14.17
-56.50
-56.50
-56.50
-56.50
216.65
216.65
216.65
216.65
295.2
295.2
295.2
295.2
0.165
0.141
0.120
0.103
0.266
0.227
0.194
0.165
14.17
14.17
14.17
14.17
-56.50
-56.50
-56.50
-56.60
216.65
216.65
216.65
216.65
295.2
295.2
295.2
295.2
0.0878
0.0751
0.0641
0.0548
0.141
0.121
0.103
0.088
14.17
14.17
14.17
14.17
17000
18000
19000
20000
arn
w.
Le
ww
13000
14000
15000
16000
En
gin
e
2600
2700
2800
2900
3000
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Isentropic Flow of Perfect Gases
21
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
A
M
M*
T/T0
p/p0
A/A*
F/F*
A
*
p
p0
0.000
0.0214
0.0429
0.064
0.086
0.107
1.000
0.999
0.999
0.999
0.999
0.998
1.000
0.999
0.998
0.997
0.995
0.994
∞
29.268
14.644
9.774
7.342
5.885
∞
23.324
11.679
7.805
5.874
4.720
∞
29.261
14.629
9.751
7.312
5.848
0.12
0.14
0.16
0.18
0.20
0.1285
0.150
0.171
0.193
0.214
0.998
0.997
0.996
0.995
0.994
0.991
0.987
0.984
0.979
0.975
4.917
4.228
3.712
3.312
2.994
3.954
3.410
3.005
2.693
2.445
4.872
4.174
3.651
3.243
2.917
0.22
0.24
0.26
0.28
0.30
0.235
0.256
0.277
0.298
0.319
0.993
0.991
0.989
0.988
0.987
0.969
0.963
0.957
0.951
0.944
2.735
2.520
2.340
2.186
2.054
2.245
2.079
1.941
1.824
1.724
2.651
2.428
2.239
2.078
1.938
0.32
0.34
0.36
0.38
0.40
0.341
0.362
0.383
0.403
0.424
0.985
0.983
0.981
0.979
0.977
0.936
0.928
0.920
0.911
0.902
1.939
1.838
1.750
1.672
1.602
1.638
1.564
1.498
1.442
1.391
1.874
1.759
1.610
1.523
1.446
0.42
0.44
0.46
0.48
0.50
0.444
0.465
0.486
0.506
0.526
0.974
0.972
0.969
0.967
0.964
0.893
0.883
0.873
0.863
0.853
1.540
1.484
1.434
1.388
1.348
1.347
1.308
1.273
1.241
1.213
1.343
1.281
1.225
1.173
1.149
0.547
0.567
0.587
0.607
0.627
0.961
0.958
0.955
0.952
0.948
0.842
0.831
0.819
0.807
0.796
1.310
1.277
1.246
1.218
1.193
1.188
1.165
1.145
1.127
1.111
1.103
1.061
1.021
0.984
0.950
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
0.00
0.02
0.04
0.06
0.08
0.10
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Gas Tables for Compressible Flow Calculations
22
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
A
p
p0
M*
T/T0
p/p0
A/A*
F/F*
0.62
0.64
0.66
0.68
0.70
0.646
0.666
0.686
0.705
0.725
0.945
0.942
0.938
0.935
0.932
0.784
0.772
0.760
0.748
0.735
1.170
1.149
1.130
1.113
1.097
1.097
1.084
1.072
1.062
1.052
0.918
0.887
0.859
0.832
0.807
0.72
0.74
0.76
0.78
0.80
0.744
0.763
0.782
0.800
0.820
0.928
0.924
0.920
0.916
0.912
0.723
0.710
0.697
0.685
0.673
1.083
1.070
1.059
1.048
1.039
1.044
1.037
1.030
1.025
1.020
0.783
0.760
0.738
0.718
0.698
0.82
0.84
0.86
0.88
0.90
0.838
0.857
0.875
0.893
0.911
0.908
0.904
0.900
0.896
0.892
0.659
0.647
0.634
0.621
0.608
1.032
1.025
1.018
1.013
1.009
1.015
1.012
1.009
1.006
1.004
0.680
0.663
0.645
0.629
0.614
0.92
0.94
0.96
0.98
1.00
0.929
0.947
0.965
0.983
1.000
0.887
0.883
0.878
0.874
0.870
0.596
0.583
0.571
0.558
0.546
1.006
1.003
1.001
1.0004
1.000
1.003
1.002
1.0006
1.0002
1.000
0.599
0.585
0.571
0.558
0.546
1.02
1.04
1.06
1.08
1.10
1.017
1.035
1.052
1.068
1.085
0.865
0.860
0.856
0.851
0.846
0.533
0.521
0.509
0.497
0.485
1.0003
1.001
1.003
1.005
1.008
1.0001
1.0006
1.001
1.002
1.003
0.534
0.522
0.511
0.500
0.489
1.102
1.118
1.135
1.151
1.167
0.842
0.837
0.832
0.827
0.822
0.474
0.462
0.451
0.439
0.428
1.012
1.016
1.021
1.026
1.032
1.005
1.006
1.008
1.010
1.012
0.479
0.469
0.460
0.450
0.442
1.12
1.14
1.16
1.18
1.20
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
M
A
*
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Isentropic Flow of Perfect Gases
23
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
p
p0
T/T0
p/p0
A/A*
F/F*
1.22
1.24
1.26
1.28
1.30
1.183
1.198
1.214
1.230
1.245
0.817
0.813
0.807
0.803
0.798
0.418
0.407
0.396
0.386
0.376
1.038
1.045
1.053
1.062
1.070
1.014
1.016
1.019
1.022
1.024
0.434
0.425
0.417
0.409
0.402
1.32
1.34
1.36
1.38
1.40
1.260
1.276
1.291
1.305
1.320
0.793
0.788
0.783
0.778
0.773
0.365
0.356
0.346
0.337
0.327
1.080
1.089
1.100
1.111
1.123
1.027
1.029
1.033
1.036
1.039
0.398
0.387
0.381
0.374
0.367
1.42
1.44
1.46
1.48
1.50
1.334
1.348
1.363
1.377
1.391
0.768
0.763
0.758
0.752
0.748
0.318
0.309
0.300
0.292
0.284
1.135
1.148
1.161
1.175
1.189
1.042
1.045
1.048
1.051
1.055
0.361
0.352
0.346
0.340
0.337
1.52
1.54
1.56
1.58
1.60
1.405
1.418
1.432
1.445
1.458
0.743
0.737
0.732
0.727
0.723
0.275
0.267
0.259
0.252
0.245
1.205
1.220
1.237
1.254
1.271
1.058
1.062
1.065
1.068
1.072
0.332
0.326
0.321
0.316
0.310
1.62
1.64
1.66
1.68
1.70
1.472
1.485
1.497
1.510
1.523
0.717
0.712
0.707
0.703
0.698
0.237
0.230
0.223
0.216
0.210
1.289
1.308
1.328
1.348
1.369
1.075
1.079
1.083
1.086
1.089
0.306
0.301
0.296
0.292
0.288
1.72
1.74
1.76
1.78
1.80
1.535
1.547
1.559
1.572
1.584
0.693
0.687
0.683
0.678
0.673
0.203
0.197
0.191
0.185
0.180
1.391
1.413
1.436
1.459
1.484
1.093
1.097
1.100
1.104
1.108
0.283
0.279
0.275
0.271
0.267
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
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Gas Tables for Compressible Flow Calculations
24
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
A
p
p0
M*
T/T0
p/p0
A/A*
F/F*
1.82
1.84
1.86
1.88
1.90
1.595
1.607
1.618
1.629
1.641
0.688
0.663
0.658
0.654
0.648
0.174
0.168
0.163
0.158
0.153
1.509
1.535
1.562
1.589
1.618
1.111
1.115
1.118
1.122
1.125
0.263
0.259
0.255
0.252
0.248
1.92
1.94
1.96
1.98
2.00
1.652
1.663
1.674
1.685
1.696
0.644
0.639
0.634
0.629
0.625
0.148
0.144
0.139
0.135
0.131
1.647
1.678
1.708
1.740
1.773
1.128
1.132
1.136
1.139
1.143
0.245
0.241
0.238
0.235
0.231
2.02
2.04
2.06
2.08
2.10
1.706
1.717
1.727
1.737
1.747
0.620
0.616
0.611
0.606
0.602
0.127
0.122
0.118
0.114
0.111
1.807
1.842
1.877
1.914
1.951
1.146
1.150
1.153
1.156
1.160
0.228
0.225
0.222
0.219
0.216
2.12
2.14
2.16
2.18
2.20
1.757
1.767
1.776
1.786
1.796
0.597
0.593
0.588
0.583
0.579
0.107
0.104
0.100
0.097
0.094
1.990
2.029
2.071
2.133
2.156
1.163
1.166
1.169
1.173
1.175
0.213
0.211
0.208
0.205
0.203
2.22
2.24
2.26
2.28
2.30
1.805
1.815
1.824
1.833
1.842
0.575
0.571
0.566
0.562
0.558
0.091
0.088
0.085
0.082
0.080
2.199
2.245
2.292
2.339
2.388
1.179
1.183
1.186
1.189
1.192
0.200
0.197
0.195
0.192
0.190
1.851
1.859
1.868
1.877
1.885
0.553
0.549
0.545
0.541
0.537
0.077
0.074
0.072
0.069
0.067
2.439
2.490
2.543
2.598
2.654
1.196
1.198
1.202
1.205
1.208
0.187
0.185
0.183
0.180
0.178
2.32
2.34
2.36
2.38
2.40
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
M
A
*
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Isentropic Flow of Perfect Gases
25
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
p
p0
T/T0
p/p0
A/A*
F/F*
2.42
2.44
2.46
2.48
2.50
1.894
1.902
1.910
1.918
1.926
0.532
0.528
0.524
0.520
0.516
0.065
0.063
0.061
0.059
0.057
2.711
2.769
2.829
2.891
2.954
1.211
1.214
1.217
1.219
1.223
0.176
0.174
0.172
0.170
0.168
2.52
2.54
2.56
2.58
2.60
1.934
1.942
1.950
1.957
1.965
0.512
0.508
0.504
0.500
0.496
0.055
0.053
0.051
0.049
0.048
3.019
3.086
3.154
3.224
3.295
1.226
1.228
1.231
1.234
1.237
0.166
0.164
0.162
0.160
0.158
2.62
2.64
2.66
2.68
2.70
1.972
1.980
1.987
1.994
2.001
0.493
0.489
0.485
0.481
0.478
0.046
0.045
0.043
0.042
0.041
3.370
3.444
3.521
3.600
3.681
1.240
1.242
1.245
1.248
1.250
0.157
0.155
0.153
0.151
0.150
2.72
2.74
2.76
2.78
2.80
2.008
2.015
2.022
2.029
2.036
0.474
0.470
0.467
0.463
0.460
0.039
0.038
0.037
0.036
0.034
3.764
3.849
3.936
4.025
4.116
1.253
1.256
1.258
1.261
1.264
0.148
0.146
0.145
0.143
0.142
2.82
2.84
2.86
2.88
2.90
2.042
2.048
2.055
2.062
2.068
0.456
0.453
0.449
0.446
0.442
0.033
0.032
0.031
0.030
0.029
4.210
4.306
4.404
4.504
4.607
1.266
1.268
1.271
1.273
1.275
0.140
0.138
0.137
0.135
0.134
2.92
2.94
2.96
2.98
3.00
2.074
2.081
2.087
2.093
2.099
0.439
0.435
0.432
0.429
0.426
0.028
0.027
0.026
0.0256
0.025
4.713
4.821
4.931
5.044
5.160
1.278
1.281
1.283
1.285
1.288
0.133
0.131
0.129
0.128
0.127
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
26
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
p
p0
T/T0
p/p0
A/A*
F/F*
3.05
3.10
3.15
3.20
3.25
2.113
2.127
2.141
2.155
2.168
0.417
0.409
0.402
0.394
0.387
0.0227
0.0209
0.0193
0.0177
0.0163
5.461
5.781
6.119
6.477
6.857
1.293
1.298
1.304
1.309
1.315
0.124
0.121
0.118
0.115
0.112
3.30
3.35
3.40
3.45
3.50
2.181
2.193
2.205
2.217
2.228
0.379
0.373
0.366
0.359
0.352
0.0151
0.0139
0.0128
0.0118
0.011
7.258
7.684
8.133
8.608
9.110
1.319
1.325
1.329
1.334
1.338
0.109
0.107
0.104
0.101
0.099
3.55
3.60
3.65
3.70
3.75
2.239
2.250
2.261
2.271
2.281
0.346
0.339
0.334
0.327
0.322
0.010
0.0093
0.0086
0.0079
0.0073
9.640
10.200
10.792
11.416
12.075
1.343
1.347
1.351
1.356
1.360
0.097
0.095
0.093
0.092
0.088
3.80
3.85
3.90
3.95
4.00
2.290
2.299
2.308
2.318
2.326
0.316
0.310
0.305
0.299
0.294
0.0068
0.0063
0.0058
0.0054
0.005
12.769
13.502
14.274
15.087
15.940
1.363
1.367
1.371
1.375
1.378
0.086
0.085
0.083
0.081
0.079
4.05
4.10
4.15
4.20
4.25
2.335
2.343
2.351
2.359
2.367
0.289
0.284
0.279
0.274
0.270
4.6 × 10−3
4.27 × 10−3
3.9 × 10−3
3.68 × 10−3
3.41 × 10−3
16.846
17.796
18.796
19.850
20.953
1.382
1.385
1.388
1.391
1.395
0.077
0.076
0.075
0.073
0.072
4.30
4.35
4.40
4.45
4.50
2.374
2.381
2.383
2.395
2.402
0.265
0.261
0.256
0.252
0.248
3.17 × 10−3
2.94 × 10−3
2.73 × 10−3
2.54 × 10−3
2.36 × 10−3
22.116
23.338
24.622
25.971
27.390
1.397
1.400
1.403
1.406
1.408
0.070
0.068
0.067
0.066
0.065
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Isentropic Flow of Perfect Gases
27
TABLE 3.1
Isentropic flow of perfect gases (γγ = 1.3)
M
M*
T/T0
p/p0
A/A*
F/F*
A
A
*
p
p0
2.408
2.415
2.421
2.427
2.433
0.243
0.240
0.235
0.232
0.228
2.2 × 10−3
2.05 × 10−3
1.91 × 10−3
1.77 × 10−3
1.65 × 10−3
28.874
30.434
32.070
33.786
35.585
1.412
1.414
1.417
1.420
1.422
0.063
0.062
0.061
0.060
0.059
4.80
4.85
4.90
4.95
5.00
2.438
2.444
2.450
2.455
2.460
0.224
0.221
0.217
0.214
0.211
1.54 × 10−3
1.44 × 10−3
1.34 × 10−3
1.25 × 10−3
1.17 × 10−3
37.472
39.448
41.518
43.687
45.950
1.424
1.427
1.429
1.431
1.433
0.058
0.057
0.055
0.0547
0.054
6.00
7.00
8.00
9.00
10.00
∞
2.543
2.598
2.635
2.662
2.680
2.769
0.156
0.119
0.094
0.076
0.063
0
120.100
285.300
625.000
1275.000
2438.000
∞
1.468
1.491
1.508
1.520
1.527
1.565
0.038
0.029
0.023
0.018
0.015
0
32.0 × 10−5
10.0 × 10−5
3.6 × 10−5
1.4 × 10−5
0.6 × 10−5
0
ww
w.
Le
arn
En
gin
e
eri
ng
.i n
4.55
4.60
4.65
4.70
4.75
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Gas Tables for Compressible Flow Calculations
28
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
M*
T/T0
p/p0
A/A*
F/F*
A
A
*
p
p0
0.000
0.011
0.022
0.033
0.044
0.0548
1.000
0.999
0.999
0.999
0.999
0.999
1.000
0.999
0.999
0.999
0.998
0.998
∞
57.874
28.942
19.300
14.482
11.592
∞
45.65
22.834
15.232
11.435
9.158
∞
57.869
28.934
19.288
14.465
11.571
0.06
0.07
0.08
0.09
0.10
0.0657
0.0766
0.0876
0.0985
0.1094
0.999
0.999
0.998
0.998
0.998
0.997
0.996
0.995
0.994
0.993
9.666
8.292
7.262
6.461
5.822
7.643
6.562
5.753
5.125
4.624
9.642
8.263
7.229
6.425
5.781
0.11
0.12
0.13
0.14
0.15
0.1204
0.1313
0.1422
0.1531
0.1640
0.9976
0.9971
0.9966
0.996
0.995
0.992
0.989
0.988
0.986
0.984
5.299
4.864
4.497
4.182
3.910
4.215
3.875
3.588
3.343
3.132
5.255
4.815
4.445
4.126
3.849
0.16
0.17
0.18
0.19
0.20
0.1750
0.186
0.1965
0.207
0.218
0.9949
0.9943
0.994
0.993
0.992
0.982
0.980
0.978
0.975
0.973
3.673
3.464
3.278
3.112
2.964
2.947
2.786
2.642
2.515
2.400
3.607
3.394
3.205
3.035
2.882
0.21
0.22
0.23
0.24
0.25
0.229
0.239
0.251
0.261
0.272
0.991
0.990
0.989
0.988
0.987
0.9697
0.967
0.964
0.961
0.957
2.829
2.707
2.597
2.495
2.403
2.297
2.205
2.120
2.043
1.973
2.744
2.618
2.503
2.398
2.300
0.26
0.27
0.28
0.29
0.30
0.283
0.294
0.304
0.315
0.325
0.986
0.9855
0.985
0.983
0.982
0.954
0.951
0.947
0.943
0.939
2.317
2.238
2.166
2.098
2.035
1.909
1.849
1.795
1.745
1.698
2.211
2.128
2.051
1.979
1.912
w.
Le
arn
En
gin
e
eri
ng
.i n
0.00
0.01
0.02
0.03
0.04
0.05
ww
M
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Isentropic Flow of Perfect Gases
29
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
p
p0
T/T0
p/p0
A/A*
F/F*
0.31
0.336
0.981
0.936
1.976
1.655
1.849
0.32
0.33
0.34
0.35
0.347
0.357
0.368
0.378
0.979
0.978
0.977
0.976
0.932
0.927
0.923
0.918
1.922
1.871
1.823
1.778
1.614
1.577
1.542
1.509
1.790
1.735
1.683
1.634
0.36
0.37
0.38
0.39
0.40
0.389
0.400
0.410
0.421
0.431
0.975
0.973
0.972
0.970
0.969
0.914
0.909
0.905
0.900
0.895
1.735
1.696
1.658
1.623
1.590
1.479
1.450
1.424
1.398
1.375
1.587
1.543
1.501
1.462
1.424
0.41
0.42
0.43
0.44
0.45
0.442
0.452
0.463
0.473
0.483
0.967
0.966
0.964
0.963
0.961
0.891
0.886
0.881
0.876
0.870
1.558
1.529
1.500
1.474
1.448
1.353
1.332
1.312
1.294
1.276
1.388
1.354
1.322
1.290
1.261
0.46
0.47
0.48
0.49
0.50
0.494
0.504
0.514
0.524
0.534
0.959
0.958
0.956
0.954
0.952
0.865
0.859
0.854
0.848
0.843
1.425
1.402
1.380
1.360
1.340
1.259
1.244
1.230
1.216
1.203
1.232
1.205
1.178
1.154
1.129
0.51
0.52
0.53
0.54
0.55
0.545
0.555
0.565
0.575
0.585
0.951
0.948
0.947
0.945
0.943
0.837
0.832
0.826
0.820
0.814
1.321
1.303
1.287
1.270
1.255
1.190
1.178
1.167
1.157
1.147
1.106
1.084
1.062
1.042
1.022
0.56
0.57
0.58
0.59
0.60
0.595
0.605
0.615
0.625
0.635
0.941
0.939
0.937
0.935
0.933
0.808
0.802
0.796
0.790
0.784
1.240
1.226
1.213
1.200
1.188
1.138
1.129
1.121
1.113
1.105
1.002
0.984
0.966
0.948
0.932
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
30
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
M*
T/T0
p/p0
A/A*
F/F*
A
A
*
p
p0
0.645
0.655
0.664
0.674
0.684
0.931
0.928
0.926
0.924
0.922
0.778
0.772
0.765
0.759
0.753
1.177
1.166
1.155
1.145
1.136
1.098
1.091
1.085
1.078
1.073
0.915
0.900
0.885
0.869
0.855
0.66
0.67
0.68
0.69
0.70
0.693
0.703
0.713
0.722
0.732
0.919
0.917
0.915
0.913
0.911
0.746
0.740
0.734
0.727
0.721
1.126
1.118
1.109
1.102
1.094
1.068
1.063
1.058
1.053
1.049
0.841
0.827
0.814
0.802
0.789
0.71
0.72
0.73
0.74
0.75
0.741
0.751
0.760
0.769
0.779
0.908
0.906
0.904
0.901
0.899
0.714
0.708
0.701
0.695
0.688
1.087
1.081
1.074
1.068
1.062
1.045
1.041
1.038
1.035
1.031
0.777
0.765
0.753
0.742
0.732
0.76
0.77
0.78
0.79
0.80
0.788
0.797
0.807
0.816
0.825
0.896
0.894
0.892
0.889
0.886
0.682
0.676
0.669
0.663
0.656
1.057
1.052
1.047
1.043
1.038
1.028
1.026
1.023
1.021
1.018
0.721
0.711
0.700
0.691
0.681
0.81
0.82
0.83
0.84
0.85
0.834
0.843
0.852
0.861
0.870
0.884
0.881
0.879
0.876
0.874
0.649
0.643
0.636
0.630
0.624
1.034
1.031
1.027
1.024
1.021
1.017
1.015
1.013
1.011
1.009
0.672
0.663
0.654
0.645
0.636
0.86
0.87
0.88
0.89
0.90
0.879
0.888
0.897
0.906
0.915
0.871
0.868
0.869
0.863
0.861
0.617
0.610
0.604
0.598
0.591
1.018
1.015
1.013
1.011
1.009
1.008
1.007
1.006
1.005
1.004
0.628
0.620
0.612
0.604
0.596
w.
Le
arn
En
gin
e
eri
ng
.i n
0.61
0.62
0.63
0.64
0.65
ww
M
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Isentropic Flow of Perfect Gases
31
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
p
p0
T/T0
p/p0
A/A*
F/F*
0.91
0.92
0.93
0.94
0.95
0.923
0.932
0.941
0.949
0.958
0.858
0.855
0.853
0.849
0.847
0.585
0.578
0.572
0.566
0.559
1.007
1.006
1.004
1.003
1.002
1.003
1.0025
1.002
1.0014
1.0009
0.589
0.582
0.575
0.567
0.561
0.96
0.97
0.98
0.99
1.00
0.966
0.975
0.983
0.992
1.000
0.844
0.842
0.839
0.836
0.834
0.553
0.547
0.541
0.534
0.528
1.0014
1.0008
1.0003
1.0001
1.000
1.0006
1.0003
1.0001
1.000
1.000
0.554
0.547
0.541
0.535
0.528
1.01
1.02
1.03
1.04
1.05
1.0083
1.017
1.025
1.033
1.041
0.831
0.828
0.825
0.822
0.819
0.522
0.516
0.510
0.504
0.498
1.0001
1.0003
1.0007
1.0013
1.002
1.000
1.0001
1.0003
1.0005
1.0008
0.522
0.516
0.510
0.505
0.498
1.06
1.07
1.08
1.09
1.10
1.049
1.057
1.065
1.073
1.081
0.816
0.814
0.811
0.808
0.805
0.492
0.486
0.480
0.474
6.468
1.003
1.004
1.005
1.006
1.008
1.0012
1.0016
1.002
1.0025
1.003
0.493
0.488
0.483
0.477
0.472
1.11
1.12
1.13
1.14
1.15
1.089
1.097
1.105
1.113
1.120
0.802
0.799
0.796
0.794
0.791
0.463
0.457
0.451
0.445
0.439
1.009
1.011
1.013
1.015
1.017
1.0036
1.004
1.005
1.0057
1.006
0.467
0.462
0.457
0.452
0.447
1.16
1.17
1.18
1.19
1.20
1.128
1.136
1.143
1.151
1.158
0.788
0.785
0.782
0.779
0.776
0.434
0.428
0.423
0.418
0.412
1.019
1.022
1.025
1.028
1.030
1.007
1.008
1.009
1.010
1.011
0.443
0.438
0.434
0.429
0.425
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
32
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
p
p0
T/T0
p/p0
A/A*
F/F*
1.21
1.22
1.23
1.24
1.25
1.166
1.173
1.181
1.188
1.195
0.774
0.771
0.768
0.765
0.762
0.407
0.402
0.396
0.391
0.386
1.034
1.037
1.039
1.043
1.047
1.012
1.013
1.014
1.015
1.016
0.421
0.416
0.412
0.408
0.404
1.26
1.27
1.28
1.29
1.30
1.203
1.210
1.217
1.224
1.231
0.759
0.756
0.753
0.750
0.747
0.381
0.376
0.371
0.366
0.361
1.050
1.054
1.058
1.062
1.066
1.017
1.018
1.019
1.021
1.022
0.400
0.396
0.392
0.388
0.385
1.31
1.32
1.33
1.34
1.35
1.238
1.245
1.252
1.259
1.266
0.745
0.742
0.738
0.736
0.733
0.356
0.351
0.346
0.342
0.337
1.071
1.075
1.079
1.084
1.089
1.023
1.024
1.025
1.027
1.028
0.381
0.378
0.374
0.370
0.367
1.36
1.37
1.38
1.39
1.40
1.273
1.280
1.286
1.293
1.300
0.730
0.727
0.724
0.721
0.718
0.332
0.328
0.323
0.318
0.314
1.094
1.099
1.104
1.110
1.115
1.029
1.031
1.032
1.033
1.035
0.364
0.360
0.357
0.354
0.350
1.41
1.42
1.43
1.44
1.45
1.306
1.313
1.319
1.326
1.333
0.716
0.713
0.709
0.706
0.704
0.309
0.305
0.301
0.297
0.293
1.121
1.126
1.132
1.138
1.144
1.036
1.037
1.039
1.040
1.042
0.347
0.344
0.341
0.338
0.335
1.46
1.47
1.48
1.49
1.50
1.339
1.345
1.352
1.358
1.365
0.701
0.698
0.695
0.693
0.689
0.288
0.285
0.280
0.276
0.272
1.150
1.156
1.163
1.170
1.176
1.043
1.044
1.046
1.047
1.048
0.332
0.329
0.326
0.323
0.320
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Isentropic Flow of Perfect Gases
33
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
M*
T/T0
p/p0
A/A*
F/F*
A
A
*
p
p0
1.371
1.377
1.383
1.389
1.395
0.687
0.684
0.681
0.678
0.675
0.268
0.265
0.261
0.257
0.253
1.183
1.189
1.197
1.204
1.211
1.050
1.052
1.053
1.055
1.056
0.317
0.315
0.312
0.309
0.307
1.56
1.57
1.58
1.59
1.60
1.402
1.408
1.414
1.419
1.425
0.673
0.670
0.667
0.664
0.661
0.249
0.246
0.242
0.238
0.235
1.219
1.227
1.234
1.242
1.250
1.057
1.059
1.061
1.062
1.063
0.304
0.302
0.300
0.297
0.294
1.61
1.62
1.63
1.64
1.65
1.431
1.437
1.443
1.448
1.454
0.658
0.656
0.653
0.650
0.647
0.232
0.228
0.225
0.222
0.218
1.258
1.267
1.275
1.284
1.292
1.065
1.067
1.068
1.069
1.071
0.292
0.289
0.287
0.285
0.282
1.66
1.67
1.68
1.69
1.70
1.460
1.466
1.471
1.477
1.483
0.645
0.642
0.639
0.636
0.634
0.215
0.212
0.208
0.206
0.203
1.301
1.310
1.319
1.328
1.337
1.073
1.074
1.076
l.077
1.078
0.280
0.278
0.275
0.273
0.271
1.71
1.72
1.73
1.74
1.75
1.485
1.494
1.499
1.504
1.509
0.631
0.628
0.626
0.623
0.620
0.200
0.196
0.194
0.191
0.187
1.347
1.357
1.367
1.376
1.387
1.080
1.082
1.083
1.085
1.086
0.269
0.267
0.265
0.262
0.260
1.76
1.77
1.78
1.79
1.80
1.515
1.520
1.526
1.531
1.536
0.617
0.615
0.612
0.609
0.607
0.185
0.182
0.179
0.177
0.174
1.397
1.407
1.418
1.428
1.439
1.087
1.089
1.091
1.092
1.094
0.258
0.256
0.254
0.252
0.250
w.
Le
arn
En
gin
e
eri
ng
.i n
1.51
1.52
1.53
1.54
1.55
ww
M
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
34
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
p
p0
T/T0
p/p0
A/A*
F/F*
1.81
1.82
1.83
1.84
1.85
1.541
1.546
1.551
1.556
1.561
0.604
0.602
0.598
0.596
0.594
0.171
0.168
0.166
0.164
0.161
1.450
1.461
1.472
1.484
1.495
1.095
1.096
1.098
1.099
1.100
0.248
0.247
0.245
0.243
0.241
1.86
1.87
1.88
1.89
1.90
1.566
1.571
1.576
1.581
1.586
0.591
0.588
0.585
0.583
0.581
0.158
0.156
0.154
0.152
0.149
1.507
1.518
1.531
1.543
1.555
1.102
1.104
1.105
1.107
1.108
0.239
0.237
0.235
0.234
0.232
1.91
1.92
1.93
1.94
1.95
1.591
1.596
1.600
1.605
1.609
0.578
0.575
0.573
0.570
0.568
0.147
0.145
0.142
0.140
0.138
1.568
1.580
1.593
1.606
1.619
1.110
1.111
1.113
1.114
1.116
0.230
0.228
0.227
0.225
0.223
1.96
1.97
1.98
1.99
2.00
1.615
1.619
1.624
1.628
1.633
0.566
0.563
0.561
0.558
0.555
0.136
0.134
0.132
0.129
0.128
1.633
1.646
1.659
1.674
1.687
1.117
1.118
1.120
1.121
1.123
0.222
0.220
0.219
0.217
0.216
2.01
2.02
2.03
2.04
2.05
1.638
1.642
1.646
1.651
1.655
0.553
0.551
0.548
0.546
0.543
0.126
0.114
0.122
0.120
0.118
1.702
1.716
1.731
1.745
1.760
1.124
1.126
1.127
1.128
1.130
0.214
0.213
0.211
0.209
0.208
2.06
2.07
2.08
2.09
2.10
1.660
1.664
1.668
1.673
1.677
0.541
0.538
0.536
0.534
0.531
0.116
0.115
0.113
0.111
0.109
1.775
1.790
1.805
1.821
1.837
1.131
1.133
1.134
1.135
1.137
0.207
0.205
0.204
0.202
0.200
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Isentropic Flow of Perfect Gases
35
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
p
p0
T/T0
p/p0
A/A*
F/F*
2.11
2.12
2.13
2.14
2.15
1.681
1.685
1.689
1.694
1.698
0.529
0.527
0.524
0.522
0.519
0.108
0.106
0.1043
0.1027
0.1010
1.853
1.869
1.885
1.902
1.918
1.138
1.139
1.141
1.142
1.143
0.199
0.198
0.197
0.195
0.194
2.16
2.17
2.18
2.19
2.20
1.702
1.706
1.710
1.714
1.718
0.517
0.515
0.513
0.510
0.508
0.0996
0.0980
0.0965
0.095
0.0935
1.935
1.953
1.969
1.987
2.005
1.145
1.146
1.147
1.148
1.150
0.193
0.191
0.190
0.188
0.187
2.21
2.22
2.23
2.24
2.25
1.722
1.726
1.730
1.734
1.737
0.506
0.504
0.501
0.499
0.497
0.0921
0.0906
0.0892
0.0878
0.0865
2.023
2.041
2.059
2.078
2.096
1.151
1.153
1.154
1.155
1.156
0.186
0.185
0.184
0.183
0.181
2.26
2.27
2.28
2.29
2.30
1.741
1.745
1.749
1.753
1.756
0.495
0.492
0.490
0.488
0.486
0.0851
0.0838
0.0825
0.0812
0.0800
2.115
2.135
2.154
2.173
2.193
1.158
1.159
1.160
1.162
1.163
0.180
0.179
0.178
0.1765
0.175
2.31
2.32
2.33
2.34
2.35
1.760
1.764
1.767
1.771
1.775
0.484
0.482
0.479
0.477
0.475
0.0787
0.0775
0.0763
0.0751
0.0740
2.213
2.233
2.254
2.274
2.295
1.164
1.165
1.167
1.168
1.169
0.174
0.173
0.172
0.171
0.169
2.36
2.37
2.38
2.39
2.40
1.778
1.782
1.785
1.789
1.792
0.473
0.471
0.469
0.467
0.464
0.0728
0.0717
0.0706
0.0695
0.0684
2.316
2.338
2.359
2.381
2.403
1.170
1.172
1.173
1.174
1.175
0.168
0.167
0.166
0.165
0.164
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
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Gas Tables for Compressible Flow Calculations
36
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
p
p0
T/T0
p/p0
A/A*
F/F*
2.41
2.42
2.43
2.44
2.45
1.796
1.799
1.803
1.806
1.809
0.463
0.461
0.458
0.456
0.454
0.0673
0.0663
0.0653
0.0643
0.0633
2.425
2.448
2.471
2.494
2.517
1.176
1.178
1.179
1.180
1.181
0.163
0.162
0.161
0.160
0.159
2.46
2.47
2.48
2.49
2.50
1.813
1.816
1.819
1.823
1.826
0.452
0.450
0.448
0.446
0.444
0.0623
0.0613
0.0604
0.0595
0.0585
2.540
2.564
2.588
2.612
2.637
1.182
1.183
1.184
1.186
1.187
0.158
0.157
0.156
0.155
0.154
2.51
2.52
2.53
2.54
2.55
1.829
1.832
1.835
1.838
1.842
0.442
0.441
0.438
0.436
0.434
0.0576
0.0567
0.0558
0.0550
0.0542
2.662
2.686
2.712
2.737
2.763
1.188
1.189
1.190
1.191
1.192
0.153
0.152
0.151
0.150
0.149
2.56
2.57
2.58
2.59
2.60
1.845
1.848
1.851
1.854
1.857
0.433
0.431
0.429
0.427
0.425
0.0533
0.0525
0.0517
0.0509
0.0501
2.789
2.815
2.842
2.869
2.896
1.193
1.195
1.196
1.197
1.198
0.1487
0.1475
0.147
0.146
0.145
2.61
2.62
2.63
2.64
2.65
1.860
1.863
1.866
1.869
1.872
0.423
0.421
0.419
0.417
0.415
0.0494
0.0486
0.0478
0.0471
0.0464
2.923
2.951
2.980
3.007
3.306
1.199
1.200
1.201
1.202
1.203
0.144
0.143
0.1425
0.142
0.141
2.66
2.67
2.68
2.69
2.70
1.875
1.878
1.881
1.884
1.886
0.414
0.412
0.410
0.408
0.407
0.0457
0.0449
0.0443
0.0436
0.043
3.065
3.094
3.123
3.153
3.183
1.204
1.205
1.206
1.207
1.208
0.140
0.139
0.138
0.1375
0.137
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
A
M
A
*
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Isentropic Flow of Perfect Gases
37
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
M*
T/T0
p/p0
A/A*
F/F*
A
A
*
p
p0
1.889
1.892
1.895
1.898
1.900
0.405
0.403
0.402
0.399
0.398
0.0423
0.0417
0.0410
0.0404
0.0398
3.213
3.244
3.275
3.306
3.337
1.209
1.210
1.211
1.212
1.213
0.136
0.135
0.134
0.1335
0.133
2.76
2.77
2.78
2.79
2.80
1.903
1.906
1.908
1.911
1.914
0.396
0.395
0.393
0.391
0.389
0.0392
0.0386
0.0379
0.0374
0.0369
3.369
3.402
3.434
3.467
3.500
1.214
1.215
1.216
1.217
1.218
0.132
0.131
0.130
0.1297
0.129
2.81
2.82
2.83
2.84
2.85
1.915
1.919
1.922
1.925
1.927
0.388
0.386
0.384
0.382
0.381
0.0363
0.0357
0.0352
0.0347
0.0342
3.534
3.567
3.602
3.636
3.670
1.219
1.220
1.221
1.222
1.223
0.128
0.1275
0.127
0.126
0.125
2.86
2.87
2.88
2.89
2.90
1.929
1.932
1.935
1.937
1.940
0.379
0.378
0.376
0.375
0.373
0.0336
0.0331
0.0326
0.0321
0.0317
3.706
3.741
3.777
3.813
3.850
1.224
1.225
1.226
1.227
1.228
0.1245
0.124
0.123
0.1225
0.122
2.91
2.92
2.93
2.94
2.95
1.942
1.945
1.947
1.950
1.952
0.371
0.369
0.368
0.367
0.365
0.0312
0.0307
0.0303
0.0298
0.0294
3.887
3.924
3.961
4.000
4.037
1.229
1.230
1.2305
1.231
1.232
0.121
0.120
0.1198
0.119
0.1185
2.96
2.97
2.98
2.99
3.00
1.955
1.957
1.959
1.962
1.964
0.363
0.362
0.360
0.358
0.357
0.0289
0.0285
0.0281
0.0276
0.0272
4.076
4.115
4.155
4.195
4.235
1.233
1.234
1.235
1.236
1.237
0.118
0.117
0.117
0.116
0.115
w.
Le
arn
En
gin
e
eri
ng
.i n
2.71
2.72
2.73
2.74
2.75
ww
M
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Gas Tables for Compressible Flow Calculations
38
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
A
p
p0
M*
T/T0
p/p0
A/A*
F/F*
3.05
3.10
3.15
3.20
3.25
1.976
1.987
1.997
2.008
2.018
0.349
0.342
0.335
0.328
0.321
0.0253
0.0235
0.0218
0.0202
0.0188
4.441
4.657
4.884
5.121
5.369
1.241
1.246
1.249
1.253
1.257
0.112
0.109
0.106
0.104
0.101
3.30
3.35
3.40
3.45
3.50
2.028
2.037
2.047
2.056
2.064
0.315
0.308
0.302
0.296
0.289
0.0175
0.0163
0.0151
0.0141
0.0131
5.628
5.900
6.184
6.480
6.789
1.260
1.264
1.268
1.272
1.274
0.098
0.096
0.0935
0.091
0.089
3.55
3.60
3.65
3.70
3.75
2.073
2.081
2.089
2.095
2.104
0.284
0.278
0.273
0.268
0.262
7.113
7.450
7.802
8.169
8.552
1.278
1.281
1.284
1.287
1.289
0.087
0.085
0.083
0.081
0.079
3.80
3.85
3.90
3.95
4.00
2.111
2.118
2.125
2.132
2.138
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
4.45
4.50
5.00
arn
En
gin
e
eri
ng
.i n
M
12.2 × 10−3
11.38 × 10−3
10.62 × 10−3
9.9 × 10−3
9.24 × 10−3
A
*
8.63 × 10−3
8.06 × 10−3
7.53 × 10−3
7.04 × 10−3
6.592 × 10−3
8.950
9.366
9.800
10.249
10.719
1.292
1.295
1.298
1.300
1.303
0.077
0.075
0.0738
0.072
0.071
2.145
2.151
2.156
2.162
2.168
0.234
0.229
0.235
0.221
0.217
6.16 × 10−3
5.77 × 10−3
5.4 × 10−3
5.06 × 10−3
4.74 × 10−3
11.207
11.715
12.243
12.792
13.362
1.305
1.308
1.310
1.312
1.315
0.069
0.0676
0.066
0.0648
0.0635
2.173
2.178
2.184
2.188
2.194
2.236
0.213
0.209
0.205
0.202
0.198
0.167
4.45 × 10−3
4.17 × 10−3
3.92 × 10−3
3.68 × 10−3
3.46 × 10−3
1.89 × 10−3
13.955
14.571
15.210
15.872
16.562
25.000
1.317
1.319
1.321
1.323
1.325
1.341
0.062
0.0608
0.060
0.058
0.057
0.047
ww
w.
Le
0.257
0.252
0.247
0.243
0.238
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Isentropic Flow of Perfect Gases
39
TABLE 3.2
Isentropic flow of perfect gases (γγ = 1.4)
M*
T/T0
6.00
7.00
8.00
9.00
10.00
2.295
2.333
2.359
2.377
2.390
0.122
0.093
0.072
0.058
0.047
∞
2.45
0
p/p0
63.3 × 10-5
24.2 × 10−5
10.2 × 10−5
4.74 × 10−5
2.36 × 10−5
p
p0
F/F*
53.180
104.143
190.110
327.189
536.00
1.365
1.381
1.392
1.399
1.404
0.033
0.025
0.0195
0.0156
0.0126
1.429
0
∞
A
*
ww
w.
Le
arn
En
gin
e
0
A
A/A*
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
40
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
M*
T/T0
p/p0
A/A*
F/F*
A
A
*
p
p0
0.000
0.023
0.046
0.069
0.092
0.115
1.000
0.999
0.999
0.998
0.997
0.997
1.000
0.999
0.998
0.997
0.995
0.992
∞
28.132
14.078
9.397
7.061
5.661
∞
21.662
10.851
7.255
5.464
4.392
∞
28.113
14.054
9.366
7.021
5.615
0.12
0.14
0.16
0.18
0.20
0.138
0.161
0.184
0.207
0.229
0.995
0.994
0.992
0.989
0.987
0.988
0.984
0.979
0.973
0.967
4.733
4.070
3.576
3.193
2.886
3.686
3.184
2.809
2.522
2.293
4.675
4.003
3.499
3.107
2.793
0.22
0.24
0.26
0.28
0.30
0.252
0.275
0.297
0.319
0.342
0.984
0.981
0.978
0.975
0.971
0.961
0.954
0.945
0.937
0.928
2.640
2.435
2.262
2.115
1.989
2.110
1.958
1.833
1.725
1.635
2.535
2.320
2.138
1.982
1.848
0.32
0.34
0.36
0.38
0.40
0.363
0.385
0.407
0.428
0.450
0.967
0.963
0.958
0.954
0.949
0.919
0.909
0.899
0.889
0.878
1.880
1.784
1.700
1.626
1.560
1.558
1.491
1.432
1.381
1.336
1.728
1.623
1.529
1.445
1.370
0.42
0.44
0.46
0.48
0.50
0.471
0.493
0.513
0.534
0.555
0.945
0.939
0.934
0.928
0.923
0.867
0.855
0.843
0.831
0.818
1.502
1.448
1.401
1.358
1.320
1.297
1.262
1.231
1.203
1.178
1.300
1.238
1.181
1.128
1.080
0.52
0.54
0.56
0.58
0.60
0.575
0.595
0.615
0.635
0.655
0.917
0.911
0.905
0.899
0.893
0.806
0.793
0.780
0.767
0.753
1.286
1.254
1.225
1.200
1.176
1.157
1.137
1.120
1.105
1.091
1.035
0.994
0.955
0.919
0.885
w.
Le
arn
En
gin
e
eri
ng
.i n
0.00
0.02
0.04
0.06
0.08
0.10
ww
M
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Isentropic Flow of Perfect Gases
41
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
p
p0
T/T0
p/p0
A/A*
0.62
0.64
0.66
0.68
0.70
0.674
0.693
0.712
0.731
0.750
0.886
0.879
0.873
0.866
0.859
0.739
0.726
0.712
0.698
0.685
1.154
1.135
1.118
1.102
1.087
1.085
1.068
1.058
1.049
1.042
0.854
0.824
0.796
0.769
0.745
0.72
0.74
0.76
0.78
0.80
0.768
0.786
0.804
0.821
0.839
0.853
0.845
0.838
0.831
0.823
0.671
0.657
0.644
0.630
0.616
1.075
1.063
1.053
1.043
1.035
1.035
1.029
1.024
1.019
1.016
0.721
0.698
0.677
0.657
0.638
0.82
0.84
0.86
0.88
0.90
0.856
0.873
0.889
0.906
0.922
0.817
0.809
0.802
0.795
0.787
0.603
0.589
0.570
0.563
0.550
1.028
1.022
1.016
1.011
1.008
1.012
1.009
1.007
1.005
1.003
0.619
0.602
0.585
0.569
0.555
0.92
0.94
0.96
0.98
1.00
0.938
0.954
0.969
0.985
1.000
0.779
0.772
0.765
0.757
0.749
0.537
0.524
0.511
0.499
0.487
1.005
1.003
1.001
1.0003
1.000
1.002
1.001
1.0005
1.0001
1.000
0.539
0.525
0.512
0.499
0.487
1.02
1.04
1.06
1.08
1.10
1.015
1.029
1.044
1.058
1.072
0.742
0.735
0.727
0.720
0.712
0.475
0.463
0.451
0.440
0.428
1.0003
1.001
1.003
1.005
1.007
1.0001
1.0004
1.001
1.0015
1.002
0.475
0.463
0.452
0.442
0.432
1.12
1.14
1.16
1.18
1.20
1.086
1.100
1.113
1.126
1.139
0.705
0.698
0.690
0.682
0.675
0.418
0.407
0.396
0.385
0.375
1.010
1.014
1.018
1.022
1.027
1.003
1.005
1.006
1.007
1.008
0.421
0.412
0.402
0.393
0.385
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
F/F*
A
M
A
*
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Gas Tables for Compressible Flow Calculations
42
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
p
p0
T/T0
p/p0
A/A*
1.22
1.24
1.26
1.28
1.30
1.152
1.164
1.176
1.188
1.200
0.668
0.661
0.654
0.647
0.638
0.365
0.355
0.346
0.336
0.327
1.032
1.038
1.044
1.051
1.057
1.010
1.011
1.013
1.015
1.017
0.376
0.368
0.361
0.353
0.346
1.32
1.24
1.36
1.38
1.40
1.212
1.224
1.235
1.246
1.257
0.632
0.625
0.618
0.612
0.604
0.318
0.309
0.300
0.293
0.284
1.065
1.073
1.081
1.089
1.098
1.018
1.021
1.022
1.024
1.026
0.338
0.332
0.325
0.318
0.312
1.42
1.44
1.46
1.48
1.50
1.268
1.278
1.289
1.299
1.308
0.598
0.591
0.585
0.578
0.570
0.276
0.268
0.261
0.253
0.246
1.108
1.117
1.127
1.138
1.148
1.028
1.030
1.032
1.035
1.036
0.306
0.300
0.294
0.289
0.283
1.52
1.54
1.56
1.58
1.60
1.319
1.329
1.338
1.348
1.356
0.565
0.558
0.552
0.545
0.538
0.239
0.233
0.226
0.220
0.214
1.160
1.171
1.183
1.195
1.207
1.038
1.041
1.043
1.045
1.047
0.278
0.273
0.267
0.263
0.258
1.62
1.64
1.66
1.68
1.70
1.365
1.375
1.384
1.393
1.400
0.533
0.527
0.521
0.515
0.508
0.208
0.202
0.196
0.191
0.185
1.220
1.234
1.247
1.261
1.275
1.049
1.051
1.053
1.055
1.057
0.253
0.248
0.244
0.239
0.236
1.72
1.74
1.76
1.78
1.80
1.409
1.417
1.425
1.433
1.440
0.503
0.498
0.492
0.486
0.480
0.179
0.175
0.169
0.165
0.160
1.290
1.305
1.320
1.336
1.351
1.060
1.062
1.064
1.065
1.067
0.232
0.228
0.224
0.220
0.216
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
F/F*
A
M
A
*
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Isentropic Flow of Perfect Gases
43
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
p
p0
T/T0
p/p0
A/A*
1.82
1.84
1.86
1.88
1.90
1.448
1.456
1.464
1.471
1.477
0.475
0.469
0.464
0.459
0.453
0.155
0.151
0.147
0.143
0.138
1.368
1.385
1.402
1.419
1.435
1.069
1.072
1.073
1.075
1.077
0.213
0.209
0.206
0.202
0.199
1.92
1.94
1.96
1.98
2.00
1.485
1.492
1.498
1.505
1.511
0.448
0.443
0.438
0.433
0.428
0.135
0.131
0.127
0.124
0.120
1.455
1.474
1.493
1.511
1.530
1.079
1.081
1.083
1.085
1.086
0.196
0.193
0.189
0.187
0.184
2.02
2.04
2.06
2.08
2.10
1.518
1.525
1.531
1.537
1.542
0.424
0.418
0.414
0.405
0.404
0.117
0.114
0.110
0.107
0.104
1.551
1.571
1.592
1.613
1.632
1.088
1.090
1.092
1.094
1.095
0.181
0.178
0.175
0.173
0.170
2.12
2.14
2.16
2.18
2.20
1.548
1.554
1.560
1.566
1.570
0.400
0.396
0.391
0.387
0.380
0.101
0.098
0.096
0.093
0.091
1.656
1.678
1.700
1.723
1.745
1.097
1.099
1.101
1.102
1.104
0.168
0.165
0.163
0.160
0.158
2.22
2.24
2.26
2.28
2.30
1.577
1.582
1.587
1.592
1.596
0.378
0.374
0.370
0.366
0.361
0.088
0.085
0.083
0.081
0.078
1.769
1.793
1.817
1.842
1.865
1.106
1.107
1.108
1.110
1.111
0.156
0.153
0.151
0.149
0.147
2.32
2.34
2.36
2.38
2.40
1.603
1.607
1.612
1.617
1.620
0.358
0.354
0.350
0.346
0.341
0.077
0.075
0.073
0.071
0.068
1.893
1.918
1.945
1.971
1.995
1.113
1.115
1.116
1.118
1.120
0.145
0.143
0.141
0.139
0.137
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
F/F*
A
M
A
*
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Gas Tables for Compressible Flow Calculations
44
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
p
p0
T/T0
p/p0
A/A*
2.42
2.44
2.46
2.48
2.50
1.626
1.631
1.635
1.639
1.642
0.338
0.335
0.331
0.328
0.323
0.067
0.065
0.063
0.062
0.060
2.025
2.053
2.081
2.109
2.135
1.121
1.122
1.123
1.124
1.125
0.135
0.133
0.131
0.129
0.128
2.52
2.54
2.56
2.58
2.60
1.648
1.652
1.656
1.660
1.663
0.321
0.317
0.314
0.311
0.306
0.058
0.057
0.055
0.053
0.052
2.168
2.197
2.228
2.258
2.285
1.127
1.128
1.130
1.131
1.132
0.126
0.124
0.123
0.121
0.120
2.62
2.64
2.66
2.68
2.70
1.668
1.672
1.676
1.680
1.682
0.304
0.301
0.298
0.295
0.291
0.051
0.049
0.048
0.047
0.046
2.321
2.353
2.385
2.417
2.445
1.134
1.135
1.136
1.137
1.138
0.118
0.117
0.115
0.114
0.112
2.72
2.74
2.76
2.78
2.80
1.687
1.690
1.694
1.697
1.700
0.288
0.285
0.282
0.279
0.276
0.045
0.044
0.042
0.041
0.040
2.484
2.518
2.552
2.587
2.615
1.139
1.141
1.142
1.143
1.145
0.111
0.109
0.108
0.107
0.106
2.82
2.84
2.86
2.88
2.90
1.704
1.707
1.710
1.713
1.714
0.274
0.271
0.268
0.265
0.262
0.039
0.038
0.037
0.036
0.035
2.660
2.694
2.731
2.768
2.800
1.146
1.147
1.148
1.149
1.150
0.104
0.103
0.101
0.100
0.099
2.92
2.94
2.96
2.98
3.00
1.720
1.723
1.726
1.728
1.730
0.260
0.258
0.225
0.252
0.250
0.034
0.0337
0.033
0.032
0.031
2.843
2.881
2.920
2.960
2.990
1.151
1.152
1.153
1.154
1.155
0.098
0.097
0.096
0.095
0.094
w.
Le
arn
En
gin
e
eri
ng
.i n
M*
ww
F/F*
A
M
A
*
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Isentropic Flow of Perfect Gases
45
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
p/p0
3.05
3.10
3.15
3.20
3.25
1.739
1.746
1.752
1.760
1.765
0.244
0.238
0.232
0.226
0.221
0.0294
0.0276
0.0259
0.0245
0.0230
3.100
3.205
3.312
3.423
3.536
1.157
1.159
1.162
1.164
1.166
0.0908
0.088
0.086
0.083
0.081
3.30
3.35
.3.40
3.45
3.50
1.771
1.776
1.782
1.787
1.790
0.216
0.211
0.206
0.201
0.196
0.0217
0.0204
0.0193
0.0182
0.0170
3.653
3.772
3.895
4.022
4.135
1.168
1.169
1.172
1.173
1.175
0.079
0.077
0.075
0.073
0.071
3.55
3.60
3.65
3.70
3.75
1.797
1.802
1.807
1.811
1.815
0.192
0.188
0.184
0.179
0.176
16.21 × 10−3
15.32 × 10−3
14.5 × 10−3
13.7 × 10−3
12.97 × 10−3
4.284
4.421
4.559
4.704
4.849
1.177
1.178
1.180
1.182
1.183
0.0693
0.0676
0.0659
0.0643
0.063
3.80
3.85
3.90
3.95
4.00
1.819
1.824
1.827
1.832
1.834
0.172
0.168
0.165
0.161
0.157
12.28 × 10−3
11.6 × 10−3
11.02 × 10−3
10.45 × 10−3
9.94 × 10−3
5.000
5.154
5.311
5.472
5.607
1.185
1.186
1.187
1.188
1.189
0.061
0.0598
0.0584
0.057
0.056
4.05
4.10
4.15
4.20
4.25
1.838
1.842
1.845
1.848
1.852
0.154
0.151
0.148
0.145
0.142
9.4 × 10−3
8.93 × 10−3
8.48 × 10−3
8.06 × 10−3
7.66 × 10−3
5.806
5.978
6.155
6.336
6.519
1.191
1.193
1.194
1.195
1.196
0.054
0.053
0.052
0.051
0.049
4.30
4.35
4.40
4.45
4.50
1.855
1.858
1.861
1.864
1.865
0.139
0.137
0.134
0.132
0.128
7.28 × 10−3
6.93 × 10−3
6.6 × 10−3
6.28 × 10−3
6.00 × 10−3
6.708
6.900
7.097
7.298
7.455
1.197
1.198
1.199
1.200
1.201
0.0487
0.0477
0.0467
0.0457
0.045
arn
En
gin
e
eri
ng
.i n
T/T0
w.
Le
F/F*
p
p0
M*
ww
A/A*
A
M
A
*
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Gas Tables for Compressible Flow Calculations
46
TABLE 3.3
Isentropic flow of perfect gases (γγ = 1.67)
T/T0
p/p0
4.55
4.60
4.65
4.70
4.75
1.869
1.871
1.874
1.876
1.878
0.126
0.124
0.122
0.119
0.117
5.7 × 10−3
5.4 × 10−3
5.2 × 10−3
4.9 × 10−3
4.7 × 10−3
7.712
7.925
8.143
8.365
8.591
1.202
1.203
1.204
1.205
1.206
0.044
0.043
0.042
0.041
0.040
4.80
4.85
4.90
4.95
5.00
1.881
1.883
1.885
1.887
1.888
0.115
0.113
0.111
0.109
0.107
4.5 × 10−3
4.3 × 10−3
4.1 × 10−3
3.9 × 10−3
3.7 × 10−3
8.822
9.058
9.298
9.543
9.720
1.206
1.207
1.208
1.208
1.209
0.039
0.0389
0.0381
0.0374
0.037
6.00
7.00
8.00
9.00
10.00
1.918
1.937
1.950
1.960
1.965
0.076
0.057
0.045
0.036
0.029
165.0 × 10−5
81.0 × 10−5
43.0 × 10−5
24.5 × 10−5
14.5 × 10−5
15.680
23.850
34.600
48.250
65.200
1.220
1.228
1.232
1.234
1.238
0.026
0.019
0.015
0.012
0.009
∞
1.995
∞
1.248
0
En
gin
e
arn
w.
Le
0
A
*
ww
0
F/F*
p
p0
M*
eri
ng
.i n
A/A*
A
M
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Normal Shocks in Perfect Gases
47
TABLE 4.1
Normal shocks in perfect gases (γγ = 1.3)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
1.00
1.02
1.04
1.06
1.08
1.10
1.000
0.981
0.962
0.944
0.927
0.911
1.000
1.046
1.092
1.139
1.185
1.237
1.000
1.010
1.021
1.031
1.041
1.051
1.000
0.999
0.999
0.999
0.999
0.999
1.832
1.875
1.918
1.963
2.010
2.058
1.12
1.14
1.16
1.18
1.20
0.896
0.881
0.867
0.853
0.840
1.287
1.338
1.391
1.444
1.497
1.061
1.070
1.080
1.089
1.099
0.998
0.997
0.995
0.994
0.993
2.107
2.157
2.209
2.262
2.316
1.22
1.24
1.26
1.28
1.30
0.828
0.816
0.804
0.793
0.783
1.552
1.608
1.664
1.722
1.780
1.109
1.119
1.128
1.138
1.148
0.990
0.987
0.985
0.982
0.978
2.372
2.428
2.486
2.545
2.605
1.32
1.34
1.36
1.38
1.40
0.772
0.762
0.753
0.744
0.735
1.839
1.899
1.960
2.022
2.085
1.158
1.167
1.177
1.187
1.197
0.975
0.971
0.966
0.961
0.956
2.667
2.728
2.792
2.856
2.922
0.726
0.714
0.709
0.702
0.694
2.149
2.214
2.279
2.346
2.413
1.207
1.217
1.227
1.237
1.247
0.951
0.945
0.939
0.933
0.926
2.988
3.056
3.125
3.195
3.265
0.687
0.680
0.673
0.666
0.660
2.481
2.551
2.621
2.692
2.764
1.257
1.268
1.278
1.288
1.300
0.919
0.912
0.905
0.897
0.889
3.337
3.410
3.484
3.559
3.635
1.52
1.54
1.56
1.58
1.60
En
gin
e
arn
w.
Le
ww
1.42
1.44
1.46
1.48
1.50
eri
ng
.i n
Mx
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Gas Tables for Compressible Flow Calculations
48
TABLE 4.1
Normal shocks in perfect gases (γγ = 1.3)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
1.62
1.64
1.66
1.68
1.70
0.654
0.647
0.642
0.636
0.630
2.836
2.910
2.985
3.060
3.137
1.310
1.320
1.331
1.342
1.353
0.881
0.873
0.864
0.856
0.847
3.712
3.791
3.870
3.991
4.031
1.72
1.74
1.76
1.78
1.80
0.625
0.620
0.615
0.609
0.605
3.214
3.292
3.371
3.451
3.532
1.364
1.375
1.386
1.397
1.407
0.837
0.828
0.819
0.810
0.800
4.155
4.196
4.281
4.366
4.452
1.82
1.84
1.86
1.88
1.90
0.600
0.596
0.591
0.587
0.583
1.420
1.432
1.443
1.455
1.466
0.790
0.781
0.771
0.761
0.751
4.539
4.628
4.717
4.807
4.898
1.92
1.94
1.96
1.98
2.00
0.578
0.574
0.570
0.567
0.563
4.037
4.124
4.212
4.301
4.390
1.479
1.491
1.503
1.515
1.527
0.741
0.731
0.721
0.711
0.700
4.991
5.084
5.178
5.274
5.370
0.559
0.556
0.552
0.548
0.546
4.482
4.574
4.667
4.760
4.856
1.539
1.552
1.565
1.578
1.590
0.690
0.680
0.670
0.660
0.650
5.467
5.565
5.665
5.765
5.867
0.542
0.539
0.536
0.533
0.530
4.950
5.046
5.144
5.242
5.341
1.600
1.617
1.630
1.643
1.656
0.639
0.629
0.619
0.609
0.600
5.968
6.071
6.176
6.281
6.387
2.12
2.14
2.16
2.18
2.20
En
gin
e
arn
3.614
3.697
3.780
3.865
3.950
w.
Le
ww
2.02
2.04
2.06
2.08
2.10
eri
ng
.i n
Mx
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Normal Shocks in Perfect Gases
49
TABLE 4.1
Normal shocks in perfect gases (γγ = 1.3)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
2.22
2.24
2.26
2.28
2.30
0.527
0.524
0.522
0.519
0.516
5.441
5.542
5.643
5.746
5.849
1.669
1.683
1.697
1.711
1.725
0.590
0.580
0.571
0.561
0.552
6.494
6.603
6.712
6.822
6.934
2.32
2.34
2.36
2.38
2.40
0.514
0.511
0.508
0.506
0.505
5.954
6.059
6.166
6.273
6.380
1.738
1.753
1.767
1.781
1.797
0.542
0.533
0.523
0.515
0.505
7.045
7.158
7.272
7.387
7.504
2.42
2.44
2.46
2.48
2.50
0.502
0.499
0.497
0.495
0.493
1.810
1.825
1.840
1.854
1.869
0.496
0.487
0.478
0.469
0.460
7.621
7.740
7.857
7.977
8.098
2.52
2.54
2.56
2.58
2.60
0.491
0.489
0.487
0.485
0.483
7.050
7.163
7.278
7.394
7.512
1.885
1.899
1.915
1.930
1.945
0.452
0.444
0.436
0.427
0.420
8.220
8.343
8.467
8.592
8.715
0.481
0.479
0.477
0.475
0.474
7.629
7.748
7.865
7.988
8.770
1.962
1.977
1.993
2.009
2.025
0.411
0.404
0.396
0.388
0.381
8.845
8.973
9.101
9.231
9.361
0.472
0.470
0.468
0.467
0.466
8.233
8.351
8.481
8.606
8.733
2.042
2.058
2.074
2.091
2.107
0.374
0.366
0.359
0.352
0.345
9.494
9.626
9.760
9.895
10.031
2.72
2.74
2.76
2.78
2.80
En
gin
e
arn
6.489
6.599
6.711
6.822
6.935
w.
Le
ww
2.62
2.64
2.66
2.68
2.70
eri
ng
.i n
Mx
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Gas Tables for Compressible Flow Calculations
50
TABLE 4.1
Normal shocks in perfect gases (γγ = 1.3)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
2.82
2.84
2.86
2.88
2.90
0.464
0.462
0.461
0.459
0.458
8.859
8.987
9.116
9.246
9.380
2.124
2.141
2.158
2.175
2.194
0.338
0.332
0.325
0.318
0.313
10.167
10.305
10.444
10.583
10.725
2.92
2.94
2.96
2.98
3.00
0.456
0.455
0.454
0.452
0.451
9.508
9.641
9.774
9.908
10.041
2.210
2.227
2.245
2.263
2.280
0.306
0.300
0.294
0.288
0.282
16.865
11.008
11.151
11.295
11.450
3.05
3.10
3.15
3.20
3.25
0.448
0.445
0.442
0.439
0.436
2.325
2.371
2.418
2.465
2.513
0.268
0.255
0.242
0.229
0.218
11.735
12.183
12.563
13.027
13.421
3.30
3.35
3.40
3.45
3.50
0.434
0.431
0.428
0.426
0.424
12.180
12.556
12.937
13.325
13.720
2.561
2.611
2.661
2.711
2.762
0.207
0.196
0.186
0.178
0.168
13.740
14.145
14.556
14.972
15.391
0.422
0.420
0.418
0.416
0.414
14.116
14.520
14.930
15.345
15.766
2.815
2.868
2.922
2.976
3.031
0.159
0.151
0.143
0.136
0.129
15.823
16.259
16.700
17.147
17.600
0.412
0.411
0.409
0.407
0.406
16.193
16.625
17.063
17.507
17.960
3.087
3.144
3.201
3.259
3.317
0.122
0.116
0.110
0.105
0.099
18.060
18.526
18.997
19.475
19.961
3.80
3.85
3.90
3.95
4.00
En
gin
e
arn
10.385
10.733
11.086
11.445
11.809
w.
Le
ww
3.55
3.60
3.65
3.70
3.75
eri
ng
.i n
Mx
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Normal Shocks in Perfect Gases
51
TABLE 4.1
Normal shocks in perfect gases (γγ = 1.3)
Ty /Tx
p0y /p0x
p0y /px
0.404
0.403
0.401
0.400
0.398
18.411
18.872
19.338
19.810
20.288
3.378
3.438
3.498
3.561
3.623
0.094
0.089
0.085
0.081
0.077
20.449
20.945
21.447
21.956
22.470
4.30
4.35
4.40
4.45
4.50
0.397
0.396
0.395
0.394
0.393
20.771
21.260
21.755
22.255
22.760
3.686
3.750
3.815
3.880
3.945
0.073
0.069
0.066
0.062
0.0594
22.999
23.516
24.049
24.588
25.181
4.55
4.60
4.65
4.70
4.75
0.392
0.391
0.389
0.388
0.387
4.013
4.081
4.149
4.218
4.287
0.056
0.054
0.051
0.048
0.046
25.683
26.241
26.804
27.373
27.948
4.80
4.85
4.90
4.95
5.00
0.387
0.386
0.385
0.384
0.383
25.915
26.460
27.011
27.568
28.130
4.358
4.429
4.502
4.574
4.646
0.044
0.042
0.039
0.038
0.036
28.529
29.117
29.710
30.309
30.901
40.570
55.261
72.220
91.430
112.911
6.271
8.189
10.401
12.907
15.710
0.014
0.0061
0.00283
0.0014
0.00074
∞
0
∞
0.370
0.363
0.357
0.354
0.351
ww
6.00
7.00
8.00
9.00
10.00
En
gin
e
4.05
4.10
4.15
4.20
4.25
0.340
eri
ng
.i n
py /px
23.272
23.789
24.312
24.841
25.375
arn
My
w.
Le
Mx
∞
44.320
60.140
78.400
99.101
122.25
∞
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Gas Tables for Compressible Flow Calculations
52
TABLE 4.2
Normal shocks in perfect gases (γγ = 1.4)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
1.00
1.02
1.04
1.06
1.08
1.10
1.000
0.981
0.962
0.945
0.928
0.911
1.000
1.047
1.095
1.144
1.194
1.245
1.000
1.013
1.026
1.039
1.052
1.065
1.000
0.999
0.999
0.999
0.999
0.998
1.893
1.938
1.984
2.032
2.082
2.133
1.12
1.14
1.16
1.18
1.20
0.897
0.882
0.868
0.855
0.842
1.297
1.349
1.403
1.458
1.513
1.078
1.090
1.103
1.115
1.128
0.998
0..997
0.996
0.994
0.993
2.185
2.238
2.294
2.350
2.407
1.22
1.24
1.26
1.28
1.30
0.830
0.818
0.807
0.796
0.786
1.570
1.627
1.685
1.745
1.805
1.141
1.153
1.166
1.178
1.191
0.991
0.988
0.985
0.983
0.979
2.466
2.526
2.587
2.650
2.714
1.32
1.34
1.36
1.38
1.40
0.776
0.766
0.757
0.748
0.740
1.866
1.928
1.991
2.055
2.120
1.204
1.216
1.229
1.242
1.255
0.976
0.972
0.967
0.963
0.958
2.778
2.845
2.911
2.979
3.049
0.731
0.723
0.716
0.708
0.701
2.186
2.253
2.320
2.389
2.458
1.267
1.281
1.294
1.307
1.320
0.953
0.947
0.942
0.936
0.930
3.120
3.192
3.265
3.338
3.413
0.694
0.687
0.681
0.675
0.668
2.529
2.600
2.673
2.746
2.820
1.334
1.347
1.361
1.374
1.388
0.923
0.917
0.909
0.903
0.895
3.489
3.567
3.645
3.725
3.805
1.52
1.54
1.56
1.58
1.60
En
gin
e
arn
w.
Le
ww
1.42
1.44
1.46
1.48
1.50
eri
ng
.i n
Mx
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Normal Shocks in Perfect Gases
53
TABLE 4.2
Normal shocks in perfect gases (γγ = 1.4)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
1.62
1.64
1.66
1.68
1.70
0.663
0.657
0.651
0.646
0.641
2.895
2.971
3.048
3.126
3.205
1.402
1.416
1.430
1.444
1.458
0.887
0.880
0.872
0.864
0.856
3.886
3.969
4.053
4.138
4.224
1.72
1.74
1.76
1.78
1.80
0.635
0.631
0.626
0.621
0.616
3.285
3.336
3.447
3.530
3.613
1.473
1.487
1.502
1.517
1.532
0.847
0.839
0.830
0.822
0.813
4.315
4.443
4.533
4.578
4.670
1.82
1.84
1.86
1.88
1.90
0.612
0.608
0.604
0.599
0.596
1.547
1.562
1.578
1.593
1.608
0.804
0.795
0.786
0.776
0.767
4.762
4.855
4.947
5.043
5.142
1.92
1.94
1.96
1.98
2.00
0.592
0.588
0.584
0.581
0.577
4.134
4.224
4.315
4.407
4.500
1.624
1.639
1.656
1.671
1.687
0.758
0.749
0.739
0.730
0.721
5.239
5.338
5.438
5.538
5.641
0.574
0.571
0.567
0.564
0.561
4.594
4.688
4.784
4.881
4.978
1.704
1.720
1.737
1.754
1.770
0.712
0.702
0.693
0.684
0.674
5.743
5.847
5.953
6.058
6.166
0.558
0.556
0.553
0.550
0.547
5.077
5.176
5.276
5.378
5.480
1.787
1.805
1.822
1.839
1.857
0.665
0.656
0.646
0.637
0.628
6.274
6.383
6.493
6.604
6.716
2.12
2.14
2.16
2.18
2.20
En
gin
e
arn
3.698
3.781
3.870
3.957
4.045
w.
Le
ww
2.02
2.04
2.06
2.08
2.10
eri
ng
.i n
Mx
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Gas Tables for Compressible Flow Calculations
54
TABLE 4.2
Normal shocks in perfect gases (γγ = 1.4)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
2.22
2.24
2.26
2.28
2.30
0.545
0.542
0.539
0.537
0.534
5.583
5.687
5.792
5.898
6.005
1.875
1.892
1.910
1.928
1.947
0.619
0.610
0.601
0.592
0.583
6.829
6.945
7.060
7.176
7.294
2.32
2.34
2.36
2.38
2.40
0.532
0.529
0.527
0.525
0.523
6.113
6.222
6.331
6.442
6.553
1.965
1.984
2.003
2.021
2.040
0.574
0.566
0.557
0.548
0.540
7.412
7.532
7.653
7.775
7.897
2.42
2.44
2.46
2.48
2.50
0.521
0.519
0.517
0.515
0.513
6.666
6.780
6.894
7.008
7.125
2.059
2.079
2.098
2.118
2.138
0.532
0.523
0.515
0.507
0.499
8.027
8.145
8.271
8.398
8.526
2.52
2.54
2.56
2.58
2.60
0.511
0.509
0.507
0.506
0.504
7.242
7.360
7.479
7.599
7.720
2.157
2.177
2.197
2.218
2.238
0.491
0.483
0.475
0.467
0.460
8.655
8.785
8.916
9.145
9.181
0.502
0.500
0.498
0.497
0.496
7.842
7.965
8.088
8.213
8.338
2.259
2.279
2.300
2.322
2.343
0.453
0.445
0.438
0.431
0.423
9.315
9.451
9.587
9.724
9.863
0.494
0.493
0.491
0.490
0.488
8.465
8.592
8.721
8.849
8.980
2.364
2.386
2.407
2.429
2.451
0.416
0.409
0.403
0.396
0.389
10.002
10.142
10.283
10.426
10.569
2.72
2.74
2.76
2.78
2.80
En
gin
e
arn
w.
Le
ww
2.62
2.64
2.66
2.68
2.70
eri
ng
.i n
Mx
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Normal Shocks in Perfect Gases
55
TABLE 4.2
Normal shocks in perfect gases (γγ = 1.4)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
2.82
2.84
2.86
2.88
2.90
0.487
0.485
0.484
0.483
0.481
9.111
9.243
9.376
9.510
9.645
2.473
2.495
2.518
2.540
2.563
0.383
0.376
0.370
0.364
0.358
10.714
10.859
11.006
11.154
11.302
2.92
2.94
2.96
2.98
3.00
0.480
0.478
0.477
0.476
0.475
9.781
9.917
10.055
10.194
10.333
2.586
2.609
2.632
2.656
2.679
0.352
0.346
0.339
0.334
0.328
11.452
11.603
11.754
11.907
12.061
3.05
3.10
3.15
3.20
3.25
0.472
0.469
0.467
0.464
0.462
10.686
11.045
11.409
11.780
12.156
2.738
2.798
2.860
2.922
2.985
0.315
0.301
0.288
0.276
0.264
12.450
12.846
13.247
13.656
14.071
3.30
3.35
3.40
3.54
3.50
0.459
0.457
0.455
0.453
0.451
12.538
12.926
13.320
13.791
14.125
3.049
3.114
3.180
3.247
3.315
0.253
0.243
0.232
0.222
0.213
14.492
14.920
15.354
15.795
16.242
0.449
0.447
0.445
0.444
0.442
14.536
14.953
15.376
15.805
16.239
3.384
3.454
3.525
3.596
3.669
0.204
0.195
0.187
0.179
0.172
16.700
17.156
17.715
18.095
18.575
0.441
0.439
0.438
0.436
0.435
16.680
17.126
17.578
18.036
18.500
3.743
3.817
3.893
3.969
4.047
0.164
0.157
0.151
0.145
0.138
19.060
19.553
20.051
20.556
21.068
3.80
3.85
3.90
3.95
4.00
En
gin
e
arn
w.
Le
ww
3.55
3.60
3.65
3.70
3.75
eri
ng
.i n
Mx
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Gas Tables for Compressible Flow Calculations
56
TABLE 4.2
Normal shocks in perfect gases (γγ = 1.4)
Ty /Tx
p0y /p0x
p0y /px
0.434
0.432
0.431
0.430
0.429
18.969
19.445
19.926
20.413
20.906
4.125
4.205
4.285
4.367
4.449
0.133
0.127
0.122
0.117
0.113
21.586
22.111
22.642
23.179
23.723
4.30
4.35
4.40
4.45
4.50
0.428
0.427
0.426
0.425
0.424
21.405
21.909
22.420
22.936
23.458
4.532
4.616
4.702
4.788
4.875
0.108
0.104
0.099
0.095
0.0917
24.273
24.829
25.393
26.078
26.539
4.55
4.60
4.65
4.70
4.75
0.423
0.422
0.421
0.420
0.419
4.963
5.052
5.142
5.233
5.325
0.088
0.085
0.081
0.078
0.075
27.120
27.710
28.305
28.907
29.516
4.80
4.85
4.90
4.95
5.00
0.418
0.417
0.4167
0.416
0.415
26.713
27.276
27.845
28.419
29.000
5.418
5.512
5.607
5.703
5.800
0.072
0.069
0.067
0.0642
0.0617
30.130
30.751
31.379
32.013
32.654
0.404
0.397
0.393
0.389
0.388
41.833
57.000
74.500
94.333
116.500
7.941
10.469
13.387
16.693
20.388
0.0296
0.0154
0.0085
0.005
0.003
46.815
63.552
82.865
104.753
129.217
0.378
∞
ww
6.00
7.00
8.00
9.00
10.000
∞
En
gin
e
4.05
4.10
4.15
4.20
4.25
eri
ng
.i n
py /px
23.986
24.520
25.059
25.605
26.156
arn
My
w.
Le
Mx
∞
0
∞
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Normal Shocks in Perfect Gases
57
TABLE 4.3
Normal shocks in perfect gases (γγ = 1.67)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
1.00
1.02
1.04
1.06
1.08
1.10
1.000
0.981
0.962
0.945
0.928
0.913
1.000
1.051
1.102
1.155
1.208
1.262
1.000
1.020
1.040
1.059
l.078
1.098
1.000
0.999
0.999
0.999
0.999
0.999
2.055
2.107
2.161
2.217
2.274
2.333
1.12
1.14
1.16
1.18
1.20
0.898
0.884
0.871
0.858
0.846
1.318
1.375
1.432
1.490
1.551
1.118
1.137
1.157
1.176
1.195
0.998
0.997
0.996
0.995
0.993
2.393
2.455
2.518
2.584
2.649
1.22
1.24
1.26
1.28
1.30
0.835
0.824
0.813
0.805
0.794
1.611
1.672
1.735
1.798
1.863
1.215
1.234
1.253
1.273
1.293
0.991
0.989
0.987
0.984
0.981
2.718
2.787
2.857
2.929
3.002
1.32
1.34
1.36
1.38
1.40
0.784
0.775
0.767
0.758
0.751
1.928
1.995
2.062
2.131
2.201
1.312
1.332
1.352
1.372
1.394
0.978
0.975
0.971
0.967
0.963
3.076
3.152
3.229
3.308
3.388
0.743
0.736
0.729
0.723
0.716
2.271
2.342
2.415
2.488
2.562
1.412
1.433
1.453
1.475
1.497
0.958
0.953
0.948
0.943
0.938
3.468
3.551
3.634
3.719
3.805
0.709
0.703
0.697
0.692
0.687
2.638
2.715
2.792
2.871
2.950
1.516
1.537
1.560
1.580
1.605
0.933
0.927
0.921
0.915
0.908
3.892
3.981
4.071
4.162
4.255
1.52
1.54
1.56
1.58
1.60
En
gin
e
arn
w.
Le
ww
1.42
1.44
1.46
1.48
1.50
eri
ng
.i n
Mx
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Gas Tables for Compressible Flow Calculations
58
TABLE 4.3
Normal shocks in perfect gases (γγ = 1.67)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
1.62
1.64
1.66
1.68
1.70
0.681
0.676
0.671
0.667
0.662
3.031
3.112
3.195
3.278
3.365
1.624
1.646
1.668
1.691
1.715
0.902
0.896
0.889
0.882
0.875
4.347
4.442
4.538
4.635
4.734
1.72
1.74
1.76
1.78
1.80
0.657
0.653
0.649
0.645
0.641
3.448
3.535
3.622
3.711
3.800
1.736
1.760
1.783
1.806
1.832
0.868
0.861
0.854
0.847
0.840
4.833
4.933
5.036
5.139
5.244
1.82
1.84
1.86
1.88
1.90
0.637
0.633
0.630
0.626
0.623
3.891
3.982
4.075
4.168
4.266
1.853
1.878
1.903
1.927
1.954
0.832
0.824
0.817
0.809
0.802
5.349
5.456
5.564
5.673
5.785
1.92
1.94
1.96
1.98
2.00
0.619
0.616
0.613
0.610
0.607
4.358
4.454
4.552
4.651
4.753
1.976
2.002
2.027
2.053
2.080
0.794
0.786
0.778
0.771
0.763
5.895
6.008
6.122
6.237
6.355
0.604
0.601
0.598
0.596
0.594
4.851
4.952
5.055
5.158
5.266
2.105
2.131
2.157
2.184
2.213
0.756
0.747
0.740
0.732
0.725
6.472
6.500
6.711
6.832
6.953
0.591
0.588
0.586
0.584
0.582
5.368
5.475
5.582
5.891
5.805
2.238
2.266
2.293
2.321
2.354
0.717
0.709
0.701
0.694
0.687
7.078
7.203
7.328
7.456
7.586
2.12
2.14
2.16
2.18
2.20
En
gin
e
arn
w.
Le
ww
2.02
2.-04
2.06
2.08
2.10
eri
ng
.i n
Mx
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Normal Shocks in Perfect Gases
59
TABLE 4.3
Normal shocks in perfect gases (γγ = 1.67)
My
py /px
Ty /Tx
p0y /p0x
p0y /px
2.22
2.24
2.26
2.28
2.30
0.579
0.577
0.575
0.573
0.571
5.911
6.022
6.135
6.248
6.367
2.378
2.405
2.435
2.464
2.500
0.678
0.671
0.664
0.656
0.649
7.714
7.845
7.977
8.110
8.245
2.32
2.34
2.36
2.38
2.40
0.569
0.567
0.565
0.563
0.562
6.478
6.595
6.713
6.831
6.953
2.523
2.553
2.583
2.613
2.651
0.641
0.634
0.627
0.619
0.614
8.379
8.517
8.654
8.794
8.935
2.42
2.44
2.46
2.48
2.50
0.560
0.558
0.556
0.555
0.554
7.071
7.193
7.315
7.438
7.567
2.674
2.705
2.736
2.767
2.805
0.605
0.598
0.591
0.584
0.578
9.004
9.218
9.362
9.507
9.651
2.52
2.54
2.56
2.58
2.60
0.552
0.550
0.548
0.547
0.546
7.689
7.815
7.943
8.071
8.205
2.831
2.863
2.895
2.928
2.968
0.571
0.564
0.557
0.551
0.545
9.800
9.949
10.098
10.249
10.401
0.544
0.543
0.541
0.540
0.539
8.333
8.463
8.595
8.729
8.870
2.994
3.027
3.061
3.094
3.138
0.538
0.531
0.525
0.518
0.514
10.556
10.709
10.865
11.022
11.180
0.538
0.536
0.535
0.534
0.533
8.995
9.135
9.273
9.411
9.557
3.163
3.197
3.232
3.267
3.311
0.506
0.500
0.494
0.488
0.483
11.339
11.500
11.662
11.824
12.000
2.72
2.74
2.76
2.78
2.80
En
gin
e
arn
w.
Le
ww
2.62
2.64
2.66
2.68
2.70
eri
ng
.i n
Mx
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Gas Tables for Compressible Flow Calculations
60
TABLE 4.3
Normal shocks in perfect gases (γγ = 1.67)
Ty /Tx
p0y /p0x
p0y /px
0.532
0.531
0.529
0.528
0.527
9.691
9.833
9.976
10.118
10.270
3.337
3.373
3.409
3.445
3.492
0.476
0.471
0.465
0.459
0.455
12.153
12.319
12.487
12.656
12.831
2.92
2.94
2.96
2.98
3.00
0.526
0.525
0.524
0.523
0.523
10.408
10.555
10.703
10.851
11.010
3.518
3.555
3.593
3.630
3.680
0.448
0.443
0.438
0.433
0.428
12.997
13.169
13.342
13.517
13.690
3.05
3.10
3.15
3.20
3.25
0.520
0.518
0.516
0.514
0.511
11.379
11.763
12.154
12.551
12.954
3.763
3.860
3.958
4.053
4.160
0.415
0.402
0.390
0.378
0.367
14.137
14.589
15.048
15.515
15.989
3.30
3.35
3.40
3.45
3.50
0.509
0.508
0.506
0.505
0.504
13.363
13.779
14.201
14.620
15.075
4.262
4.367
4.473
4.581
4.705
0.357
0.346
0.336
0.326
0.318
16.471
16.960
17.456
17.959
18.471
0.502
0.500
0.498
0.497
0.496
15.504
15.951
16.404
16.864
17.330
4.800
4.912
5.026
5.141
5.258
0.309
0.298
0.290
0.282
0.274
18.988
19.514
20.047
20.588
21.135
0.495
0.494
0.493
0.492
0.491
17.801
18.279
18.764
19.255
19.761
5.376
5.496
5.618
5.741
5.886
0.266
0.258
0.251
0.244
0.239
21.691
22.253
22.823
23.400
23.990
3.80
3.85
3.90
3.95
4.00
ww
3.55
3.60
3.65
3.70
3.75
En
gin
e
2.82
2.84
2.86
2.88
2.90
eri
ng
.i n
py /px
arn
My
w.
Le
Mx
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Normal Shocks in Perfect Gases
61
TABLE 4.3
Normal shocks in perfect gases (γγ = 1.67)
Ty /Tx
p0y /p0x
p0y /px
0.489
0.488
0.487
0.486
0.485
20.255
20.764
21.280
24.802
22.330
5.992
6.119
6.249
6.379
6.511
0.231
0.225
0.218
0.213
0.207
24.577
25.175
25.783
26.397
27.018
4.30
4.35
4.40
4.45
4.50
0.485
0.484
0.483
0.482
0.482
22.864
23.405
23.952
24.505
25.081
6.645
6.781
6.918
7.057
7.222
0.201
0.196
0.191
0.186
0.181
27.647
28.283
28.926
29.578
30.250
4.55
4.60
4.65
4.70
4.75
0.481
0.480
0.479
0.479
0.478
7.338
7.482
7.626
7.773
7.921
0.176
0.171
0.167
0.163
0.158
30.901
31.574
32.254
32.942
33.637
4.80
4.85
4.90
4.95
5.00
0.478
0.477
0.476
0.476
0.476
28.552
29.155
29.765
30.380
31.021
8.070
8.221
8.373
8.528
8.700
0.155
0.151
0.147
0.143
0.140
34.340
35.049
35.766
36.491
37.230
44.780
61.050
79.810
101.080
124.85
12.165
16.250
20.960
26.300
32.260
0.089
0.058
0.041
0.029
0.022
53.400
72.530
94.600
119.600
147.50
∞
0.467
0.462
0.459
0.457
0.456
ww
6.00
7.00
8.00
9.00
10.00
En
gin
e
4.05
4.10
4.15
4.20
4.25
0.448
eri
ng
.i n
py /px
25.630
26.202
26.780
27.365
27.955
arn
My
w.
Le
Mx
∞
∞
0
∞
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Gas Tables for Compressible Flow Calculations
62
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 2°)
σ
M1
1.02
1.04
1.06
1.08
1.10
83.49
80.93
79.05
77.56
76.30
1.62
1.64
1.66
1.68
1.70
1.12
1.14
1.16
1.18
1.20
75.22
68.71
65.55
63.10
61.10
1.72
1.74
1.76
1.78
1.80
1.22
1.24
1.26
1.28
1.30
59.24
57.50
56.15
54.75
53.50
1.32
1.34
1.36
1.38
1.40
52.30
51.15
50.10
49.12
48.15
1.52
1.54
1.56
1.58
1.60
M1
σ
2.22
2.24
2.26
2.28
2.30
28.32
28.05
27.80
27.54
27.30
37.45
36.93
36.45
36.00
35.50
2.32
2.34
2.36
2.38
2.40
27.05
26.81
26.51
26.35
26.12
1.82
1.84
1.86
1.88
1.90
35.10
34.70
34.25
33.85
33.45
2.42
2.44
2.46
2.48
2.50
25.90
25.70
25.50
25.25
25.05
1.92
1.94
1.96
1.98
2.00
33.05
32.70
32.35
32.00
31.65
2.52
2.54
2.56
2.58
2.60
24.85
24.65
24.45
24.25
24.06
47.27
46.42
45.60
44.82
44.05
2.02
2.04
2.06
2.08
2.10
31.30
30.95
30.65
30.35
30.03
2.62
2.64
2.66
2.68
2.70
23.90
23.70
23.52
23.35
23.15
43.35
42.65
42.00
41.35
40.75
2.12
2.14
2.16
2.18
2.20
29.74
29.40
29.15
28.85
28.59
2.72
2.74
2.76
2.78
2.80
23.00
22.83
22.65
22.50
22.35
w.
Le
arn
En
gin
e
40.15
39.50
39.00
38.45
37.93
ww
1.42
1.44
1.46
1.48
1.50
σ
eri
ng
.i n
M1
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Oblique Shocks in Perfect Gases
63
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 2°)
σ
M1
σ
2.82
2.84
2.86
2.88
2.90
22.20
22.05
21.88
21.74
21.58
4.05
4.10
4.15
4.20
4.25
15.63
15.45
15.25
15.10
14.94
2.92
2.94
2.96
2.98
3.00
21.45
21.30
21.15
21.00
20.85
4.30
4.35
4.40
4.45
4.50
3.05
3.10
3.15
3.20
3.25
20.53
20.20
19.90
19.60
19.29
3.30
3.35
3.40
3.45
3.50
19.00
18.75
18.45
18.21
17.95
3.80
3.85
3.90
3.95
4.00
σ
En
gin
e
14.75
14.62
14.45
14.30
14.15
14.03
13.88
13.75
13.60
13.48
4.80
4.85
4.90
4.95
5.00
13.35
13.23
13.10
12.98
12.85
17.70
17.50
17.25
17.05
16.81
5.50
6.00
6.50
7.00
7.50
11.80
10.91
10.16
9.55
9.00
16.60
16.40
16.20
16.00
15.81
8.00
8.50
9.00
9.50
10.00
8.50
8.08
7.70
7.35
7.00
w.
Le
arn
4.55
4.60
4.65
4.70
4.75
ww
3.55
3.60
3.65
3.70
3.75
M1
eri
ng
.i n
M1
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Gas Tables for Compressible Flow Calculations
64
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 6°)
σ
M1
σ
1.02
1.04
1.06
1.08
1.10
1.62
1.64
1.66
1.68
1.70
44.65
44.00
43.36
42.75
42.15
2.22
2.24
2.26
2.28
2.30
31.70
31.42
31.15
30.85
30.60
1.12
1.14
1.16
1.18
1.20
1.72
1.74
1.76
1.78
1.80
41.56
41.02
40.50
40.00
39.47
2.32
2.34
2.36
2.38
2.40
30.35
30.10
29.84
29.60
29.38
1.82
1.84
1.86
1.88
1.90
39.00
38.55
38.05
37.65
37.22
2.42
2.44
2.46
2.48
2.50
29.15
28.92
28.70
28.47
28.25
1.92
1.94
1.96
1.98
2.00
36.80
36.40
36.00
35.62
35.24
2.52
2.54
2.56
2.58
2.60
28.05
27.85
27.64
27.45
27.25
53.42
52.30
51.24
50.25
49.35
2.02
2.04
2.06
2.08
2.10
34.90
34.50
34.16
33.83
33.50
2.62
2.64
2.66
2.68
2.70
27.05
26.85
26.66
26.50
26.30
48.45
47.62
46.81
46.05
45.35
2.12
2.14
2.16
2.18
2.20
33.20
32.88
32.60
32.28
31.97
2.72
2.74
2.76
2.78
2.80
26.13
25.95
25.80
25.61
25.46
1.32
1.34
1.36
1.38
1.40
61.05
59.08
57.45
55.96
54.65
1.52
1.54
1.56
1.58
1.60
ww
1.42
1.44
1.46
1.48
1.50
arn
71.35
70.80
70.30
67.38
63.50
w.
Le
1.22
1.24
1.26
1.28
1.30
eri
ng
.i n
M1
En
gin
e
σ
M1
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Oblique Shocks in Perfect Gases
65
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 6°)
σ
M1
σ
2.82
2.84
2.86
2.88
2.90
25.30
25.15
25.00
24.81
24.67
4.05
4.10
4.15
4.20
4.25
18.60
18.45
18.27
18.10
17.95
2.92
2.94
2.96
2.98
3.00
24.32
24.38
24.21
24.05
23.95
4.30
4.35
4.40
4.45
4.50
3.05
3.10
3.15
3.20
3.25
23.60
23.30
22.95
22.63
22.32
3.30
3.35
3.40
3.45
3.50
22.05
21.76
21.50
21.23
21.00
3.80
3.85
3.90
3.95
4.00
σ
En
gin
e
17.78
17.65
17.45
17.30
17.17
17.00
16.90
16.75
16.62
16.50
4.80
4.85
4.90
4.95
5.00
16.36
16.25
16.10
16.00
15.89
20.73
20.50
20.25
20.00
19.80
5.50
6.00
6.50
7.00
7.50
14.84
14.00
13.27
12.70
12.16
19.60
19.40
19.20
19.00
18.80
8.00
8.50
9.00
9.50
10.00
11.70
11.34
11.00
10.70
10.45
w.
Le
arn
4.55
4.60
4.65
4.70
4.75
ww
3.55
3.60
3.65
3.70
3.75
M1
eri
ng
.i n
M1
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Gas Tables for Compressible Flow Calculations
66
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 10°)
M1
σ
M1
σ
1.02
1.04
1.06
1.08
1.10
1.62
1.64
1.66
1.68
1.70
50.20
49.40
48.63
47.90
47.15
2.22
2.24
2.26
2.28
2.30
35.45
35.15
34.90
34.60
34.34
1.12
1.14
1.16
1.18
1.20
1.72
1.74
1.76
1.78
1.80
46.50
45.83
45.22
44.65
44.06
2.32
2.34
2.36
2.38
2.40
34.00
33.80
33.53
33.30
33.00
1.82
1.84
1.86
1.88
1.90
43.50
43.00
42.47
42.00
41.50
2.42
2.44
2.46
2.48
2.50
32.80
32.54
32.30
32.00
31.85
68.30
68.00
67.75
1.92
1.94
1.96
1.98
2.00
41.00
40.60
40.15
39.73
39.30
2.52
2.54
2.56
2.58
2.60
31.65
31.40
31.20
31.00
30.80
67.50
62.30
60.00
58.20
56.71
2.02
2.04
2.06
2.08
2.10
38.91
38.50
38.15
37.80
37.43
2.62
2.64
2.66
2.68
2.70
30.60
30.40
30.20
30.00
29.82
55.34
54.16
53.05
52.10
51.10
2.12
2.14
2.16
2.18
2.20
37.10
36.76
36.43
36.10
35.80
2.72
2.74
2.76
2.78
2.80
29.65
29.45
29.27
29.11
28.95
1.52
1.54
1.56
1.58
1.60
En
gin
e
w.
Le
ww
1.42
1.44
1.46
1.48
1.50
arn
1.22
1.24
1..26
1.28
1.30
1.32
1.34
1.36
1.38
1.40
eri
ng
.i n
σ
M1
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Oblique Shocks in Perfect Gases
67
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 10°)
σ
M1
σ
2.82
2.84
2.86
2.88
2.90
28.78
28.60
28.44
28.30
28.15
4.05
4.10
4.15
4.20
4.25
22.04
21.90
21.70
21.54
21.36
2.92
2.94
2.96
2.98
3.00
28.00
27.81
27.70
27.55
27.35
4.30
4.35
4.40
4.45
4.50
3.05
3.10
3.15
3.20
3.25
27.00
26.70
26.36
26.10
25.80
3.30
3.35
3.40
3.45
3.50
25.45
25.16
24.90
24.65
24.38
3.80
3.85
3.90
3.95
4.00
σ
En
gin
e
21.25
21.05
20.90
20.78
20.61
20.50
20.35
20.21
20.10
19.95
4.80
4.85
4.90
4.95
5.00
19.85
19.72
19.60
19.50
19.40
24.14
23.90
23.66
23.45
23.25
5.50
6.00
6.50
7.00
7.50
18.40
17.60
16.95
16.40
15.93
23.00
22.80
22.60
22.42
22.25
8.00
8.50
9.00
9.50
10.00
15.53
15.20
14.90
14.65
14.45
w.
Le
arn
4.55
4.60
4.65
4.70
4.75
ww
3.55
3.60
3.65
3.70
3.75
M1
eri
ng
.i n
M1
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Gas Tables for Compressible Flow Calculations
68
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 20°)
σ
M1
σ
1.62
1.64
1.66
1.68
1.70
2.22
2.24
2.26
2.28
2.30
47.50
47.14
46.74
46.37
46.00
2.82
2.84
2.86
2.88
2.90
39.30
39.12
38.95
38.76
38.57
1.72
1.74
1.76
1.78
1.80
65.08
65.00
64.95
2.32
2.34
2.36
2.38
2.40
45.65
45.30
44.98
44.65
44.35
2.92
2.94
2.96
2.98
3.00
38.40
38.25
38.10
37.90
37.75
1.82
1.84
1.86
1.88
1.90
64.94
64.90
60.90
59.20
57.90
2.42
2.44
2.46
2.48
2.50
44.04
43.75
43.45
43.16
42.90
3.05
3.10
3.15
3.20
3.25
37.37
37.00
36.70
36.35
36.00
1.92
1.94
1.96
1.98
2.00
56.80
55.83
54.95
54.15
53.40
2.52
2.54
2.56
2.58
2.60
42.60
42.35
42.10
41.85
41.60
3.30
3.35
3.40
3.45
3.50
35.70
35.41
35.15
34.86
34.60
52.75
52.10
51.50
50.90
50.35
2.62
2.64
2.66
2.68
2.70
41.40
41.15
40.93
40.70
40.50
3.55
3.60
3.65
3.70
3.75
34.35
34.10
33.90
33.65
33.45
49.84
49.35
48.88
48.40
48.00
2.72
2.74
2.76
2.78
2.80
40.30
40.10
39.90
39.70
39.50
3.80
3.85
3.90
3.95
4.00
33.25
33.05
32.85
32.65
32.45
2.12
2.14
2.16
2.18
2.20
arn
w.
Le
ww
2.02
2.04
2.06
2.08
2.10
eri
ng
.i n
M1
En
gin
e
σ
M1
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Oblique Shocks in Perfect Gases
69
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 20°)
4.30
4.35
4.40
4.45
4.50
31.50
31.35
31.20
31.05
30.95
4.55
4.60
4.65
4.70
4.75
30.80
30.70
30.56
30.45
30.33
4.80
4.85
4.90
4.95
5.00
30.22
30.11
30.00
29.90
29.80
8.00
8.50
9.00
9.50
10.00
σ
28.93
28.25
27.70
27.29
26.92
ww
5.50
6.00
6.50
7.00
7.50
M1
eri
ng
.i n
32.30
32.12
31.96
31.80
31.64
σ
En
gin
e
4.05
4.10
4.15
4.20
4.25
M1
arn
σ
w.
Le
M1
26.62
26.36
26.15
25.98
25.80
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Gas Tables for Compressible Flow Calculations
70
TABLE 5.1
Oblique shocks in perfect gases
Wave angles for given deflection (γγ = 1.4, δ = 30°)
σ
M1
σ
2.22
2.24
2.26
2.28
2.30
2.82
2.84
2.86
2.88
2.90
54.50
54.15
53.85
53.55
53.30
4.05
4.10
4.15
4.20
4.25
45.05
44.85
44.64
44.46
44.30
2.32
2.34
2.36
2.38
2.40
64.69
64.70
64.71
2.92
2.94
2.96
2.98
3.00
53.00
52.73
52.50
52.25
52.00
4.30
4.35
4.40
4.45
4.50
44.13
44.00
43.83
43.70
43.55
2.42
2.44
2.46
2.48
2.50
64.72
64.73
64.75
64.77
64.78
3.05
3.10
3.15
3.20
3.25
51.50
50.80
50.50
50.00
49.60
4.55
4.60
4.65
4.70
4.75
43.40
43.30
43.15
43.00
42.90
2.52
2.54
2.56
2.58
2.60
64.30
62.00
60.95
60.10
59.35
3.30
3.35
3.40
3.45
3.50
49.15
48.80
48.40
48.10
47.75
4.80
4.85
4.90
4.95
5.00
42.75
42.67
42.50
42.45
42.35
58.70
58.15
57.62
57.15
56.70
3.55
3.60
3.65
3.70
3.75
47.45
47.15
46.90
46.60
46.35
5.50
6.00
6.50
7.00
7.50
41.47
40.80
40.30
39.85
39.50
56.26
55.88
55.50
55.10
54.80
3.80
3.85
3.90
3.95
4.00
46.10
45.87
45.65
45.40
45.21
8.00
8.50
9.00
9.50
10.00
39.23
39.00
38.80
38.67
38.50
2.72
2.74
2.76
2.78
2.80
arn
w.
Le
ww
2.62
2.64
2.66
2.68
2.70
eri
ng
.i n
M1
En
gin
e
σ
M1
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Oblique Shocks in Perfect Gases
71
TABLE 5.2
Oblique shocks in perfect gases (γγ = 1.4)
Upstream and downstream Mach numbers and deflection from
normal shock relations
σ
M1
1.05
1.10
1.15
1.20
1.25
60
60
60
60
60
1.212
1.270
1.328
1.385
1.443
1.30
1.35
1.40
1.45
1.50
60
60
60
60
60
1.501
1.559
1.616
1.674
1.732
1.55
1.60
1.65
1.70
1.75
60
60
60
60
60
1.80
1.85
1.90
1.95
2.00
60
60
60
60
60
δ
M2
0.953
0.912
0.875
0.842
0.812
1.124
1.100
1.081
1.065
1.053
11.189
12.780
14.290
15.720
17.072
0.786
0.762
0.739
0.719
0.701
1.044
1.038
1.033
1.031
1.029
1.789
1.847
1.905
1.963
2.021
18.348
19.553
20.688
21.758
22.766
0.684
0.668
0.654
0.641
0.628
1.0293
1.030
1.032
1.035
1.038
2.078
2.136
2.194
2.252
2.309
23.715
24.609
25.453
26.246
26.995
0.616
0.605
0.596
0.586
0.577
1.042
1.045
1.050
1.055
1.060
arn
En
gin
e
2.039
4.018
5.927
7.761
9.515
2.10
2.20
2.30
2.40
2.50
ww
w.
Le
My
eri
ng
.i n
Mx
60
60
60
60
60
2.425
2.540
2.656
2.771
2.887
28.368
29.591
30.685
31.664
32.543
0.561
0.547
0.534
0.523
0.513
1.070
1.081
1.091
1.102
1.112
2.60
2.70
2.80
2.90
3.00
60
60
60
60
60
3.002
3.117
3.233
3.348
3.464
33.334
34.049
34.696
35.283
35.817
0.504
0.495
0.488
0.481
0.475
1.123
1.133
1.142
1.151
1.160
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Gas Tables for Compressible Flow Calculations
72
TABLE 5.2
Oblique shocks in perfect gases (γγ = 1.4)
Mx
σ
M1
3.10
3.20
3.30
3.40
3.50
60
60
60
60
60
3.579
3.695
3.811
3.926
4.041
3.60
3.70
3.80
3.90
4.00
60
60
60
60
60
4.157
4.272
4.387
4.503
4.618
1.05
1.10
1.15
1.20
1.25
70
70
70
70
70
1.30
1.35
1.40
1.45
1.50
70
70
70
70
70
1.80
1.82
1.90
1.95
2.00
M2
36.305
36.750
37.158
37.533
37.878
0.469
0.464
0.459
0.455
0.451
1.168
1.176
1.184
1.191
1.198
38.196
38.490
38.762
39.015
39.249
0.447
0.444
0.441
0.438
0.435
1.205
1.211
1.217
1.222
1.227
1.531
3.050
4.551
6.027
7.473
0.953
0.912
0.875
0.842
0.813
1.025
0.991
0.962
0.937
0.916
1.383
1.437
1.489
1.543
1.596
8.884
10.258
11.591
12.881
14.127
0.786
0.762
0.739
0.719
0.701
0.897
0.882
0.868
0.857
0.847
70
70
70
70
70
1.649
1.703
1.756
1.809
1.862
15.328
16.483
17.592
18.656
19.676
0.684
0.668
0.654
0.641
0.628
0.838
0.831
0.825
0.820
0.816
70
70
70
70
70
1.916
1.968
2.022
2.075
2.128
20.652
21.586
22.478
23.331
24.145
0.616
0.606
0.596
0.586
0.577
0.813
0.809
0.807
0.806
0.805
En
gin
e
eri
ng
.i n
My
arn
1.117
1.171
1.224
1.277
1.330
w.
Le
ww
1.55
1.60
1.65
1.70
1.75
δ
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Oblique Shocks in Perfect Gases
73
TABLE 5.2
Oblique shocks in perfect gases (γγ = 1.4)
Mx
σ
M1
2.10
2.20
2.30
2.40
2.50
70
70
70
70
70
2.235
2.341
2.447
2.554
2.660
2.60
2.70
2.80
2.90
3.00
70
70
70
70
70
2.767
2.873
2.979
3.086
3.193
3.10
3.20
3.30
3.40
3.50
70
70
70
70
70
3.60
3.70
3.80
3.90
4.00
70
70
70
70
70
δ
M2
25.664
27.047
28.308
29.456
30.503
0.561
0.547
0.534
0.523
0.513
0.8031
0.8028
0.8035
0.8047
0.806
31.459
32.332
33.132
33.865
34.537
0.504
0.496
0.488
0.481
0.475
0.8087
0.811
0.814
0.816
0.819
3.299
3.405
3.512
3.618
3.725
35.156
35.725
36.251
36.736
37.185
0.469
0.464
0.459
0.455
0.451
0.822
0.825
0.827
0.830
0.833
3.831
3.937
4.044
4.150
4.257
37.602
37.988
38.347
38.682
38.993
0.447
0.444
0.441
0.438
0.435
0.835
0.837
0.839
0.842
0.844
1.05
1.10
1.15
1.20
1.25
ww
w.
Le
arn
En
gin
e
eri
ng
.i n
My
80
80
80
80
80
1.066
1.117
1.168
1.218
1.269
0.821
1.648
2.478
3.309
4.138
0.953
0.912
0.875
0.842
0.812
0.970
0.931
0.896
0.865
0.838
1.30
1.35
1.40
1.45
1.50
80
80
80
80
80
1.320
1.371
1.422
1.472
1.523
4.963
5.781
6.591
7.390
8.177
0.786
0.762
0.739
0.719
0.701
0.813
0.791
0.772
0.754
0.738
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Gas Tables for Compressible Flow Calculations
74
TABLE 5.2
Oblique shocks in perfect gases (γγ = 1.4)
Mx
σ
M1
1.55
1.60
1.65
1.70
1.75
80
80
80
80
80
1.574
1.625
1.675
1.726
1.777
1.80
1.85
1.90
1.95
2.00
80
80
80
80
80
1.828
1.878
1.929
1.980
2.031
2.10
2.20
2.30
2.40
2.50
80
80
80
80
80
2.60
2.70
2.80
2.90
3.00
80
80
80
80
80
δ
M2
0.684
0.668
0.654
0.641
0.628
0.723
0.710
0.698
0.687
0.677
12.587
13.263
13.921
14.561
15.183
0.616
0.605
0.595
0.586
0.577
0.668
0.659
0.652
0.644
0.638
2.132
2.234
2.335
2.437
2.538
16.373
17.491
18.541
19.525
20.445
0.561
0.547
0.534
0.523
0.513
0.626
0.617
0.608
0.601
0.595
2.640
2.741
2.843
2.945
3.046
21.306
22.110
22.862
23.564
24.220
0.504
0.496
0.488
0.481
0.475
0.589
0.585
0.581
0.578
0.575
arn
En
gin
e
eri
ng
.i n
8.950
9.710
10.454
11.182
11.893
3.10
3.20
3.30
3.40
3.50
ww
w.
Le
My
80
80
80
80
80
3.147
3.249
3.351
3.452
3.554
24.834
25.408
25.945
26.447
26.918
0.469
0.464
0.459
0.455
0.451
0.572
0.569
0.567
0.565
0.564
3.60
3.70
3.80
3.90
4.00
80
80
80
80
80
3.656
3.757
3.858
3.960
4.062
27.359
27.773
28.162
28.527
28.871
0.447
0.444
0.441
0.438
0.435
0.563
0.561
0.560
0.559
0.558
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Flow of Perfect Gases with Friction
75
TABLE 6.1
Flow of perfect gases with friction (Fanno flow, γ = 1.3)
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
0.02
0.04
0.06
0.08
0.10
53.617
26.806
17.868
13.398
10.716
0.021
0.043
0.064
0.086
0.107
1.150
1.150
1.150
1.149
1.148
29.268
14.644
9.775
7.342
5.885
23.324
11.679
7.805
5.874
4.720
1915.510
474.428
208.052
115.078
72.200
0.12
0.14
0.16
0.18
0.20
8.927
7.648
6.690
5.943
5.346
0.128
0.150
0.171
0.193
0.214
1.147
1.146
1.145
1.144
1.143
4.917
4.228
3.712
3.312
2.994
3.954
3.410
3.005
2.693
2.445
49.020
35.120
26.157
20.058
15.730
0.22
0.24
0.26
0.28
0.30
4.856
4.450
4.104
3.807
3.551
0.235
0.256
0.277
0.298
0.319
1.142
1.140
1.138
1.136
1.134
2.735
2.520
2.340
2.186
2.054
2.245
2.071
1.941
1.825
1.725
12.562
10.176
8.341
6.904
5.759
0.32
0.34
0.36
0.38
0.40
3.326
3.127
2.950
2.792
2.649
0.341
0.362
0.382
0.403
0.424
1.132
1.130
1.128
1.126
1.123
1.939
1.839
1.750
1.672
1.602
1.639
1.564
1.499
1.442
1.391
4.837
4.085
3.465
2.950
2.520
0.42
0.44
0.46
0.48
0.50
2.520
2.403
2.295
2.196
2.106
0.445
0.465
0.485
0.506
0.526
1.120
1.118
1.115
1.111
1.108
1.540
1.484
1.434
1.389
1.348
1.347
1.308
1.272
1.241
1.213
2.157
1.850
1.588
1.364
1.172
2.022
1.944
1.872
1.804
1.741
0.547
0.567
0.587
0.607
0.627
1.105
1.102
1.098
1.095
1.091
1.311
1.277
1.246
1.219
1.193
1.188
1.166
1.145
1.127
1.111
1.007
0.864
0.741
0.634
0.541
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
76
TABLE 6.1
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
0.62
0.64
0.66
0.68
0.70
1.682
1.626
1.574
1.525
1.479
0.646
0.667
0.686
0.705
0.725
1.087
1.083
1.079
1.075
1.071
1.170
1.149
1.130
1.113
1.097
1.097
1.084
1.072
1.062
1.052
0.460
0.390
0.329
0.276
0.231
0.72
0.74
0.76
0.78
0.80
1.435
1.393
1.354
1.316
1.280
0.744
0.763
0.782
0.800
0.820
1.067
1.063
1.058
1.054
1.049
1.083
1.070
1.059
1.048
1.039
1.044
1.037
1.030
1.025
1.020
0.191
0.157
0.127
0.102
0.081
0.82
0.84
0.86
0.88
0.90
1.246
1.214
1.183
1.153
1.125
0.838
0.857
0.875
0.893
0.911
1.045
1.040
1.035
1.030
1.025
1.032
1.025
1.019
1.013
1.009
1.016
1.012
1.009
1.006
1.004
0.062
0.047
0.035
0.024
0.016
0.92
0.94
0.96
0.98
1.00
1.098
1.072
1.047
1.023
1.000
0.929
0.947
0.965
0.983
1.000
1.020
1.015
1.010
1.005
1.000
1.006
1.003
1.001
1.0004
1.000
1.003
1.002
1.001
1.0002
1.000
0.010
0.005
0.0023
0.0005
0.000
1.02
1.04
1.06
1.08
1.10
0.978
0.956
0.936
0.916
0.897
1.017
1.035
1.051
1.068
1.085
0.995
0.989
0.984
0.978
0.973
1.0003
1.0014
1.003
1.005
1.008
1.0001
1.0006
1.001
1.002
1.003
0.0005
0.0020
0.0043
0.0074
0.0112
1.12
1.14
1.16
1.18
1.20
0.878
0.861
0.843
0.827
0.810
1.102
1.118
1.135
1.151
1.167
0.968
0.962
0.957
0.951
0.946
1.012
1.016
1.021
1.026
1.032
1.005
1.006
1.008
1.010
1.012
0.015
0.020
0.026
0.032
0.0382
w.
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Flow of perfect gases with friction (Fanno flow, γ = 1.3)
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Flow of Perfect Gases with Friction
77
TABLE 6.1
Flow of perfect gases with friction (Fanno flow, γ = 1.3)
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
1.22
1.24
1.26
1.28
1.30
0.795
0.780
0.765
0.751
0.737
1.183
1.198
1.214
1.230
1.245
0.940
0.934
0.928
0.923
0.917
1.038
1.046
1.053
1.062
1.070
1.014
1.017
1.019
1.022
1.024
0.045
0.052
0.059
0.066
0.074
1.32
1.34
1.36
1.38
1.40
0.723
0.710
0.697
0.685
0.673
1.260
1.275
1.290
1.305
1.320
0.912
0.906
0.900
0.894
0.889
1.080
1.089
1.100
1.111
1.123
1.027
1.030
1.033
1.036
1.039
0.082
0.089
0.098
0.106
0.114
1.42
1.44
1.46
1.48
1.50
0.662
0.650
0.639
0.629
0.618
1.334
1.349
1.363
1.377
1.391
0.883
0.877
0.871
0.866
0.860
1.135
1.147
1.160
1.175
1.189
1.042
1.045
1.048
1.052
1.055
0.123
0.131
0.139
0.148
0.156
1.52
1.54
1.56
1.58
1.60
0.608
0.598
0.588
0.579
0.569
1.404
1.418
1.432
1.445
1.458
0.854
0.848
0.842
0.837
0.831
1.205
1.220
1.237
1.254
1.271
1.058
1.062
1.065
1.068
1.072
0.165
0.173
0.182
0.190
0.199
1.62
1.64
1.66
1.68
1.70
0.561
0.552
0.543
0.535
0.527
1.472
1.485
1.497
1.510
1.523
0.825
0.819
0.814
0.808
0.802
1.290
1.308
1.328
1.348
1.369
1.076
1.079
1.083
1.086
1.089
0.207
0.216
0.224
0.233
0.241
0.519
0.511
0.503
0.496
0.488
1.535
1.547
1.559
1.572
1.584
0.796
0.791
0.785
0.780
0.774
1.391
1.413
1.436
1.459
l.484
1.093
1.097
1.100
1.104
1.108
0.249
0.257
0.265
0.273
0.281
1.72
1.74
1.76
1.78
1.80
En
gin
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
78
TABLE 6.1
Flow of perfect gases with friction (Fanno flow, γ = 1.3)
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
1.82
1.84
1.86
1.88
1.90
0.482
0.475
0.467
0.461
0.455
1.595
1.607
1.618
1.630
1.641
0.768
0.763
0.757
0.752
0.746
1.509
1.535
1.562
1.590
1.618
1.111
1.115
1.118
1.122
1.125
0.289
0.297
0.307
0.313
0.320
1.92
1.94
1.96
1.98
2.00
0.448
0.442
0.436
0.429
0.424
1.652
1.663
1.674
1.684
1.696
0.741
0.735
0.729
0.724
0.719
1.647
1.678
1.708
1.740
1.773
1.129
1.132
1.136
1.139
1.143
0.328
0.335
0.343
0.350
0.357
2.02
2.04
2.06
2.08
2.10
0.418
0.412
0.407
0.402
0.396
1.706
1.716
1.727
1.737
1.747
0.713
0.708
0.703
0.697
0.692
1.807
1.842
1.878
1.914
1.951
1.146
1.150
1.153
1.156
1.160
0.364
0.372
0.378
0.386
0.393
2.12
2.14
2.16
2.18
2.20
0.391
0.386
0.381
0.376
0.371
1.757
1.767
1.777
1.786
1.796
0.687
0.682
0.676
0.671
0.667
1.990
2.030
2.070
2.113
2.156
1.163
1.167
1.169
1.173
1.176
0.399
0.406
0.412
0.419
0.426
2.22
2.24
2.26
2.28
2.30
0.366
0.362
0.357
0.353
0.348
1.805
1.815
1.824
1.833
1.842
0.661
0.656
0.651
0.646
0.641
2.200
2.245
2.292
2.339
2.388
1.179
1.183
1.186
1.189
1.192
0.432
0.438
0.444
0.451
0.457
0.344
0.340
0.335
0.331
0.327
1.851
1.859
1.868
1.877
1.885
0.636
0.631
0.627
0.622
0.617
2.438
2.490
2.543
2.598
2.654
1.196
1.199
1.202
1.205
1.209
0.463
0.469
0.474
0.480
0.486
2.32
2.34
2.36
2.38
2.40
En
gin
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Friction
79
TABLE 6.1
Flow of perfect gases with friction (Fanno flow, γ = 1.3)
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
2.42
2.44
2.46
2.48
2.50
0.323
0.319
0.316
0.312
0.308
1.893
1.902
1.910
1.918
1.926
0.612
0.608
0.603
0.598
0.594
2.710
2.770
2.829
2.891
2.954
1.211
1.214
1.217
1.220
1.223
0.492
0.497
0.503
0.508
0.514
2.52
2.54
2.56
2.58
2.60
0.305
0.300
0.297
0.294
0.291
1.934
1.942
1.950
1.957
1.965
0.589
0.585
0.580
0.575
0.571
3.019
3.086
3.154
3.224
3.295
1.226
1.228
1.231
1.234
1.237
0.519
0.524
0.529
0.534
0.539
2.62
2.64
2.66
2.68
2.70
0.287
0.284
0.280
0.278
0.275
1.972
1.980
1.987
1.994
2.001
0.567
0.562
0.558
0.554
0.549
3.369
3.443
3.521
3.601
3.681
1.240
1.243
1.245
1.248
1.250
0.544
0.549
0.554
0.559
0.564
2.72
2.74
2.76
2.78
2.80
0.271
0.268
0.265
0.263
0.260
2.008
2.015
2.022
2.029
2.036
0.545
0.541
0.537
0.533
0.529
3.765
3.849
3.936
4.025
4.116
1.253
1.256
1.258
1.261
1.263
0.568
0.573
0.578
0.582
0.586
2.82
2.84
2.86
2.88
2.90
0.257
0.254
0.251
0.248
0.246
2.042
2.048
2.055
2.062
2.068
0.525
0.520
0.516
0.512
0.508
4.210
4.306
4.404
4.505
4.607
1.266
1.268
1.271
1.273
1.276
0.591
0.595
0.599
0.604
0.608
0.243
0.241
0.238
0.235
0.233
2.074
2.080
2.097
2.093
2.099
0.505
0.500
0.497
0.493
0.489
4.713
4.820
4.931
5.045
5.160
1.278
1.281
1.283
1.285
1.288
0.611
0.616
0.619
0.624
0.628
2.90
2.94
2.96
2.98
3.00
En
gin
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
80
TABLE 6.1
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
3.10
3.20
3.30
3.40
3.50
0.221
0.210
0.200
0.191
0.182
2.127
2.155
2.181
2.205
2.228
0.471
0.453
0.437
0.421
0.405
5.781
6.477
7.259
8.133
9.110
1.299
1.310
1.319
1.330
1.338
0.647
0.664
0.681
0.697
0.711
3.60
3.70
3.80
3.90
4.00
0.174
0.166
0.159
0.152
0.145
2.250
2.271
2.290
2.308
2.326
0.391
0.377
0.363
0.351
0.338
10.200
11.420
12.790
14.274
15.940
1.347
1.356
1.363
1.371
1.378
0.725
0.738
0.751
0.762
0.773
4.10
4.20
4.30
4.40
4.50
0.139
0.134
0.128
0.123
0.118
2.343
2.358
2.374
2.388
2.402
0.327
0.315
0.305
0.294
0.285
17.796
19.848
22.116
24.622
27.390
1.385
1.391
1.398
1.403
1.409
0.783
0.792
0.802
0.811
0.819
4.60
4.70
4.80
4.90
5.00
0.114
0.110
0.105
0.102
0.098
2.415
2.427
2.438
2.449
2.460
0.276
0.267
0.258
0.250
0.242
30.433
33.786
37.472
41.520
45.950
1.414
1.420
1.424
1.429
1.433
0.827
0.834
0.841
0.848
0.854
6.00
7.00
8.00
9.00
10.00
2.543
2.598
2.635
2.662
2.681
0.179
0.138
0.108
0.088
0.072
1.468
1.491
1.507
1.519
1.527
0.904
0.936
0.957
0.972
0.983
En
gin
e
arn
w.
Le
0.071
0.053
0.041
0.033
0.0277
eri
ng
.i n
M
ww
Flow of perfect gases with friction (Fanno flow, γ = 1.3)
120.1
285.3
625.2
1275.0
2438.0
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Flow of Perfect Gases with Friction
81
TABLE 6.2
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
0.02
0.04
0.06
0.08
0.10
54.770
27.382
18.251
13.684
10.943
0.022
0.044
0.066
0.087
0.109
1.199
1.199
1.199
1.198
1.197
28.942
14.482
9.666
7.262
5.822
22.834
11.435
7.643
5.753
4.624
1778.450
440.352
193.031
106.718
66.922
0.12
0.14
0.16
0.18
0.20
9.116
7.809
6.830
6.067
5.455
0.131
0.153
0.175
0.196
0.218
1.196
1.195
1.194
1.192
1.190
4.864
4.183
3.673
3.278
2.964
3.875
3.343
2.950
2.643
2.400
45.407
32.511
24.197
18.543
14.533
0.22
0.24
0.26
0.28
0.30
4.955
4.538
4.185
3.882
3.619
0.239
0.261
0.283
0.304
0.326
1.188
1.186
1.184
1.181
1.178
2.708
2.496
2.317
2.166
2.035
2.205
2.043
1.909
1.795
1.698
11.596
9.387
7.687
6.357
5.299
0.32
0.34
0.36
0.38
0.40
3.388
3.185
3.004
2.842
2.695
0.347
0.368
0.389
0.410
0.431
1.176
1.172
1.169
1.166
1.163
1.922
1.823
1.736
1.658
1.590
1.615
1.542
1.479
1.423
1.375
4.447
3.752
3.180
2.705
2.308
0.42
0.44
0.46
0.48
0.50
2.563
2.442
2.333
2.231
2.138
0.452
0.473
0.494
0.514
0.534
1.159
1.155
1.151
1.147
1.143
1.529
1.474
1.425
1.380
1.340
1.332
1.294
1.260
1.230
1.203
1.974
1.692
1.451
1.245
1.069
0.52
0.54
0.56
0.58
0.60
2.052
1.972
1.897
1.828
1.763
0.555
0.575
0.595
0.615
0.635
1.138
1.134
1.129
1.124
1.119
1.303
1.270
1.240
1.213
1.188
1.179
1.157
1.138
1.120
1.105
0.917
0.787
0.674
0.575
0.491
w.
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En
gin
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eri
ng
.i n
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ww
Flow of perfect gases with friction (Fanno flow, γ = 1.4)
4 f Lmax D
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Gas Tables for Compressible Flow Calculations
82
TABLE 6.2
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
0.62
0.64
0.66
0.68
0.70
1.703
1.645
1.592
1.541
1.493
0.654
0.674
0.693
0.713
0.732
1.114
1.109
1.104
1.098
1.093
1.166
1.145
1.127
1.109
1.094
1.092
1.079
1.068
1.058
1.049
0.417
0.353
0.298
0.249
0.208
0.72
0.74
0.76
0.78
0.80
1.448
1.405
1.365
1.326
1.289
0.751
0.770
0.788
0.807
0.825
1.087
1.082
1.076
1.069
1.064
1.081
1.068
1.057
1.047
1.038
1.041
1.035
1.028
1.023
1.018
0.172
0.141
0.114
0.092
0.073
0.82
0.84
0.86
0.88
0.90
1.254
1.221
1.189
1.158
1.129
0.843
0.861
0.879
0.897
0.915
1.058
1.051
1.045
1.039
1.003
1.031
1.024
1.018
1.013
1.009
1.015
1.011
1.008
1.006
1.004
0.056
0.042
0.031
0.022
0.015
0.92
0.94
0.96
0.98
1.00
1.101
1.074
1.048
1.024
1.000
0.932
0.949
0.966
0.983
1.000
1.026
1.020
1.013
1.006
1.000
1.006
1.003
1.001
1.0003
1.000
1.003
1.001
1.0006
1.0001
1.000
0.0089
0.005
0.0020
0.0005
0.000
1.02
1.04
1.06
1.08
1.10
0.977
0.955
0.933
0.913
0.894
1.016
1.033
1.049
1.065
1.081
0.993
0.986
0.979
0.973
0.966
1.0003
1.0013
1.003
1.005
1.008
1.0001
1.0005
1.0012
1.002
1.003
0.00046
0.0018
0.004
0.0066
0.0099
1.12
1.14
1.16
1.18
1.20
0.875
0.856
0.838
0.821
0.804
1.097
1.113
1.128
1.143
1.158
0.959
0.952
0.945
0.938
0.932
1.011
1.015
1.020
1.025
1.030
1.004
1.006
1.007
1.009
1.011
0.0138
0.0182
0.023
0.028
0.034
w.
Le
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En
gin
e
eri
ng
.i n
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ww
Flow of perfect gases with friction (Fanno flow, γ = 1.4)
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Friction
83
TABLE 6.2
p/p*
c/c* = ρ*/ρ
T/T*
p0/p0*
F/F*
1.22
1.24
1.26
1.28
1.30
0.788
0.773
0.757
0.743
0.728
1.173
1.188
1.202
1.217
1.231
0.925
0.918
0.911
0.903
0.897
1.037
1.043
1.050
1.058
1.066
1.013
1.015
1.017
1.019
1.022
0.039
0.045
0.0517
0.0582
0.065
1.32
1.34
1.36
1.38
1.40
0.715
0.701
0.688
0.676
0.663
1.245
1.259
1.273
1.286
1.300
0.889
0.883
0.876
0.869
0.862
1.075
1.084
1.094
1.104
1.115
1.024
1.027
1.029
1.032
1.035
0.0716
0.0785
0.0855
0.093
0.099
1.42
1.44
1.46
1.48
1.50
0.651
0.640
0.628
0.617
0.606
1.313
1.326
1.339
1.352
1.364
0.855
0.848
0.841
0.834
0.828
1.126
1.138
1.150
1.163
1.176
1.037
1.040
1.043
1.046
1.048
0.107
0.114
0.121
0.128
0.136
1.52
1.54
1.56
1.58
1.60
0.596
0.586
0.576
0.566
0.557
1.377
1.389
1.401
1.413
1.425
0.821
0.814
0.807
0.800
0.794
1.189
1.204
1.219
1.234
1.250
1.052
1.055
1.057
1.061
1.063
0.143
0.151
0.158
0.165
0.172
1.62
1.64
1.66
1.68
1.70
0.547
0.538
0.529
0.521
0.513
1.437
1.448
1.460
1.471
1.482
0.787
0.780
0.774
0.767
0.760
1.267
1.284
1.301
1.319
1.340
1.067
1.069
1.073
1.075
1.078
0.179
0.187
0.194
0.201
0.208
1.72
1.74
1.76
1.78
1.80
0.505
0.496
0.489
0.481
0.474
1.493
1.504
1.515
1.525
1.536
0.754
0.747
0.741
0.735
0.728
1.357
1.376
1.397
1.418
1.439
1.082
1.085
1.088
1.091
1.093
0.215
0.222
0.228
0.235
0.242
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.i n
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Flow of perfect gases with friction (Fanno flow, γ = 1.4)
4 f Lmax D
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Gas Tables for Compressible Flow Calculations
84
TABLE 6.2
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
1.82
1.84
1.86
1.88
1.90
0.467
0.459
0.453
0.446
0.439
1.546
1.556
1.566
1.576
1.586
0.722
0.716
0.709
0.703
0.697
1.461
1.484
1.507
1.530
1.555
1.096
1.099
1.102
1.105
1.108
0.248
0.255
0.262
0.268
0.274
1.92
1.94
1.96
1.99
2.00
0.433
0.426
0.420
0.414
0.408
1.596
1.605
1.615
1.624
1.633
0.691
0.685
0.678
0.673
0.667
1.580
1.610
1.633
1.660
1.687
1.111
1.114
1.117
1.120
1.123
0.281
0.287
0.293
0.299
0.305
2.02
2.04
2.06
2.08
2.10
0.402
0.397
0.391
0.386
0.380
1.642
1.651
1.659
1.668
1.677
0.661
0.655
0.649
0.643
0.637
1.716
1.747
1.775
1.806
1.837
1.126
1.128
1.131
1.134
1.137
0.311
0.317
0.323
0.328
0.334
2.12
2.14
2.16
2.18
2.20
0.375
0.369
0.365
0.359
0.355
1.685
1.694
1.702
1.710
1.718
0.632
0.623
0.621
0.615
0.609
1.870
1.902
1.935
1.970
2.005
1.139
1.142
1.145
1.147
1.150
0.339
0.345
0.350
0.356
0.361
2.22
2.24
2.26
2.28
2.30
0.350
0.346
0.341
0.336
0.332
1.726
1.733
1.741
1.748
1.756
0.604
0.598
0.594
0.588
0.583
2.041
2.078
2.115
2.154
2.193
1.153
1.155
1.158
1.160
1.163
0.366
0.371
0.376
0.381
0.386
2.32
2.34
2.36
2.38
2.40
0.327
0.323
0.319
0.315
0.311
1.764
1.771
1.778
1.785
1.792
0.578
0.573
0.567
0.563
0.557
2.233
2.274
2.316
2.360
2.403
1.165
1.168
1.170
1.173
1.175
0.391
0.396
0.400
0.405
0.409
w.
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.i n
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ww
Flow of perfect gases with friction (Fanno flow, γ = 1.4)
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Friction
85
TABLE 6.2
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
2.42
2.44
2.46
2.48
2.50
0.307
0.303
0.299
0.296
0.292
1.799
1.806
1.813
1.819
1.826
0.553
0.548
0.543
0.538
0.533
2.448
2.494
2.540
2.588
2.637
1.178
1.179
1.182
1.185
1.187
0.414
0.419
0.423
0.427
0.432
2.52
2.54
2.56
2.58
2.60
0.289
0.285
0.281
0.278
0.275
1.832
1.838
1.845
1.851
1.857
0.528
0.524
0.519
0.515
0.510
2.687
2.737
2.789
2.842
2.896
1.189
1.191
1.193
1.195
1.198
0.436
0.440
0.445
0.448
0.453
2.62
2.64
2.66
2.68
2.70
0.271
0.268
0.265
0.262
0..258
1.863
1.869
1.875
1.881
1.886
0.506
0.501
0.497
0.493
0.488
2.951
3.007
3.065
3.123
3.183
1.200
1.202
1.204
1.206
1.208
0.457
0.460
0.464
0.468
0.472
2.72
2.74
2.76
2.79
2.80
0.256
0.253
0.250
0.247
0.244
1.892
1.898
1.903
1.908
1.914
0.484
0.479
0.476
0.471
0.467
3.244
3.306
3.370
3.435
3.500
1.210
1.212
1.214
1.216
1.218
0.476
0.479
0.483
0.486
0.489
2.82
2.84
2.86
2.88
2.90
0.241
0.238
0.236
0.233
0.231
1.919
1.925
1.929
1.935
1.940
0.463
0.459
0.455
0.451
0.447
3.567
3.636
3.706
3.780
3.850
1.220
1.222
1.224
1.226
1.228
0.493
0.497
0.499
0.503
0.506
2.92
2.94
2.96
2.98
3.00
0.228
0.226
0.223
0.220
0.218
1.945
1.949
1.954
1.959
1.964
0.443
0.439
0.436
0.432
0.428
3.924
4.000
4.076
4.155
4.235
1.229
1.231
1.233
1.235
1.237
0.509
0.513
0.516
0.519
0.522
w.
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gin
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eri
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.i n
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ww
Flow of perfect gases with friction (Fanno flow, γ = 1.4)
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
86
TABLE 6.2
Flow of perfect gases with friction (Fanno flow, γ = 1.4)
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
3.10
3.20
3.30
3.40
3.50
0.207
0.196
0.186
0.177
0.168
1.987
2.008
2.028
2.046
2.064
0.411
0.394
0.377
0.362
0.348
4.657
5.121
5.628
6.184
6.789
1.245
1.253
1.260
1.267
1..274
0.537
0.550
0.563
0.575
0.586
3.60
3.70
3.80
3.90
4.00
0.160
0.153
0.146
0.139
0.134
2.081
2.096
2.111
2.125
2.138
0.334
0.321
0.308
0.297
0.286
7.450
8.169
8.951
9.800
10.720
1.281
1.287
1.293
1.298
1.303
0.597
0.607
0.616
0.625
0.633
4.10
4.20
4.30
4.40
4.50
0.128
0.123
0.117
0.113
0.108
2.150
2.162
2.173
2.184
2.194
0.275
0.265
0.255
0.246
0.237
11.715
12.792
13.955
15.210
16.562
1.308
1.312
1.317
1.321
1.325
0.641
0.648
0.655
0.662
0.668
4.60
4.70
4.80
4.90
5.00
0.104
0.100
0.096
0.093
0.089
2.203
2.212
2.220
2.228
2.236
0.229
0.221
0.214
0.207
0.200
18.018
19.583
21.264
23.070
25.000
1.330
1.332
1.335
1.339
1.342
0.673
0.678
0.684
0.689
0.694
6.00
7.00
8.00
9.00
10.00
0.064
0.047
0.037
0.029
0.024
2.295
2.333
2.359
2.377
2.391
0.146
0.111
0.087
0.069
0.057
53.180
104.14
190.11
327.19
535.94
1.366
1.381
1.392
1.399
1.404
0.730
0.753
0.768
0.779
0.787
En
gin
e
arn
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ng
.i n
M
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Friction
87
TABLE 6.3
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
0.02
0.04
0.06
0.08
0.10
57.753
28.862
19.235
14.420
11.535
0.023
0.046
0.069
0.092
0.115
1.333
1.332
1.332
1.331
1.330
28.132
14.078
9.397
7.061
5.661
21.662
10.851
7.256
5.465
4.392
1493.072
369.405
161.762
89.320
55.830
0.12
0.14
0.16
0.18
0.20
9.600
8.220
7.187
6.381
5.739
0.138
0.161
0.184
0.207
0.229
1.327
1.325
1.322
1.319
1.317
4.733
4.071
3.576
3.193
2.887
3.686
3.183
2.810
2.532
2.293
37.892
27.086
20.125
15.393
12.110
0.22
0.24
0.26
0.28
0.30
5.207
4.766
4.392
4.071
3.795
0.252
0.275
0.297
0.319
0.342
1.313
1.308
1.304
1.300
1.296
2.640
2.435
2.262
2.115
1.989
2.110
1.959
1.833
1.726
1.635
9.589
7.747
6.332
5.225
4.337
0.32
0.34
0.36
0.38
0.40
3.549
3.333
3.141
2.968
2.814
0.364
0.385
0.407
0.429
0.450
1.289
1.284
1.278
1.273
1.267
1.880
1.785
1.700
1.626
1.560
1.558
1.490
1.432
1.381
1.336
3.639
3.063
2.591
2.200
1.868
0.42
0.44
0.46
0.48
0.50
2.672
2.545
2.427
2.318
2.220
0.472
0.493
0.514
0.534
0.555
1.260
1.253
1.245
1.238
1.232
1.501
1.450
1.402
1.359
1.320
1.297
1.262
1.231
1.203
1.178
1.597
1.365
1.168
1.0005
0.855
0.52
0.54
0.56
0.58
0.60
2.127
2.042
1.962
1.888
1.819
0.575
0.596
0.616
0.635
0.655
1.223
1.215
1.807
1.200
1.191
1.286
1.255
1.225
1.200
1.176
1.157
1.138
1.120
1.105
1.091
0.734
0.628
0.536
0.457
0.388
w.
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En
gin
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ng
.i n
M
ww
Flow of perfect gases with friction (Fanno flow, γ = 1.67)
4 f Lmax D
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
88
TABLE 6.3
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
0.62
0.64
0.66
0.68
0.70
1.754
1.693
1.635
1.581
1.530
0.674
0.693
0.712
0.731
0.750
1.182
1.173
1.165
1.155
1.146
1.155
1.135
1.118
1.102
1.087
1.079
1.068
1.058
1.050
1.042
0.329
0.278
0.234
0.196
0.163
0.72
0.74
0.76
0.78
0.80
1.481
1.435
1.391
1.350
1.311
0.768
0.786
0.804
0.821
0.839
1.137
1.128
1.118
1.108
1.099
1.075
1.063
1.053
1.043
1.035
1.035
1.029
1.024
1.019
1.016
0.134
0.110
0.089
0.071
0.056
0.82
0.84
0.86
0.88
0.90
1.273
1.237
1.203
1.170
1.139
0.856
0.873
0.889
0.906
0.922
1.089
1.079
1.070
1.060
1.050
1.028
1.022
1.016
1.012
1.008
1.012
1.010
1.007
1.005
1.003
0.043
0.0325
0.0238
0.0167
0.011
0.92
0.94
0.96
0.98
1.00
1.108
1.080
1.052
1.026
1.000
0.938
0.954
0.969
0.985
1.000
1.040
1.030
1.020
1.010
1.000
1.005
1.003
1.0012
1.0003
1.000
1.002
1.001
1.0005
1.0001
1.000
0.007
0.0037
0.00156
0.00037
0.000
1.02
1.04
1.06
1.08
1.10
0.975
0.952
0.929
0.907
0.886
1.015
1.029
1.044
1.058
1.072
0.990
0.980
0.970
0.960
0.950
1.0003
1.0012
1.0026
1.005
1.007
1.0001
1.0004
1.001
1.0016
1.002
0.00035
0.0013
0.0029
0.005
0.0074
1.12
1.14
1.16
1.18
1.20
0.866
0.846
0.827
0.809
0.791
1.086
1.099
1.113
1.126
1.139
0.940
0.930
0.920
0.911
0.900
1.010
1.014
1.018
1.022
1.027
1.0034
1.0045
1.006
1.007
1.008
0.010
0.0135
0.017
0.021
0.025
w.
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arn
En
gin
e
eri
ng
.i n
M
ww
Flow of perfect gases with friction (Fanno flow, γ = 1.67)
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Friction
89
TABLE 6.3
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
1.22
1.24
1.26
1.28
1.30
0.774
0.757
0.741
0.726
0.710
1.151
1.164
1.176
1.188
1.200
0.891
0.882
0.872
0.862
0.852
1.032
1.038
1.044
1.051
1.057
1.010
1.012
1.013
1.015
1.017
0.0291
0.0335
0.038
0.043
0.047
J.32
1.34
1.36
1.38
1.40
0.696
0.682
0.668
0.654
0.641
1.211
1.223
1.235
1.246
1.257
0.843
0.834
0.825
0.816
0.806
1.065
1.073
1.081
1.089
1.098
1.019
1.021
1.022
1.024
1.026
0.052
0.057
0.062
0.067
0.072
1.42
1.44
1.46
1.48
1.50
0.629
0.616
0.605
0.593
0.582
1.268
1.278
1.288
1.298
1.309
0.797
0.788
0.780
0.771
0.761
1.108
1.117
1.127
1.138
1.148
1.028
1.030
1.032
1.035
1.036
0.078
0.083
0.088
0.093
0.0975
1.52
1.54
1.56
1.58
1.60
0.571
0.560
0.550
0.540
0.530
1.318
1.328
1.338
1.347
1.356
0.753
0.745
0.736
0.728
0.718
1.160
1.171
1.183
1.195
1.207
1.039
1.041
1.043
1.045
1.047
0.103
0.108
0.113
0.118
0.123
1.62
1.64
1.66
1.68
1.70
0.521
0.511
0.502
0.493
0.485
1.365
1.374
1.383
1.391
1.400
0.711
0.703
0.695
0.687
0.678
1.220
1.234
1.250
1.261
1.275
1.049
1.051
1.053
1.056
1.057
0.128
0.133
0.138
0.142
0.146
1.72
1.74
1.76
1.78
1.80
0.476
0.468
0.460
0.452
0.445
1.408
1.416
1.425
1.432
1.440
0.671
0.664
0.656
0.648
0.640
1.290
1.305
1.320
1.336
1.351
1.060
1.0615
1.0635
1.065
1.067
0.152
0.156
0.161
0.165
0.169
w.
Le
arn
En
gin
e
eri
ng
.i n
M
ww
Flow of perfect gases with friction (Fanno flow, γ = 1.67)
4 f Lmax D
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Gas Tables for Compressible Flow Calculations
90
TABLE 6.3
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
1.82
1.84
1.86
1.88
1.90
0.437
0.430
0.423
0.416
0.409
1.448
1.455
1.463
1.469
1.477
0.634
0.626
0.619
0.612
0.604
1.370
1.385
1.402
1.419
1.436
1.070
1.0715
1.073
1.075
1.077
0.174
0.178
0.183
0.187
0.191
1.92
1.94
1.96
1.98
2.00
0.403
0.396
0.390
0.384
0.378
1.484
1.491
1.497
1.504
1.510
0.598
0.591
0.585
0.578
0.571
1.455
1.474
1.492
1.511
1.530
1.079
1.081
1.083
1.085
1.086
0.195
0.199
0.203
0.207
0.211
2.02
2.04
2.06
2.08
2.10
0.372
0.366
0.361
0.355
0.350
1.517
1.523
1.530
1.535
1.541
0.565
0.558
0.552
0.545
0.539
1.551
1.571
1.592
1.613
1.632
1.088
1.090
1.092
1.094
1.095
0.215
0.219
0.222
0.226
0.229
2.12
2.14
2.16
2.18
2.20
0.345
0.339
0.335
0.329
0.324
1.547
1.553
1.559
1.565
1.570
0.534
0.527
0.522
0.516
0.509
1.656
1.678
1.700
1.723
1.744
1.097
1.099
1.101
1.102
1.104
0.233
0.237
0.240
0.244
0.246
2.22
2.24
2.26
2.28
2.30
0.320
0.315
0.311
0.306
0.302
1.575
1.581
1.586
1.591
1.596
0.505
0.499
0.493
0.487
0.482
1.770
1.793
1.818
1.842
1.865
1.106
1.107
1.108
1.110
1.111
0.250
0.254
0.257
0.259
0.262
2.32
2.34
2.36
2.38
2.40
0.298
0.294
0.289
0.285
0.281
1.601
1.606
1.611
1.615
1.620
0.477
0.472
0.467
0.461
0.456
1.893
1.920
1.945
1.971
1.995
1.113
1.115
1.116
1.118
1.119
0.265
0.269
0.272
0.275
0.277
w.
Le
arn
En
gin
e
eri
ng
.i n
M
ww
Flow of perfect gases with friction (Fanno flow, γ = 1.67)
4 f Lmax D
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Flow of Perfect Gases with Friction
91
TABLE 6.3
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
2.42
2.44
2.46
2.48
2.50
0.278
0.274
0.270
0.267
0.263
1.625
1.629
1.634
1.638
1.642
0.452
0.446
0.442
0.437
0.432
2.025
2.053
2.081
2.110
2.135
1.121
1.122
1.123
1.125
1.126
0.280
0.283
0.286
0.288
0.290
2.50
2.54
2.56
2.58
2.60
0.260
0.256
0.253
0.249
0.246
1.646
1.651
1.655
1.658
1.663
0.428
0.423
0.418
0.414
0.409
2.168
2.198
2.228
2.260
2.285
1.127
1.129
1.130
1.131
1.132
0.294
0.296
0.299
0.301
0.303
2.62
2.64
2.66
2.68
2.70
0.243
0.240
0.236
0.234
0.231
1.667
1.670
1.674
1.678
1.682
0.405
0.401
0.397
0.393
0.388
2.321
2.352
2.385
2.417
2.445
1.134
1.135
1.136
1.1375
1.138
0.306
0.308
0.311
0.313
0.314
2.72
2.74
2.76
2.78
2.80
0.228
0.225
0.222
0.219
0.217
1.685
1.688
1.692
1.694
1.699
0.385
0.381
0.377
0.373
0.368
2.484
2.518
2.552
2.587
2.616
1.139
1.141
1.142
1.143
1.144
0.317
0.319
0.322
0.324
0.325
2.82
2.84
2.86
2.88
2.90
0.214
0.211
0.209
0.207
0.204
1.702
1.705
1.709
1.712
1.715
0.365
0.361
0.358
0.354
0.350
2.658
2.694
2.730
2.767
2.797
1.145
1.146
1.148
1.1485
1.149
0.328
0.330
0.332
0.334
0.335
2.92
2.94
2.96
2.98
3.00
0.202
0.199
0.197
0.195
0.192
1.718
1.721
1.724
1.727
1.730
0.347
0.343
0.340
0.337
0.333
2.843
2.881
2.920
2.960
2.990
1.150
1.152
1.153
1.1537
1.154
0.338
0.340
0.342
0.343
0.344
w.
Le
arn
En
gin
e
eri
ng
.i n
M
ww
Flow of perfect gases with friction (Fanno flow, γ = 1.67)
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Gas Tables for Compressible Flow Calculations
92
TABLE 6.3
Flow of perfect gases with friction (γγ = 1.67)
p/p*
c/c* = ρ*/ρ
T/T*
p0 /p0*
F/F*
4 f Lmax D
3.10
3.20
3.30
3.40
3.50
0.182
0.172
0.163
0.154
0.146
1.744
1.756
1.768
1.780
1.790
0.317
0.302
0.288
0.275
0.262
3.205
3.423
3.653
3.895
4.134
1.159
1.164
1.168
1.172
1.174
0.354
0.362
0.369
0.376
0.381
3.60
3.70
3.80
3.90
4.00
0.139
0.132
0.126
0.120
0.1145
1.800
1.808
1.817
1.825
1.833
0.251
0.239
0.229
0.219
0.210
4.420
4.703
5.000
5.311
5.608
1.178
1.182
1.185
1.187
1.189
0.389
0.394
0.400
0.404
0.407
4.10
4.20
4.30
4.40
4.50
0.109
0.105
0.100
0.096
0.092
1.840
1.846
1.852
1.858
1.864
0.202
0.194
0.186
0.178
0.172
5.979
6.336
6.708
7.098
7.456
1.193
1.195
1.197
1.199
1.200
0.413
0.417
0.421
0.4246
0.426
4.60
4.70
4.80
4.90
5.00
0.088
0.085
0.082
0.079
0.075
1.868
1.873
1.878
1.883
1.887
0.166
0.159
0.154
0.150
0.142
7.925
8.365
8.827
9.300
9.721
1.203
1.205
1.207
1.208
1.209
0.431
0.434
0.437
0.439
0.440
6.00
7.00
8.00
9.00
10.00
0.053
0.040
0.030
0.024
0.0199
1.918
1.938
1.951
1.960
1.967
0.102
0.077
0.059
0.047
0.038
15.680
23.850
34.580
48.240
65.180
1.220
1.227
1.232
1.235
1.238
0.459
0.472
0.479
0.485
0.489
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
M
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Isothermal Flow of Perfect Gases with Friction
93
TABLE 7.1
Isothermal flow of perfect gases with friction (γγ = 1.3)
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
4 f Lmax D
0.02
0.04
0.06
0.08
0.10
43.853
21.926
14.617
10.963
8.770
0.0228
0.0456
0.0684
0.0912
0.1140
0.897
0.897
0.897
0.897
0.897
27.328
13.674
9.128
6.858
5.499
1914.515
473.593
207.311
114.403
71.580
0.12
0.14
0.16
0.18
0.20
7.308
6.264
5.481
4.872
4.385
0.1368
0.1596
0.1824
0.2052
0.2280
0.898
0.899
0.900
0.900
0.902
4.596
3.953
3.472
3.100
2.804
48.440
34.576
25.645
19.574
15.274
0.22
0.24
0.26
0.28
0.30
3.986
3.654
3.373
3.132
2.923
0.250
0.273
0.296
0.319
0.342
0.903
0.904
0.905
0.907
0.908
2.563
2.363
2.195
2.053
1.930
12.127
9.762
7.947
6.528
5.401
0.32
0.34
0.36
0.39
0.40
2.741
2.579
2.436
2.308
2.192
0.365
0.387
0.410
0.433
0.456
0.910
0.912
0.914
0.916
0.918
1.824
1.731
1.650
1.578
1.514
4.495
3.759
3.154
2.654
2.237
2.088
1.993
1.907
1.827
1.754
0.478
0.501
0.524
0.547
0.570
0.920
0.923
0.925
0.927
0.930
1.457
1.405
1.360
1.319
1.282
1.888
1.593
1.344
1.133
0.953
1.686
1.624
1.566
1.512
1.461
0.593
0.615
0.638
0.661
0.684
0.933
0.936
0.938
0.942
0.945
1.248
1.218
1.190
1.166
1.144
0.799
0.668
0.555
0.459
0.377
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
0.42
0.44
0.46
0.48
0.50
eri
ng
.i n
p/p*t
M
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Gas Tables for Compressible Flow Calculations
94
TABLE 7.1
Isothermal flow of perfect gases with friction (γγ = 1.3)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
0.62
0.64
0.66
0.68
0.70
1.415
1.370
1.329
1.289
1.253
0.707
0.729
0.753
0.775
0.798
0.948
0.952
0.955
0.958
0.962
1.124
1.105
1.089
1.074
1.061
0.307
0.248
0.197
0.154
0.119
0.72
0.74
0.76
0.78
0.80
1.218
1.185
1.154
1.124
1.096
0.821
0.844
0.866
0.889
0.912
0.966
0.970
0.974
0.978
0.983
1.049
1.039
1.031
1.023
1.016
0.089
0.065
0.045
0.029
0.018
0.82
0.84
0.86
0.88
0.90
1.069
1.044
1.019
0.997
0.974
0.935
0.958
0.980
1.003
1.026
0.987
0.991
0.996
1.0007
1.005
1.010
1.006
1.002
0.999
0.998
0.0095
0.0038
0.0078
0.22 × 10−4
0.0013
0.92
0.94
0.96
0.98
1.00
0.953
0.933
0.913
0.895
0.877
1.049
1.072
1.095
1.117
1.140
1.010
1.015
1.020
1.025
1.031
0.997
0.997
0.9975
0.999
1.001
0.0044
0.0092
0.015
0.023
0.0316
0.859
0.843
0.827
0.812
0.797
1.163
1.185
1.208
1.231
1.254
1.036
1.042
1.047
1.053
1.059
1.004
1.008
1.012
1.017
1.023
0.0413
0.052
0.0635
0.076
0.088
0.783
0.769
0.756
0.743
0.731
1.277
1.299
1.322
1.345
1.368
1.065
1.071
1.078
1.083
1.090
1.029
1.037
1.045
1.053
1.063
0.102
0.116
0.131
0.146
0.161
1.12
1.14
1.16
1.18
1.20
En
gin
e
arn
w.
Le
ww
1.02
1.04
1.06
1.08
1.10
eri
ng
.i n
M
4 f Lmax D
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Isothermal Flow of Perfect Gases with Friction
95
TABLE 7.1
Isothermal flow of perfect gases with friction (γγ = 1.3)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
1.22
1.24
1.26
1.28
1.30
0.718
0.707
0.696
0.685
0.674
1.391
1.414
1.437
1.459
1.482
1.097
1.103
1.110
1.116
1.124
1.073
1.083
1.094
1.106
1.119
0.177
0.193
0.209
0.226
0.242
1.32
1.34
1.36
1.38
1.40
0.664
0.654
0.645
0.635
0.626
1.505
1.528
1.550
1.573
1.596
1.131
1.138
1.145
1.152
1.160
1.132
1.146
1.161
1.176
1.192
0.259
0.276
0.293
0.310
0.328
1.42
1.44
1.46
1.48
1.50
0.617
0.609
0.601
0.592
0.594
1.619
1.642
1.664
1.687
1.710
1.168
1.175
1.183
1.191
1.199
1.209
1.227
1.245
1.264
1.284
0.345
0.362
0.380
0.397
0.415
1.52
1.54
1.56
1.58
1.60
0.577
0.569
0.562
0.555
0.548
1.733
1.756
1.778
1.801
1.824
1.207
1.215
1.224
1.232
1.241
1.305
1.327
1.349
1.372
1.396
0.433
0.450
0.468
0.485
0.503
0.541
0.534
0.528
0.522
0.516
1.847
1.869
1.893
1.915
1.938
1.249
1.258
1.267
1.276
1.285
1.421
1.447
1.474
1.502
1.530
0.520
0.538
0.555
0.572
0.589
0.510
0.504
0.498
0.493
0.487
1.961
1.984
2.007
2.029
2.052
1.294
1.303
1.313
1.323
1.132
1.560
1.591
1.622
1.655
1.689
0.607
0.624
0.641
0.658
0.675
1.72
1.74
1.76
1.78
1.80
En
gin
e
arn
w.
Le
ww
1.62
1.64
1.66
1.68
1.70
eri
ng
.i n
M
4 f Lmax D
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Gas Tables for Compressible Flow Calculations
96
TABLE 7.1
Isothermal flow of perfect gases with friction (γγ = 1.3)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
1.82
1.84
1.86
1.88
1.90
0.482
0.476
0.471
0.466
0.461
2.075
2.098
2.121
2.143
2.166
1.342
1.352
1.362
1.372
1.382
1.724
1.760
1.797
1.836
1.876
0.692
0.709
0.726
0.742
0.759
1.92
1.94
1.96
1.98
2.00
0.457
0.452
0.447
0.443
0.438
2.189
2.212
2.235
2.257
2.280
1.392
1.403
1.413
1.424
1.434
1.917
1.959
2.003
2.048
2.094
0.775
0.792
0.808
0.825
0.841
2.02
2.04
2.06
2.08
2.10
0.434
0.430
0.426
0.422
0.417
2.303
2.326
2.348
2.372
2.394
1.445
1.456
1.467
1.478
1.489
2.142
2.191
2.242
2.294
2.348
0.857
0.873
0.889
0.905
0.921
2.12
2.14
2.16
2.18
2.20
0.414
0.409
0.406
0.402
0.398
2.417
2.440
2.463
2.485
2.508
1.501
1.512
1.524
1.536
1.547
2.404
2.462
2.521
2.581
2.644
0.936
0.952
0.967
0.983
0.998
0.395
0.392
0.388
0.385
0.381
2.531
2.554
2.577
2.599
2.622
1.559
1.571
1.583
1.596
1.608
2.708
2.775
2.843
2.914
2.986
1.013
1.028
1.043
1.058
1.073
0.378
0.375
0.372
0.368
0.365
2.645
2.668
2.691
2.714
2.736
1.620
1.633
1.645
1.658
1.671
3.061
3.138
3.217
3.298
3.383
1.088
1.103
1.117
1.132
1.147
2.32
2.34
2.36
2.38
2.40
En
gin
e
arn
w.
Le
ww
2.22
2.24
2.26
2.28
2.30
eri
ng
.i n
M
4 f Lmax D
For More Visit : www.LearnEngineering.in
For More Visit : www.LearnEngineering.in
Isothermal Flow of Perfect Gases with Friction
97
TABLE 7.1
Isothermal flow of perfect gases with friction (γγ = 1.3)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
2.42
2.44
2.46
2.48
2.50
0.362
0.359
0.356
0.354
0.351
2.759
2.782
2.805
2.827
2.850
1.684
1.697
1.710
1.724
1.737
3.469
3.557
3.649
3.743
3.839
1.161
1.175
1.189
1.204
1.218
2.52
2.54
2.56
2.58
2.60
0.348
0.345
0.343
0.340
0.337
2.873
2.896
2.919
2.942
2.964
1.750
1.764
1.778
1.792
1.805
3.939
4.042
4.147
4.255
4.366
1.232
1.246
1.259
1.273
1.287
2.62
2.64
2.66
2.68
2.70
0.334
0.332
0.329
0.327
0.325
2.987
3.010
3.033
3.055
3.078
1.819
1.834
1.848
1.862
1.877
4.481
4.599
4.720
4.845
4.973
1.301
1.314
1.328
1.341
1.354
2.72
2.74
2.76
2.78
2.80
0.322
0.320
0.318
0.315
0.313
3.101
3.124
3.147
3.169
3.192
1.891
1.906
1.921
1.936
1.951
5.105
5.240
5.379
5.522
5.669
1.367
1.381
1.394
1.407
1.419
0.311
0.309
0.307
0.304
0.302
3.215
3.238
3.261
3.283
3.306
1.966
1.981
1.996
2.012
2.027
5.821
5.976
6.136
6.300
6.469
1.432
1.445
1.458
1.471
1.483
0.300
0.298
0.296
0.294
0.292
3.329
3.352
3.375
3.398
3.421
2.043
2.059
2.075
2.091
2.107
6.642
6.821
7.004
7.192
7.385
1.495
1.508
1.521
1.533
1.545
2.92
2.94
2.96
2.98
3.00
En
gin
e
arn
w.
Le
ww
2.82
2.84
2.86
2.88
2.90
eri
ng
.i n
M
4 f Lmax D
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Gas Tables for Compressible Flow Calculations
98
TABLE 7.1
Isothermal flow of perfect gases with friction (γγ = 1.3)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
3.10
3.20
3.30
3.40
3.50
0.283
0.274
0.266
0.258
0.251
3.534
3.648
3.763
3.876
3.991
2.189
2.274
2.361
2.451
2.544
8.433
9.631
10.998
12.555
14.327
1.605
1.664
1.721
1.776
1.831
3.60
3.70
3.80
3.90
4.00
0.243
0.237
0.231
0.225
0.219
4.105
4.218
4.332
4.447
4.561
2.639
2.737
2.838
2.942
3.048
16.341
18.626
21.214
24.142
27.449
1.883
1.935
1.985
2.035
2.083
4.10
4.20
4.30
4.40
4.50
0.214
0.209
0.204
0.199
0.195
4.675
4.789
4.903
5.017
5.131
3.157
3.269
3.383
3.500
3.619
31.181
35.384
40.112
45.423
51.380
2.130
2.176
2.221
2.265
2.308
4.60
4.70
4.80
4.90
5.00
0.191
0.187
0.183
0.179
0.175
5.245
5.359
5.473
5.587
5.701
3.742
3.867
3.995
4.125
4.258
58.053
65.517
73.854
83.155
93.517
2.351
2.392
2.433
2.472
2.512
0.159
0.146
0.135
0.125
0.117
6.271
6.841
7.411
7.981
8.551
4.965
5.738
6.578
7.486
8.461
165.267
283.672
473.496
769.836
1221.350
2.697
2.867
3.024
3.169
3.306
0.109
0.103
0.097
0.092
0.0877
9.121
9.691
10.262
10.831
11.402
9.503
10.613
11.789
13.033
14.344
1894.190
2876.708
4285.063
6269.795
9020.438
3.433
3.553
3.667
3.773
3.875
8.00
8.50
9.00
9.50
10.00
En
gin
e
arn
w.
Le
ww
5.50
6.00
6.50
7.00
7.50
eri
ng
.i n
M
4 f Lmax D
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Isothermal Flow of Perfect Gases with Friction
99
TABLE 7.2
Isothermal flow of perfect gases with friction (γγ = 1.4)
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
4 f Lmax D
0.02
0.04
0.06
0.08
0.10
42.257
21.128
14.086
10.564
8.451
0.0237
0.0473
0.0710
0.0946
0.1183
0.8751
0.8752
0.8756
0.8761
0.8770
26.488
13.255
8.849
6.650
5.333
1777.227
439.327
192.122
105.892
66.159
0.12
0.14
0.16
0.18
0.20
7.043
6.037
5.282
4.695
4.226
0.142
0.165
0.189
0.213
0.237
0.8775
0.8784
0.8795
0.881
0.882
4.458
3.835
3.369
3.010
2.723
44.699
31.847
23.573
17.952
13.975
0.22
0.24
0.26
0.28
0.30
3.841
3.521
3.251
3.018
2.817
0.260
0.284
0.307
0.331
0.355
0.883
0.885
0.887
0.888
0.891
2.490
2.297
2.135
1.997
1.879
11.066
8.883
7.208
5.901
4.865
0.32
0.34
0.36
0.38
0.40
2.641
2.486
2.347
2.224
2.113
0.378
0.402
0.426
0.449
0.473
0.893
0.895
0.897
0.900
0.903
1.777
1.687
1.609
1.539
1.478
4.033
3.358
2.805
2.348
1.968
2.012
1.921
1.837
1.761
1.690
0.497
0.521
0.544
0.568
0.592
0.906
0.909
0.912
0.915
0.918
1.424
1.375
1.331
1.292
1.256
1.651
1.384
1.159
0.968
0.807
1.625
1.565
1.509
1.457
1.408
0.615
0.639
0.663
0.686
0.710
0.922
0.926
0.929
0.934
0.938
1.225
1.196
1.170
1.147
1.126
0.670
0.553
0.454
0.370
0.299
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
0.42
0.44
0.46
0.48
0.50
eri
ng
.i n
p/p*t
M
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Gas Tables for Compressible Flow Calculations
100
TABLE 7.2
Isothermal flow of perfect gases with friction (γγ = 1.4)
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
4 f Lmax D
0.942
0.947
0.951
0.956
0.961
1.107
1.090
1.075
1.061
1.049
0.238
0.188
0.145
0.1098
0.0808
0.966
0.971
0.976
0.981
0.987
1.039
1.029
1.022
1.015
1.009
0.0573
0.0386
0.0242
0.0135
62.5 × 10−4
0.970
0.994
1.017
1.041
1.065
0.993
0.998
1.004
1.010
1.017
1.004
1.001
0.998
0.996
0.995
18.6 × 10−4
0.75 × 10−4
6.0 × 10−4
31.8 × 10−4
75.8 × 10−4
1.088
1.112
1.135
1.159
1.183
1.023
1.029
1.036
1.043
1.050
0.995
0.9958
0.997
0.999
1.0025
1.36 × 10−2
2.11 × 10−2
2.98 × 10−2
3.98 × 10−2
5.07 × 10−2
0.828
0.813
0.797
0.783
0.768
1.207
1.230
1.254
1.278
1.302
1.057
1.064
1.072
1.079
1.087
1.0062
1.0106
1.0157
1.0215
1.028
0.0626
0.0753
0.0887
0.1028
0.1174
0.755
0.741
0.728
0.716
0.704
1.325
1.349
1.372
1.396
1.419
1.095
1.102
1.110
1.118
1.127
1.035
1.043
1.051
1.061
l.070
0.1325
0.1481
0.164
0.180
0.197
p/p*t
1.363
1.320
1.280
1.243
1.207
0.733
0.757
0.781
0.805
0.828
0.72
0.74
0.76
0.78
0.80
1.174
1.142
1.112
1.083
1.056
0.852
0.876
0.899
0.923
0.946
0.82
0.84
0.86
0.88
0.90
1.031
1.006
0.983
0.960
0.939
0.92
0.94
0.96
0.98
1.00
0.918
0.899
0.880
0.962
0.845
1.12
1.14
1.16
1.18
1.20
arn
w.
Le
ww
1.02
1.04
1.06
1.08
1.10
En
gin
e
0.62
0.64
0.66
0.68
0.70
eri
ng
.i n
M
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Isothermal Flow of Perfect Gases with Friction
101
TABLE 7.2
Isothermal flow of perfect gases with friction (γγ = 1.4)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
4 f Lmax D
1.22
1.24
1.26
1.28
1.30
0.693
0.681
0.671
0.660
0.650
1.443
1.467
1.491
1.515
1.538
1.135
1.144
1.153
1.162
1.171
1.081
1.092
1.103
1.116
1.129
0.214
0.231
0.248
0.266
0.284
1.32
1.34
1.36
1.38
1.40
0.640
0.631
0.621
0.612
0.604
1.562
1.585
1.609
1.633
1.656
1.180
1.189
1.198
1.208
1.218
1.142
1.157
1.172
1.187
1.204
0.302
0.319
0.337
0.356
0.374
1.42
1.44
1.46
1.48
1.50
0.595
0.587
0.578
0.571
0.563
1.680
1.704
1.727
1.751
1.775
1.228
1.238
1.248
1.258
1.268
1.221
1.238
1.257
1.276
1.296
0.392
0.410
0.428
0.447
0.465
1.52
1.54
1.56
1.58
1.60
0.556
0.549
0.542
0.535
0.528
1.798
1.822
1.846
1.869
1.893
1.279
1.290
1.301
1.312
1.323
1.317
1.338
1.360
1.383
1.407
0.483
0.501
0.519
0.537
0.555
0.522
0.515
0.509
0.503
0.497
1.917
1.940
1.964
1.987
2.011
1.334
1.345
1.357
1.368
1.381
1.431
1.457
1.483
1.510
1.538
0.573
0.591
0.609
0.627
0.645
0.491
0.486
0.480
0.475
0.469
2.035
2.058
2.082
2.106
2.129
1.393
1.405
1.417
1.429
1.442
1.567
1.596
1.627
1.658
1.691
0.663
0.680
0.697
0.715
0.733
1.72
1.74
1.76
1.78
1.80
En
gin
e
arn
w.
Le
ww
1.62
1.64
1.66
1.69
1.70
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
102
TABLE 7.2
Isothermal flow of perfect gases with friction (γγ = 1.4)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
1.82
1.84
1.86
1.88
1.90
0.464
0.459
0.454
0.449
0.445
2.153
2.177
2.200
2.224
2.248
1.455
1.467
1.480
1.493
1.507
1.724
1.758
1.793
1.830
1.868
0.749
0.767
0.784
0.801
0.818
1.92
1.94
1.96
1.98
2.00
0.440
0.435
0.431
0.427
0.423
2.272
2.295
2.319
2.343
2.366
1.520
1.534
1.547
1.561
1.575
1.906
1.946
1.986
2.029
2.072
0.835
0.852
0.868
0.885
0.901
2.02
2.04
2.06
2.08
2.10
0.418
0.414
0.410
0.406
0.402
2.390
2.414
2.437
2.461
2.484
1.589
1.603
1.617
1.632
1.647
2.116
2.162
2.208
2.257
2.306
0.918
0.934
0.950
0.966
0.982
2.12
2.14
2.16
2.18
2.20
0.398
0.395
0.391
0.387
0.384
2.508
2.532
2.556
2.579
2.603
1.662
1.676
1.691
1.707
1.722
2.357
2.409
2.463
2.517
2.574
0.998
1.014
1.029
1.045
1.061
0.381
0.377
0.374
0.370
0.367
2.627
2.650
2.674
2.697
2.721
1.737
1.753
1.769
1.785
1.800
2.632
2.691
2.752
2.815
2.879
1.076
1.092
1.107
1.122
1.137
0.364
0.361
0.358
0.355
0.352
2.745
2.768
2.792
2.816
2.839
1.817
1.833
1.849
1.866
1.883
2.945
3.013
3.082
3.153
3.226
1.152
1.167
1.182
1.197
1.211
2.32
2.34
2.36
2.38
2.40
En
gin
e
arn
w.
Le
ww
2.22
2.24
2.26
2.28
2.30
eri
ng
.i n
M
4 f Lmax D
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For More Visit : www.LearnEngineering.in
Isothermal Flow of Perfect Gases with Friction
103
TABLE 7.2
Isothermal flow of perfect gases with friction (γγ = 1.4)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
2.42
2.44
2.46
2.48
2.50
0.349
0.346
0.343
0.341
0.338
2.863
2.887
2.911
2.934
2.958
1.899
1.917
1.934
1.951
1.968
3.301
3.378
3.456
3.537
3.619
1.226
1.240
1.255
1.269
1.283
2.52
2.54
2.56
2.58
2.60
0.335
0.333
0.330
0.327
0.325
2.982
3.005
3.029
3.053
3.076
1.986
2.004
2.022
2.039
2.058
3.704
3.791
3.880
3.971
4.064
1.297
1.311
1.325
1.339
1.353
2.62
2.64
2.66
2.68
2.70
0.322
0.320
0.318
0.315
0.313
3.100
3.123
3.147
3.171
3.195
2.076
2.094
2.113
2.132
2.151
4.160
4.258
4.359
4.462
4.567
1.367
1.380
1.394
1.407
1.421
2.72
2.74
2.76
2.78
2.80
0.311
0.308
0.306
0.304
0.302
3.218
3.242
3.265
3.289
3.313
2.169
2.189
2.208
2.227
2.247
4.675
4.785
4.898
5.015
5.133
1.434
1.447
1.461
1.473
1.487
0.299
0.297
0.295
0.293
0.291
3.337
3.360
3.384
3.407
3.431
2.267
2.286
2.306
2.327
2.346
5.255
5.379
5.506
5.637
5.770
1.499
1.512
1.525
1.538
1.551
0.289
0.287
0.285
0.283
0.282
3.455
3.478
3.502
3.526
3.549
2.367
2.387
2.408
2.429
2.450
5.906
6.046
6.189
6.335
6.485
1.563
1.575
1.588
1.601
1.613
2.92
2.94
2.96
2.98
3.00
En
gin
e
arn
w.
Le
ww
2.82
2.84
2.86
2.88
2.90
eri
ng
.i n
M
4 f Lmax D
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
104
TABLE 7.2
Isothermal flow of perfect gases with friction (γγ = 1.4)
p/p*t
c/c*t = ρ*t/ρ
T0 /T0*t
p0 /p0*t
4 f Lmax D
3.10
3.20
3.30
3.40
3.50
0.273
0.264
0.256
0.248
0.241
3.668
3.786
3.905
4.023
4.141
2.557
2.667
2.781
2.898
3.018
7.286
8.182
9.183
10.229
11.541
1.673
1.732
1.790
1.846
1.900
3.60
3.70
3.80
3.90
4.00
0.235
0.228
0.222
0.217
0.211
4.259
4.378
4.496
4.614
4.733
3.143
3.271
3.402
3.537
3.675
12.922
14.454
16.152
18.029
20.104
1.953
2.005
2.056
2.105
2.153
4.10
4.20
4.30
4.40
4.50
0.206
0.201
0.196
0.192
0.188
4.851
4.969
5.088
5.206
5.324
3.817
3.962
4.110
4.263
4.418
22.391
24.911
27.682
30.725
34.062
2.201
2.247
2.292
2.336
2.380
4.60
4.70
4.80
4.90
5.00
0.184
0.179
0.176
0.172
0.169
5.443
5.561
5.679
5.798
5.916
4.578
4.741
4.907
5.077
5.250
37.718
41.716
46.084
50.850
56.043
2.422
2.464
2.505
2.544
2.584
0.154
0.141
0.130
0.121
0.112
6.507
7.099
7.691
8.282
8.874
6.168
7.175
8.268
9.450
10.718
89.591
139.367
211.379
313.219
454.338
2.769
2.939
3.097
3.243
3.379
0.1056
0.0994
0.0939
0.0889
0.0845
9.466
10.057
10.649
11.241
11.832
12.075
13.518
15.050
16.668
18.375
646.325
903.222
1241.856
1682.182
2247.66
3.506
3.626
3.739
3.847
3.948
8.00
8.50
9.00
9.50
10.00
En
gin
e
arn
w.
Le
ww
5.50
6.00
6.50
7.00
7.50
eri
ng
.i n
M
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Flow of Perfect Gases with Heat Transfer
105
TABLE 8.1
Flow of perfect gases with heat transfer (γγ = 1.3)
(Rayleigh flow)
p0 /p0*
T/T*
0.02
0.04
0.06
0.08
0.10
2.299
2.295
2.289
2.281
2.270
1.255
1.254
1.252
1.250
1.247
0.002
0.009
0.0189
0.0333
0.0516
0.00184
0.0073
0.0164
0.029
0.0449
0.002
0.0037
0.008
0.015
0.0227
0.12
0.14
0.16
0.18
0.20
2.258
2.243
2.226
2.207
2.186
1.244
1.239
1.235
1.230
1.224
0.073
0.098
0.127
0.158
0.191
0.064
0.086
0.110
0.138
0.167
0.0325
0.044
0.057
0.072
0.0875
0.22
0.24
0.26
0.28
0.30
2.164
2.140
2.114
2.087
2.059
1.128
1.212
1.205
1.198
1.191
0.277
0.264
0.302
0.342
0.382
0.198
0.231
0.265
0.300
0.336
1.105
0.123
0.143
0.163
0.185
0.32
0.34
0.36
0.38
0.40
2.030
1.999
1.968
1.936
1.904
1.183
1.176
1.167
1.159
1.152
0.422
0.462
0.502
0.542
0.580
0.373
0.408
0.445
0.481
0.516
0.208
0.231
0.255
0.279
0.305
1.871
1.837
1.804
1.769
1.736
1.143
1.135
1.127
1.119
1.111
0.617
0.654
0.688
0.722
0.753
0.551
0.585
0.618
0.649
0.680
0.330
0.356
0.382
0.408
0.434
1.702
1.670
1.634
1.600
1.567
1.103
1.096
1.088
1.081
1.074
0.783
0.811
0.837
0.861
0.884
0.708
0.736
0.762
0.787
0.810
0.460
0.486
0.512
0.538
0.564
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
p/p*
0.42
0.44
0.46
0.48
0.50
T0 /T0*
c/c* = ρ*/ρ
M
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Gas Tables for Compressible Flow Calculations
106
TABLE 8.1
Flow of perfect gases with heat transfer (γγ = 1.3)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
0.62
0.64
0.66
0.68
0.70
1.534
1.500
1.468
1.436
1.405
1.067
1.061
1.054
1.048
1.042
0.904
0.923
0.939
0.954
0.967
0.832
0.852
0.870
0.887
0.903
0.589
0.615
0.639
0.664
0.688
0.72
0.74
0.76
0.78
0.80
1.374
1.344
1.314
1.284
1.255
1.037
1.032
1.028
1.023
1.019
0.978
0.989
0.997
1.003
1.009
0.917
0.930
0.942
0.952
0.961
0.712
0.736
0.758
0.781
0.804
0.82
0.84
0.86
0.88
0.90
1.227
1.199
1.173
1.146
1.120
1.016
1.012
1.010
1.007
1.005
1.013
1.015
1.0172
1.0173
1.017
0.969
0.976
0.983
0.987
0.991
0.825
0.846
0.867
0.887
0.907
0.92
0.94
0.96
0.98
1.00
1.095
1.070
1.046
1.023
1.000
1.003
1.002
1.0007
1.0002
1.000
1.015
1.012
1.009
1.005
1.000
0.995
0.997
0.998
0.999
1.000
0.927
0.946
0.964
0.982
1.000
0.977
0.956
0.935
0.914
0.894
1.0002
1.0008
1.002
1.003
1.005
0.994
0.988
0.982
0.975
0.967
0.999
0.998
0.997
0.995
0.993
1.017
1.034
1.050
1.066
1.082
0.874
0.855
0.836
0.818
0.800
1.007
1.009
1.0127
1.016
1.020
0.958
0.950
0.942
0.933
0.924
0.990
0.987
0.984
0.981
0.976
1.097
1.111
1.126
1.139
1.153
1.12
1.14
1.16
1.18
1.20
En
gin
e
arn
w.
Le
ww
1.02
1.04
1.06
1.08
1.10
eri
ng
.i n
M
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Flow of Perfect Gases with Heat Transfer
107
TABLE 8.1
Flow of perfect gases with heat transfer (γγ = 1.3)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
1.22
1.24
1.26
1.28
1.30
0.784
0.767
0.751
0.735
0.719
1.024
1.028
1.034
1.039
1.045
0.914
0.904
0.894
0.885
0.875
0.972
0.967
0.963
0.958
0.953
1.166
1.179
1.192
1.204
1.216
1.32
1.34
1.36
1.38
1.40
0.705
0.689
0.676
0.662
0.648
1.051
1.058
1.065
1.073
1.081
0.865
0.854
0.844
0.834
0.824
0.948
0.943
0.938
0.932
0.927
1.227
1.238
1.249
1.260
1.270
1.42
1.44
1.46
1.48
1.50
0.635
0.622
0.609
0.598
0.586
1.089
1.098
1.108
1.117
1.128
0.813
0.803
0.793
0.783
0.773
0.921
0.915
0.910
0.904
0.898
1.281
1.291
1.300
1.309
1.318
1.52
1.54
1.56
1.58
1.60
0.575
0.563
0.552
0.542
0.531
1.138
1.149
1.161
1.173
1.185
0.763
0.753
0.743
0.733
0.723
0.893
0.887
0.882
0.876
0.870
1.327
1.336
1.344
1.352
1.360
0.521
0.512
0.502
0.492
0.484
1.195
1.213
1.227
1.241
1.256
0.713
0.704
0.694
0.685
0.676
0.865
0.859
0.853
0.847
0.842
1.368
1.376
1.383
1.390
1.397
0.475
0.465
0.457
0.449
0.441
1.272
1.288
1.305
1.322
1.340
0.670
0.657
0.648
0.639
0.631
0.837
0.831
0.825
0.821
0.815
1.404
1.411
1.417
1.423
1.430
1.72
1.74
1.76
1.78
1.80
En
gin
e
arn
w.
Le
ww
1.62
1.64
1.66
1.68
1.70
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
108
TABLE 8.1
Flow of perfect gases with heat transfer (γγ = 1.3)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
1.82
1.84
1.86
1.88
1.90
0.433
0.426
0.418
0.411
0.404
1.358
1.377
1.397
1.417
1.438
0.622
0.614
0.606
0.597
0.589
0.810
0.805
0.799
0.795
0.790
1.436
1.442
1.447
1.453
1.459
1.92
1.94
1.96
1.98
2.00
0.397
0.390
0.383
0.377
0.371
1.451
1.482
1.505
1.528
1.552
0.581
0.573
0.565
0.557
0.551
0.785
0.780
0.775
0.771
0.766
1.464
1.469
1.474
1.479
1.484
2.02
2.04
2.06
2.08
2.10
0.365
0.358
0.353
0.347
0.341
1.576
1.602
1.628
1.655
1.683
0.543
0.536
0.528
0.522
0.515
0.761
0.757
0.752
0.748
0.744
1.488
1.493
1.498
1.502
1.506
2.12
2.14
2.16
2.18
2.20
0.336
0.331
0.325
0.320
0.315
1.711
1.740
1.770
1.800
1.832
0.508
0.501
0.495
0.487
0.482
0.739
0.735
0.731
0.727
0.723
1.511
1.515
1.518
1.523
1.527
0.310
0.306
0.301
0.296
0.292
1.865
1.898
1.932
1.967
2.003
0.475
0.469
0.463
0.457
0.451
0.718
0.715
0.711
0.707
0.703
1.530
1.534
1.537
1.541
1.545
0.287
0.283
0.279
0.275
0.271
2.040
2.078
2.117
2.156
2.197
0.445
0.440
0.434
0.428
0.423
0.699
0.696
0.693
0.688
0.686
1.548
1.551
1.555
1.557
1.561
2.32
2.34
2.36
2.38
2.40
En
gin
e
arn
w.
Le
ww
2.22
2.24
2.26
2.28
2.30
eri
ng
.i n
M
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Heat Transfer
109
TABLE 8.1
Flow of perfect gases with heat transfer (γγ = 1.3)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
2.42
2.44
2.46
2.48
2.50
0.267
0.263
0.259
0.255
0.252
2.238
2.281
2.325
2.370
2.416
0.417
0.412
0.407
0.402
0.397
0.682
0.678
0.675
0.672
0.670
1.564
1.567
1.569
1.573
1.575
2.52
2.54
2.56
2.58
2.60
0.248
0.245
0.242
0.238
0.235
2.464
2.512
2.562
2.612
2.664
0.392
0.387
0.382
0.378
0.373
0.666
0.663
0.659
0.657
0.654
1.578
1.580
1.583
1.586
1.588
2.62
2.64
2.66
2.68
2.70
0.232
0.228
0.225
0.222
0.219
2.718
2.772
2.828
2.885
2.945
0.368
0.364
0.360
0.356
0.351
0.650
0.648
0.645
0.642
0.640
1.591
1.593
1.596
1.598
1.600
2.72
2.74
2.76
2.78
2.80
0.217
0.214
0.211
0.208
0.206
3.004
3.065
3.128
3.192
3.258
0.347
0.343
0.339
0.335
0.331
0.636
0.634
0.631
0.629
0.627
1.603
1.605
1.607
1.609
1.612
0.203
0.200
0.198
0.195
0.193
3.326
3.395
3.465
3.537
3.611
0.327
0.323
0.319
0.316
0.312
0.624
0.622
0.619
0.617
0.614
1.613
1.615
1.617
1.619
1.620
0.190
0.188
0.185
0.183
0.181
3.687
3.765
3.844
3.925
4.007
0.309
0.305
0.302
0.298
0.295
0.612
0.609
0.607
0.605
0.603
1.623
1.625
1.626
1.628
1.630
2.92
2.94
2.96
2.98
3.00
En
gin
e
arn
w.
Le
ww
2.82
2.84
2.86
2.88
2.90
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
110
TABLE 8.1
Flow of perfect gases with heat transfer (γγ = 1.3)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
3.10
3.20
3.30
3.40
3.50
0.170
0.161
0.152
0.143
0.136
4.451
4.947
5.500
6.118
6.806
0.279
0.264
0.251
0.238
0.226
0.593
0.583
0.574
0.566
0.558
1.638
1.645
1.653
1.659
1.665
3.60
3.70
3.80
3.90
4.00
0.128
0.122
0.116
0.110
0.106
7.571
8.422
9.365
10.411
11.570
0.215
0.205
0.195
0.186
0.178
0.551
0.544
0.538
0.532
0.527
1.670
1.675
1.680
1.684
1.688
4.10
4.20
4.30
4.40
4.50
0.100
0.096
0.092
0.088
0.084
12.850
14.265
15.825
17.545
19.440
0.170
0.163
0.156
0.149
0.143
0.521
0.516
0.512
0.508
0.504
1.692
1.6951.698
1.701
1.705
4.60
4.70
4.80
4.90
5.00
0.081
0.077
0.074
0.071
0.068
21.518
23.803
26.309
29.056
32.060
0.138
0.132
0.127
0.122
0.118
0.499
0.496
0.493
0.489
0.487
1.707
1.709
1.713
1.714
1.715
76.970
191.300
413.400
833.400
1582.00
0.083
0.062
0.048
0.038
0.031
0.464
0.450
0.440
0.434
0.429
1.732
1.742
1.748
1.753
1.756
En
gin
e
arn
w.
Le
0.048
0.035
0.027
0.0216
0.0175
ww
6.00
7.00
8.00
9.00
10.00
eri
ng
.i n
M
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Heat Transfer
111
TABLE 8.2
Flow of perfect gases with heat transfer (γγ = 1.4)
(Rayleigh flow)
p0 /p0*
T/T*
0.02
0.04
0.06
0.08
0.10
2.398
2.394
2.388
2.378
2.367
1.268
1.267
1.265
1.262
1.259
0.0023
0.0092
0.021
0.036
0.056
0.00192
0.0077
0.017
0.030
0.0468
0.00096
0.0038
0.0086
0.015
0.0237
0.12
0.14
0.16
0.18
0.20
2.353
2.336
2.317
2.295
2.273
1.255
1.251
1.246
1.241
1.235
0.079
0.107
0.137
0.171
0.207
0.066
0.089
0.115
0.143
0.174
0.034
0.0457
0.059
0.074
0.091
0.22
0.24
0.26
0.28
0.30
2.248
2.221
2.193
2.163
2.131
1.228
1.221
1.214
2.206
1.198
0.245
0.284
0.325
0.367
0.409
0.206
0.239
0.274
0.310
0.347
0.108
0.128
0.148
0.169
0.192
0.32
0.34
0.36
0.38
0.40
2.099
2.066
2.031
1.996
1.961
1.190
1.182
1.174
1.165
1.157
0.451
0.493
0.535
0.576
0.615
0.384
0.421
0.457
0.493
0.529
0.215
0.239
0.263
0.288
0.314
1.925
1.888
1.852
1.815
1.778
1.148
1.139
1.131
1.122
1.114
0.653
0.690
0.725
0.758
0.790
0.564
0.597
0.630
0.661
0.691
0.339
0.365
0.392
0.418
0.444
1.741
1.704
1.668
1.632
1.596
1.106
1.098
1.090
1.082
1.075
0.819
0.847
0.872
0.896
0.917
0.720
0.747
0.773
0.796
0.819
0.471
0.497
0.523
0.548
0.574
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
p/p*
0.42
0.44
0.46
0.48
0.50
T0 /T0*
c/c* = ρ*/ρ
M
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Gas Tables for Compressible Flow Calculations
112
TABLE 8.2
Flow of perfect gases with heat transfer (γγ = 1.4)
(Rayleigh flow)
p/p*
p0/p0*
T/T*
T0/T0*
c/c* = ρ*/ρ
0.62
0.64
0.66
0.68
0.70
1.560
1.525
1.490
1.457
1.423
1.068
1.061
1.055
1.049
1.043
0.935
0.953
0.968
0.981
0.993
0.839
0.859
0.877
0.893
0.908
0.599
0.625
0.650
0.673
0.697
0.72
0.74
0.76
0.78
0.80
1.391
1.358
1.327
1.296
1.266
1.037
1.032
1.028
1.023
1.019
1.002
1.011
1.017
1.022
1.025
0.922
0.934
0.945
0.955
0.964
0.721
0.744
0.766
0.788
0.810
0.82
0.84
0.86
0.88
0.90
1.236
1.207
1.179
1.151
1.125
1.015
1.012
1.010
1.007
1.0045
1.027
1.028
1.028
1.027
1.025
0.972
0.978
0.984
0.998
0.992
0.831
0.852
0.872
0.892
0.911
0.92
0.94
0.96
0.98
1.00
1.098
1.073
1.048
1.023
1.000
1.003
1.002
1.001
1.0002
1.000
1.021
1.017
1.012
1.006
1.000
0.995
0.997
0.998
0.999
1.000
0.930
0.950
0.966
0.983
1.000
0.977
0.955
0.933
0.911
0.891
1.0002
1.0007
1.002
1.0033
1.005
0.993
0.985
0.978
0.969
0.960
0.999
0.998
0.997
0.996
0.994
1.016
1.032
1.048
1.063
1.078
0.871
0.851
0.832
0.814
0.796
1.007
1.009
1.012
1.016
1.019
0.951
0.942
0.932
0.922
0.912
0.991
0.988
0.985
0.982
0.978
1.092
1.106
1.120
1.133
1.146
1.12
1.14
1.16
1.18
1.20
En
gin
e
arn
w.
Le
ww
1.02
1.04
1.06
1.08
1.10
eri
ng
.i n
M
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Flow of Perfect Gases with Heat Transfer
113
TABLE 8.2
Flow of perfect gases with heat transfer (γγ = 1.4)
(Rayleigh flow)
p/p*
p0/p0*
T/T*
T0/T0*
c/c* = ρ*/ρ
1.22
1.24
1.26
1.28
1.30
0.778
0.761
0.745
0.728
0.713
1.023
1.028
1.033
1.038
1.044
0.902
0.891
0.881
0.869
0.859
0.975
0.971
0.967
0.962
0.958
1.158
1.171
1.182
1.194
1.205
1.32
1.34
1.36
1.38
1.40
0.698
0.683
0.668
0.654
0.641
1.049
1.056
1.063
1.070
1.078
0.848
0.837
0.827
0.816
0.805
0.953
0.948
0.944
0.939
0.934
1.216
1.226
1.237
1.247
1.256
1.42
1.44
1.46
1.48
1.50
0.628
0.615
0.602
0.590
0.578
1.086
1.094
1.103
1.111
1.122
0.795
0.784
0.773
0.763
0.753
0.929
0.924
0.919
0.914
0.909
1.266
1.275
1.284
1.293
1.301
1.52
1.54
1.56
1.58
1.60
0.567
0.556
0.544
0.534
0.524
1.132
1.142
1.153
1.164
1.176
0.742
0.732
0.722
0.711
0.702
0.904
0.899
0.894
0.889
0.884
1.309
1.317
1.325
1.333
1.340
0.513
0.503
0.494
0.484
0.476
1.187
1.200
1.213
1.226
1.240
0.692
0.682
0.673
0.663
0.654
0.879
0.874
0.869
0.865
0.860
1.347
1.354
1.362
1.368
1.375
0.467
0.458
0.449
0.442
0.434
1.254
1.269
1.284
1.299
1.316
0.644
0.635
0.626
0.617
0.609
0.855
0.850
0.845
0.841
0.836
1.381
1.387
1.393
1.399
1.405
1.72
1.74
1.76
1.78
1.80
En
gin
e
arn
w.
Le
ww
1.62
1.64
1.66
1.68
1.70
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
114
TABLE 8.2
Flow of perfect gases with heat transfer (γγ = 1.4)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
1.82
1.84
1.86
1.88
1.90
0.425
0.418
0.411
0.403
0.396
1.332
1.349
1.367
1.385
1.403
0.600
0.592
0.584
0.575
0.567
0.832
0.827
0.823
0.818
0.814
1.410
1.415
1.421
1.426
1.431
1.92
1.94
1.96
1.98
2.00
0.389
0.383
0.376
0.369
0.364
1.422
1.442
1.462
1.482
1.503
0.559
0.551
0.544
0.536
0.529
0.810
0.806
0.801
0.797
0.793
1.436
1.441
1.446
1.450
1.455
2.02
2.04
2.06
2.08
2.10
0.357
0.352
0.345
0.340
0.334
1.525
1.547
1.569
1.592
1.616
0.522
0.514
0.507
0.500
0.494
0.789
0.785
0.782
0.778
0.774
1.459
1.463
1.467
1.471
1.475
2.12
2.14
2.16
2.18
2.20
0.329
0.324
0.318
0.314
0.308
1.640
1.665
1.690
1.717
1.743
0.487
0.480
0.474
0.467
0.461
0.770
0.767
0.763
0.759
0.756
1.480
1.483
1.487
1.490
1.494
0.304
0.299
0.294
0.290
6.285
1.771
1.798
1.827
1.856
1.886
0.455
0.448
0.443
0.437
0.431
0.750
0.749
0.746
0.743
0.739
1.497
1.500
1.504
1.507
1.510
0.281
0.277
0.273
0.268
0.265
1.916
1.947
1.980
2.012
2.045
0.426
0.420
0.415
0.409
0.404
0.736
0.733
0.730
0.727
0.724
1.513
1.516
1.519
1.522
1.525
2.32
2.34
2.36
2.38
2.40
En
gin
e
arn
w.
Le
ww
2.22
2.24
2.26
2.28
2.30
eri
ng
.i n
M
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Flow of Perfect Gases with Heat Transfer
115
TABLE 8.2
Flow of perfect gases with heat transfer (γγ = 1.4)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
2.42
2.44
2.46
2.48
2.50
0.261
0.257
0.253
0.249
0.246
2.078
2.114
2.149
2.185
2.222
0.398
0.393
0.388
0.383
0.379
0.721
0.718
0.716
0.713
0.710
1.528
1.530
1.533
1.536
1.540
2.52
2.54
2.56
2.58
2.60
0.242
0.239
0.235
0.232
0.229
2.260
2.298
2.337
2.377
2.418
0.374
0.369
0.365
0.360
0.356
0.707
0.704
0.702
0.699
0.697
1.542
1.544
1.546
1.548
1.551
2.62
2.64
2.66
2.68
2.70
0.226
0.223
0.220
0.217
0.214
2.459
2.502
2.545
2.589
2.634
0.351
0.347
0.343
0.338
0.334
0.695
0.692
0.689
0.687
0.685
1.553
1.555
1.557
1.559
1.561
2.72
2.74
2.76
2.78
2.80
0.211
0.208
0.206
0.203
0.200
2.680
2.727
2.775
2.823
2.873
0.330
0.326
0.322
0.318
0.315
0.683
0.680
0.678
0.676
0.674
1.563
1.565
1.567
1.569
1.571
0.198
0.195
0.193
0.190
0.188
2.923
2.975
3.028
3.081
3.136
0.311
0.307
0.304
0.300
0.297
0.672
0.669
0.667
0.665
0.663
1.572
1.574
1.576
1.578
1.580
0.185
0.183
0.181
0.178
0.176
3.191
3.248
3.306
3.365
3.424
0.293
0.290
0.286
0.284
0.281
0.661
0.659
0.658
0.655
0.654
1.582
1.583
1.585
1.586
1.588
2.92
2.94
2.96
2.98
3.00
En
gin
e
arn
w.
Le
ww
2.82
2.84
2.86
2.88
2.90
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
116
TABLE 8.2
Flow of perfect gases with heat transfer (γγ = 1.4)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
3.10
3.20
3.30
3.40
3.50
0.166
0.156
0.148
0.130
0.1275
3.741
4.097
4.465
4.878
5.328
0.265
0.251
0.237
0.225
0.214
0.645
0.637
0.629
0.622
0.616
1.595
1.603
1.609
1.615
1.620
3.60
3.70
3.80
3.90
4.00
0.125
0.119
0.113
0.107
0.1026
5.817
6.349
6.925
7.551
8.227
0.204
0.193
0.185
0.176
0.168
0.609
0.604
0.598
0.594
0.589
1.625
1.630
1.633
1.637
1.641
4.10
4.20
4.30
4.40
4.50
0.098
0.093
0.089
0.085
0.0818
8.958
9.747
10.598
11.515
12.502
0.161
0.154
0.147
0.141
0.135
0.585
0.581
0.577
0.573
0.569
1.645
1.647
1.653
1.654
1.656
4.60
4.70
4.80
4.90
5.00
0.078
0.075
0.072
0.069
0.0667
13.563
14.702
15.923
17.232
15.634
0.130
0.125
0.120
0.115
0.111
0.567
0.564
0.561
0.558
0.556
1.658
1.661
1.663
1.665
1.667
38.946
75.415
136.62
233.88
381.62
0.0785
0.058
0.045
0.036
0.029
0.536
0.524
0.516
0.511
0.507
1.681
1.690
1.695
1.699
1.702
En
gin
e
arn
w.
Le
0.0467
0.0345
0.0265
0.021
0.017
ww
6.00
7.00
8.00
9.00
10.00
eri
ng
.i n
M
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Heat Transfer
117
TABLE 8.3
Flow of perfect gases with heat transfer (γγ = 1.67)
(Rayleigh flow)
p0 /p0*
T/T*
0.02
0.04
0.06
0.08
0.10
2.665
2.659
2.651
2.638
2.626
1.298
1.297
1.295
1.292
1.289
0.0025
0.0113
0.025
0.044
0.069
0.0021
0.0085
0.0190
0.033
0.052
0.001
0.004
0.009
0.017
0.026
0.12
0.14
0.16
0.18
0.20
2.605
2.583
2.558
2.530
2.503
1.284
1.278
1.273
1.266
1.259
0.097
0.131
0.167
0.207
0.251
0.074
0.098
0.127
0.157
0.190
0.037
0.051
0.065
0.082
0.100
0.22
0.24
0.26
0.28
0.30
2.468
2.433
2.397
2.358
2.320
1.251
1.243
1.234
1.225
1.215
0.294
0.341
0.388
0.436
0.485
0.225
0.261
0.298
0.335
0.374
0.119
0.140
0.162
0.185
0.209
0.32
0.34
0.36
0.38
0.40
2.278
2.236
2.193
2.149
2.107
1.207
1.197
1.187
1.178
1.168
0.531
0.578
0.623
0.667
0.710
0.412
0.450
0.487
0.525
0.561
0.233
0.258
0.284
0.310
0.337
2.061
2.016
1.971
1.927
1.884
1.158
1.148
1.138
1.129
1.120
0.749
0.787
0.822
0.855
0.887
0.595
0.628
0.660
0.691
0.720
0.364
0.390
0.417
0.445
0.471
1.838
1.795
1.751
1.708
1.667
1.111
1.102
1.094
1.086
1.078
0.914
0.939
0.962
0.982
1.001
0.747
0.773
0.797
0.819
0.840
0.497
0.524
0.549
0.575
0.600
0.52
0.54
0.56
0.58
0.60
En
gin
e
arn
w.
Le
ww
eri
ng
.i n
p/p*
0.42
0.44
0.46
0.48
0.50
T0 /T0*
c/c* = ρ*/ρ
M
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
118
TABLE 8.3
Flow of perfect gases with heat transfer (γγ = 1.67)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
0.62
0.64
0.66
0.68
0.70
1.625
1.585
1.545
1.506
1.468
1.070
1.063
1.056
1.049
1.044
1.015
1.028
1.039
1.049
1.056
0.859
0.877
0.893
0.907
0.921
0.625
0.649
0.673
0.697
0.719
0.72
0.74
0.76
0.78
0.80
1.431
1.394
1.358
1.324
1.291
1.038
1.033
1.028
1.023
1.019
1.061
1.065
1.067
1.066
1.066
0.933
0.944
0.954
0.962
0.970
0.742
0.764
0.785
0.806
0.826
0.82
0.84
0.86
0.88
0.90
1.257
1.226
1.194
1.164
1.135
1.016
1.012
1.010
1.007
1.005
1.063
1.059
1.055
1.049
1.043
0.976
0.982
0.986
0.990
0.994
0.845
0.865
0.883
0.902
0.919
0.92
0.94
0.96
0.98
1.00
1.106
1.078
1.052
1.025
1.000
1.003
1.0017
1.0008
1.0002
1.000
1.036
1.028
1.019
1.009
1.000
0.996
0.998
0.999
0.999
1.000
0.936
0.953
0.969
0.985
1.000
0.975
0.951
0.928
0.906
0.884
1.0002
1.0007
1.0017
1.003
1.0046
0.989
0.979
0.968
0.957
0.945
0.999
0.999
0.998
0.997
0.995
1.015
1.029
1.043
1.056
1.070
0.863
0.842
0.822
0.803
0.784
1.0066
1.009
1.011
1.015
1.018
0.934
0.922
0.910
0.898
0.886
0.993
0.991
0.988
0.986
0.983
1.082
1.095
1.106
1.118
1.130
1.12
1.14
1.16
1.18
1.20
En
gin
e
arn
w.
Le
ww
1.02
1.04
1.06
1.08
1.10
eri
ng
.i n
M
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For More Visit : www.LearnEngineering.in
Flow of Perfect Gases with Heat Transfer
119
TABLE 8.3
Flow of perfect gases with heat transfer (γγ = 1.67)
(Rayleigh flow)
c/c* = ρ*/ρ
p/p*
p0 /p0*
T/T*
T0 /T0*
1.22
1.24
1.26
1.28
1.30
0.766
0.748
0.731
0.715
0.698
1.022
1.026
1.030
1.035
1.040
0.874
0.861
0.849
0.837
0.825
0.960
0.978
0.974
0.971
0.967
1.140
1.150
1.161
1.171
1.181
1.32
1.34
1.36
1.38
1.40
0.683
0.668
0.653
0.639
0.625
1.045
1.051
1.057
1.063
1.070
0.813
0.801
0.789
0.778
0.765
0.964
0.960
0.957
0.953
0.950
1.189
1.198
1.208
1.216
1.225
1.42
1.44
1.46
1.48
1.50
0.611
0.598
0.586
0.573
0.561
1.077
1.084
1.092
1.099
1.108
0.754
0.743
0.731
0.720
0.708
0.946
0.942
0.938
0.935
0.931
1.233
1.240
1.248
1.256
1.263
1.52
1.54
1.56
1.58
1.60
0.549
0.538
0.527
0.517
0.506
1.116
1.125
1.134
1.144
1.154
0.698
0.688
0.677
0.667
0.656
0.927
0.923
0.920
0.916
0.913
1.269
1.276
1.283
1.289
1.296
0.496
0.486
0.476
0.467
0.458
1.163
1.174
1.184
1.195
1.206
0.646
0.636
0.626
0.617
0.607
0.908
0.905
0.901
0.898
0.895
1.302
1.307
1.313
1.319
1.325
0.449
0.441
0.432
0.425
0.416
1.217
1.229
1.241
1.254
1.266
0.598
0.589
0.580
0.571
0.562
0.891
0.887
0.884
0.881
0.878
1.329
1.335
1.340
1.345
1.350
1.72
1.74
1.76
1.78
1.80
En
gin
e
arn
w.
Le
ww
1.62
1.64
1.66
1.68
1.70
eri
ng
.i n
M
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For More Visit : www.LearnEngineering.in
Gas Tables for Compressible Flow Calculations
120
TABLE 8.3
Flow of perfect gases with heat transfer (γγ = 1.67)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
1.82
1.84
1.86
1.88
1.90
0.409
0.401
0.394
0.387
0.380
1.280
1.293
1.306
1.320
1.334
0.554
0.546
0.537
0.529
0.521
0.875
0.871
0.868
0.865
0.862
1.354
1.358
1.362
1.367
1.371
1.92
1.94
1.96
1.98
2.00
0.373
0.367
0.360
0.354
0.348
1.348
1.363
1.378
1.393
1.408
0.514
0.506
0.498
0.491
0.483
0.858
0.856
0.853
0.850
0.848
1.375
1.379
1.383
1.387
1.391
2.02
2.04
2.06
2.08
2.10
0.342
0.336
0.330
0.325
0.319
1.425
1.441
1.457
1.475
1.490
0.477
0.470
0.463
0.456
0.450
0.844
0.841
0.838
0.836
0.834
1.394
1.397
1.401
1.404
1.408
2.12
2.14
2.16
2.18
2.20
0.314
0.309
0.304
0.299
0.294
1.509
1.527
1.545
1.563
1.580
0.443
0.437
0.431
0.425
0.418
0.831
0.828
0.826
0.823
0.821
1.411
1.414
1.417
1.419
1.423
0.289
0.285
0.280
0.276
0.272
1.600
1.620
1.640
1.660
1.678
0.413
0.407
0.401
0.396
0.390
0.818
0.816
0.814
0.811
0.810
1.426
1.428
1.431
1.433
1.435
0.267
0.263
0.259
0.255
0.251
1.700
1.721
1.742
1.764
1.783
0.385
0.380
0.375
0.369
0.364
0.807
0.805
0.803
0.800
0.800
1.438
1.441
1.444
1.446
1.450
2.32
2.34
2.36
2.38
2.40
En
gin
e
arn
w.
Le
ww
2.22
2.24
2.26
2.28
2.30
eri
ng
.i n
M
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Flow of Perfect Gases with Heat Transfer
121
TABLE 8.3
Flow of perfect gases with heat transfer (γγ = 1.67)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
2.42
2.44
2.46
2.48
2.50
0.248
0.244
0.241
0.237
0.233
1.807
1.830
1.853
1.876
1.897
0.359
0.355
0.350
0.345
0.341
0.796
0.795
0.793
0.791
0.789
1.450
1.453
1.455
1.457
1.459
2.52
2.54
2.56
2.58
2.60
0.230
0.227
0.223
0.220
0.217
1.923
1.947
1.971
1.996
2.018
0.336
0.332
0.328
0.324
0.319
0.786
0.785
0.783
0.781
0.780
1.461
1.460
1.465
1.467
1.469
2.62
2.64
2.66
2.68
2.70
0.214
0.211
0.208
0.206
0.203
2.050
2.073
2.098
2.125
2.148
0.315
0.311
0.307
0.304
0.299
0.778
0.776
0.774
0.773
0.772
1.470
1.472
1.474
1.476
1.477
2.72
2.74
2.76
2.78
2.80
0.200
0.197
0.195
0.192
0.189
2.179
2.207
2.234
2.263
2.287
0.296
0.292
0.288
0.285
0.281
0.769
0.768
0.767
0.765
0.764
1.479
1.481
1.482
1.484
1.485
0.187
0.185
0.182
0.180
0.178
2.320
2.350
2.379
2.409
2.435
0.278
0.275
0.272
0.268
0.265
0.762
0.761
0.759
0.758
0.757
1.487
1.488
1.489
1.491
1.492
0.175
0.173
0.171
0.168
0.167
2.471
2.502
2.533
2.565
2.587
0.262
0.259
0.256
0.253
0.250
0.755
0.754
0.753
0.751
0.750
1.494
1.495
1.496
1.498
1.500
2.92
2.94
2.96
2.98
3.00
En
gin
e
arn
w.
Le
ww
2.82
2.84
2.86
2.88
2.90
eri
ng
.i n
M
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Gas Tables for Compressible Flow Calculations
122
TABLE 8.3
Flow of perfect gases with heat transfer (γγ = 1.67)
(Rayleigh flow)
p/p*
p0 /p0*
T/T*
T0 /T0*
c/c* = ρ*/ρ
3.10
3.20
3.30
3.40
3.50
0.157
0.148
0.139
0.132
0.124
2.765
2.941
3.127
3.324
3.521
0.236
0.223
0.211
0.200
0.189
0.745
0.738
0.733
0.728
0.725
1.505
1.511
1.515
1.520
1.524
3.60
3.70
3.80
3.90
4.00
0.118
0.112
0.106
0.101
0.096
3.750
3.980
4.221
4.473
4.715
0.180
0.172
0.163
0.156
0.148
0.720
0.716
0.713
0.709
0.707
1.528
1.532
1.535
1.538
1.542
4.10
4.20
4.30
4.40
4.50
0.092
0.087
0.084
0.080
0.077
0.142
0.136
0.129
0.124
0.119
0.703
0.700
0.698
0.695
0.694
1.544
1.546
1.548
1.550
1.553
4.60
4.70
4.80
4.90
5.00
0.074
0.070
0.067
0.065
0.062
6.588
6.944
7.314
7.698
8.045
0.114
0.109
0.105
0.101
0.098
0.691
0.689
0.687
0.685
0.685
1.555
1.556
1.558
1.559
1.560
12.860
19.440
28.070
39.051
52.660
0.068
0.051
0.039
0.031
0.025
0.672
0.664
0.660
0.656
0.653
1.573
1.580
1.585
1.587
1.589
En
gin
e
arn
5.014
5.303
5.605
5.918
6.213
w.
Le
0.044
0.032
0.0248
0.0190
0.0159
ww
6.00
7.00
8.00
9.00
10.00
eri
ng
.i n
M
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Flow of Perfect Gases with Heat Transfer
123
TABLE 8.4
Maximum heat transfer in perfect gases
M
Qmax /cpT
γ = 1.4
γ = 1.67
0.00
∞
∞
∞
0.10
0.20
0.30
0.40
0.50
21.300
5.000
2.000
0.960
0.490
0.2475
0.116
0.044
0.0097
0.000
1.10
1.20
1.30
1.40
1.50
18.400
4.307
1.722
0.825
0.421
0.2368
0.111
0.0421
0.0093
0.000
0.2129
0.0994
0.0378
0.00836
0.000
0.00791
0.0292
0.0615
0.102
0.1511
0.0076
0.0280
0.0588
0.0980
0.1450
0.00682
0.0252
0.0528
0.0880
0.130
0.2065
0.268
0.337
0.411
0.489
0.1980
0.257
0.323
0.394
0.468
0.178
0.231
0.290
0.354
0.421
0.574
0.661
0.756
0.854
0.958
0.550
0.633
0.725
0.818
0.918
0.494
0.569
0.652
0.736
0.826
arn
w.
Le
2.10
2.20
2.30
2.40
2.50
ww
1.60
1.70
1.80
1.90
2.00
20.410
4.800
1.920
0.920
0.468
En
gin
e
0.60
0.70
0.80
0.90
1.00
eri
ng
.i n
γ = 1.3
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Gas Tables for Compressible Flow Calculations
124
TABLE 8.4
Maximum heat transfer in perfect gases
M
Qmax /cpT
1.067
1.179
1.298
1.419
1.546
3.50
4.00
4.50
5.00
6.00
2.245
3.060
3.978
5.000
7.397
7.00
8.00
9.00
10.00
∞
10.220
13.480
17.174
21.306
∞
γ = 1.67
1.023
1.130
1.243
1.360
1.481
0.920
1.016
1.118
1.223
1.331
2.152
2.930
3.812
4.800
7.089
1.934
2.633
3.427
4.314
6.373
9.796
12.919
16.458
20.418
∞
8.805
11.613
14.794
18.354
∞
ww
w.
Le
arn
En
gin
e
2.60
2.70
2.80
2.90
3.00
γ = 1.4
eri
ng
.i n
γ = 1.3
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Prandtl–Meyer Functions and Mach Angles
125
TABLE 9.1
Prandtl–Meyer functions and Mach angles
α
M
ω (M)
γ = 1.3
γ = 1.4
γ = 1.67
90.00
0.00
0.00
0.00
1.02
1.04
1.06
1.08
1.10
78.63
74.06
70.63
67.81
65.38
0.131
0.367
0.670
1.014
1.400
0.126
0.351
0.637
0.968
1.336
0.113
0.315
0.570
0.865
1.191
1.12
1.14
1.16
1.18
1.20
63.23
61.30
59.55
57.94
56.44
1.820
2.270
2.740
3.233
3.750
1.735
2.160
2.607
3.075
3.558
1.543
1.917
2.310
2.718
3.140
1.22
1.24
1.26
1.28
1.30
55.05
53.75
52.53
51.38
50.29
4.275
4.820
5.375
5.944
6.523
4.057
4.569
5.093
5.627
6.170
3.573
4.017
4.469
4.928
5.393
1.32
1.34
1.36
1.38
1.40
49.25
48.27
47.33
46.44
45.59
7.112
7.710
8.311
8.923
9.542
6.721
7.280
4.844
8.413
8.987
5.864
6.340
6.820
7.300
7.784
44.77
43.98
43.23
42.51
41.81
10.164
10.791
11.421
12.056
12.693
9.565
10.147
10.730
11.317
11.905
8.270
8.756
9.244
9.732
10.220
41.14
40.50
39.87
39.27
38.68
13.333
13.975
14.620
15.263
15.910
12.495
13.086
13.677
14.268
14.860
10.708
11.195
11.681
12.167
12.650
1.52
1.54
1.56
1.58
1.60
En
gin
e
arn
w.
Le
ww
1.42
1.44
1.46
1.48
1.50
eri
ng
.i n
1.00
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Gas Tables for Compressible Flow Calculations
126
TABLE 9.1
Prandtl–Meyer functions and Mach angles
α
M
ω (M)
γ = 1.3
γ = 1.4
γ = 1.67
38.12
37.57
37.04
36.53
36.03
16.556
17.203
17.850
18.500
19.144
15.452
16.043
16.633
17.222
17.810
13.131
13.611
14.089
14.564
15.037
1.72
1.74
1.76
1.78
1.80
35.55
35.08
34.62
34.18
33.75
19.790
20.435
21.080
21.723
22.360
18.397
18.982
19.565
20.146
20.725
15.508
15.976
16.441
16.903
17.363
1.82
1.84
1.86
1.88
1.90
33.33
32.92
32.53
32.13
31.75
23.004
23.644
24.281
24.916
25.550
21.302
21.877
22.450
23.020
23.586
17.820
18.273
18.723
19.170
19.614
1.92
1.94
1.96
1.98
2.00
31.39
31.03
30.68
30.34
30.00
26.181
26.805
27.435
28.060
28.681
24.151
24.712
25.271
25.827
26.380
20.054
20.491
20.925
21.355
21.782
29.67
29.35
29.04
28.74
28.44
29.300
29.915
30.530
31.120
31.750
26.930
27.476
28.020
28.561
29.097
22.206
22.626
23.042
23.455
23.865
28.15
27.86
27.58
27.31
27.04
32.350
32.952
33.561
34.150
34.750
29.631
30.161
30.690
31.212
31.733
24.271
24.674
25.073
25.468
25.860
2.12
2.14
2.16
2.18
2.20
En
gin
e
arn
w.
Le
ww
2.02
2.04
2.06
2.08
2.10
eri
ng
.i n
1.62
1.64
1.66
1.68
1.70
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Prandtl–Meyer Functions and Mach Angles
127
TABLE 9.1
Prandtl–Meyer functions and Mach angles
α
M
ω (M)
γ = 1.3
γ = 1.4
γ = 1.67
26.77
26.52
26.26
26.01
25.77
35.332
35.920
36.503
37.080
37.660
32.250
32.763
33.273
33.780
34.283
26.249
26.364
27.017
27.395
27.771
2.32
2.34
2.36
2.38
2.40
25.54
25.30
25.07
24.85
24.63
38.233
38.803
39.372
39.936
40.495
34.783
35.279
35.771
36.261
36.746
28.141
28.510
28.875
29.236
29.594
2.42
2.44
2.46
2.48
2.50
24.41
24.20
23.99
23.78
23.58
41.052
41.607
42.158
42.705
43.250
37.229
37.708
38.183
32.655
39.124
29.501
30.301
30.650
31.000
31.337
2.52
2.54
2.56
2.58
2.60
23.38
23.19
22.99
22.81
22.62
43.790
44.325
44.860
45.390
45.920
39.589
40.051
40.509
40.963
41.415
31.507
32.012
32.344
32.674
33.000
22.44
22.26
22.08
21.91
21.74
46.440
46.960
47.477
47.990
48.500
41.863
42.307
42.749
43.187
43.622
33.324
33.645
33.961
34.277
34.588
21.57
21.41
21.25
21.08
20.93
49.008
49.511
50.011
50.508
51.002
44.053
44.481
44.906
45.328
45.746
34.897
35.203
35.505
35.806
36.104
2.72
2.74
2.76
2.78
2.80
En
gin
e
arn
w.
Le
ww
2.62
2.64
2.66
2.68
2.70
eri
ng
.i n
2.22
2.24
2.26
2.28
2.30
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Gas Tables for Compressible Flow Calculations
128
TABLE 9.1
Prandtl–Meyer functions and Mach angles
α
M
ω (M)
γ = 1.3
γ = 1.4
γ = 1.67
20.77
20.62
20.46
20.32
20.17
51.490
51.980
52.463
52.943
53.420
46.161
46.573
46.982
47.388
47.790
36.398
36.691
36.980
37.267
37.551
2.92
2.94
2.96
2.98
3.00
20.03
19.89
19.75
19.61
19.47
53.895
54.365
54.831
55.300
55.758
48.190
48.586
48.980
49.370
49.757
37.832
38.111
38.387
38.661
38.932
3.05
3.10
3.15
3.20
3.25
19.14
18.82
18.51
18.21
17.92
56.900
58.020
59.120
60.202
61.266
50.713
51.650
52.569
53.470
54.355
39.600
40.252
40.890
41.513
42.122
3.30
3.35
3.40
3.45
3.50
17.63
17.37
17.10
16.85
16.60
62.311
63.341
64.350
65.341
66.318
55.222
56.073
56.907
57.726
58.530
42.720
43.301
43.871
44.430
44.975
16.36
16.13
15.91
15.68
15.47
67.277
68.220
69.150
70.060
70.954
59.316
60.092
60.850
61.595
62.327
45.510
46.032
46.544
47.045
47.535
15.26
15.05
14.86
14.67
14.48
71.833
72.700
73.551
74.388
75.210
63.044
63.748
64.440
65.118
65.785
48.015
48.485
48.946
49.397
49.840
3.80
3.85
3.90
3.95
4.00
En
gin
e
arn
w.
Le
ww
3.55
3.60
3.65
3.70
3.75
eri
ng
.i n
2.82
2.84
2.86
2.88
2.90
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Prandtl–Meyer Functions and Mach Angles
129
TABLE 9.1
Prandtl–Meyer functions and Mach angles
α
M
ω (M)
γ = 1.3
γ = 1.4
γ = 1.67
14.30
14.11
13.94
13.78
13.61
76.020
76.815
77.600
78.367
79.123
66.439
67.081
67.713
68.333
68.943
50.273
50.698
51.114
51.522
51.923
4.30
4.35
4.40
4.45
4.50
13.45
13.29
13.14
12.98
12.84
79.868
80.600
81.321
82.031
82.730
69.541
70.130
70.706
71.274
71.832
52.315
52.700
53.078
53.449
53.812
4.55
4.60
4.65
4.70
4.75
12.69
12.56
12.42
12.28
12.15
83.413
84.088
84.751
85.408
86.051
72.380
72.920
73.450
73.970
74.480
54.169
54.520
54.863
55.201
55.532
4.80
4.85
4.90
4.95
5.00
12.03
11.89
11.77
11.66
11.54
86.685
87.309
87.923
88.528
89.123
74.990
75.482
75.971
76.449
76.920
55.861
56.178
56.492
56.800
57.104
ww
w.
Le
arn
En
gin
e
eri
ng
.i n
4.05
4.10
4.15
4.20
4.25
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Gas Tables for Compressible Flow Calculations
130
TABLE 9.2
Mach numbers and Mach angles as functions of ω (M)
ω (M)
γ = 1.3
γ = 1.4
α
M
0
1.000
90.000
1.000
0.5
1.0
1.5
2.0
1.049
1.079
1.105
1.128
72.358
67.905
64.833
62.422
1.051
1.082
1.108
1.133
2.5
3.0
3.5
4.0
4.5
1.150
1.171
1.191
1.209
1.228
60.411
58.675
57.138
55.755
54.500
5.0
5.5
6.0
6.5
7.0
1.247
1.265
1.282
1.300
1.316
7.5
8.0
8.5
9.0
9.5
10.0
11.0
12.0
13.0
14.0
M
α
90.000
1.000
90.000
72.098
67.574
64.451
62.000
1.055
1.089
1.117
1.144
71.437
66.732
63.476
60.915
1.155
1.177
1.198
1.218
1.238
59.950
58.180
56.615
55.205
53.920
1.169
1.194
1.217
1.240
1.262
58.774
56.920
55.278
53.800
52.455
53.340
52.270
51.265
50.327
49.442
1.257
1.275
1.294
1.312
1.330
52.738
51.642
50.619
49.658
48.753
1.283
1.305
1.326
1.347
1.368
51.200
50.050
48.964
47.950
46.990
1.333
1.349
1.366
1.383
1.398
48.605
47.810
47.054
46.332
45.641
1.348
1.366
1.383
1.400
1.418
47.896
47.082
46.305
45.566
44.857
1.389
1.409
1.430
1.450
1.471
46.081
45.216
44.392
43.605
42.848
1.415
1.447
1.478
1.510
1.541
44.978
43.730
42.569
41.485
40.468
1.435
1.469
1.503
1.537
1.571
44.177
42.894
41.700
40.585
39.537
1.490
1.532
1.573
1.615
1.656
42.120
40.750
39.470
38.270
37.140
En
gin
e
arn
w.
Le
ww
α
eri
ng
.i n
M
γ = 1.67
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Prandtl–Meyer Functions and Mach Angles
131
TABLE 9.2
Mach numbers and Mach angles as functions of ω (M)
ω (M)
γ = 1.3
γ = 1.4
α
M
15.0
16.0
17.0
18.0
19.0
1.572
1.603
1.634
1.665
1.695
39.508
38.602
37.740
36.923
36.140
1.605
1.638
1.673
1.707
1.741
20.0
21.0
22.0
23.0
24.0
25.0
1.727
1.758
1.789
1.820
1.851
1.883
35.394
34.679
33.993
33.333
32.700
32.084
26.0
27.0
28.0
29.0
30.0
1.915
1.945
1.978
2.010
2.043
31.0
32.0
33.0
34.0
35.0
36.0
37.0
38.0
39.0
40.0
M
α
38.547
37.611
36.721
35.874
35.065
1.696
1.740
1.784
1.828
1.873
36.071
35.060
34.089
33.165
32.281
1.775
1.810
1.845
1.879
1.915
1.950
34.290
33.548
32.835
32.148
31.486
30.847
1.918
1.964
2.010
2.058
2.107
2.157
31.433
30.615
29.830
29.073
28.339
27.629
31.493
30.921
30.367
29.831
29.310
1.986
2.023
2.059
2.096
2.134
30.229
29.632
29.053
28.491
27.945
2.207
2.259
2.313
2.366
2.423
26.941
26.273
25.624
25.000
24.377
2.075
2.108
2.142
2.175
2.209
28.805
28.315
27.838
27.373
26.921
2.172
2.210
2.249
2.289
2.328
27.415
26.900
26.397
25.908
25.430
2.480
2.540
2.600
2.663
2.727
23.777
23.192
22.620
22.061
21.515
2.243
2.278
2.312
2.347
2.383
26.480
26.050
25.630
25.222
24.820
2.369
2.411
2.452
2.495
2.538
24.965
24.510
24.066
23.631
23.206
2.793
2.861
2.932
3.005
3.081
20.980
20.456
19.942
19.437
18.942
En
gin
e
arn
w.
Le
ww
α
eri
ng
.i n
M
γ = 1.67
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Gas Tables for Compressible Flow Calculations
132
TABLE 9.2
Mach numbers and Mach angles as functions of ω (M)
γ = 1.3
γ = 1.4
α
M
α
M
α
41.0
2.418
24.428
2.584
22.790
3.159
18.456
42.0
43.0
2.454
2.491
24.045
23.670
2.626
2.672
22.382
21.983
3.240
3.325
17.980
17.510
44.0
2.528
23.305
2.718
21.591
3.411
17.045
45.0
2.565
22.943
2.765
21.207
3.502
16.590
46.0
2.603
22.591
2.812
20.830
3.597
16.142
47.0
48.0
2.642
2.680
22.245
21.906
2.861
2.911
20.459
20.096
3.696
3.800
15.700
15.262
49.0
2.720
21.573
2.961
19.735
3.906
14.832
50.0
2.760
21.246
3.013
19.387
4.018
14.410
51.0
2.800
20.925
3.013
19.387
4.136
14.000
52.0
53.0
2.841
2.883
20.610
20.300
3.065
3.119
19.041
18.700
4.260
4.390
13.580
13.168
54.0
2.925
20.000
3.174
18.366
4.526
12.764
55.0
2.967
19.695
3.229
18.036
4.670
12.364
56.0
3.010
19.400
3.287
17.711
4.822
11.968
57.0
58.0
3.055
3.100
19.110
18.825
3.346
3.406
17.391
17.076
4.983
5.153
11.578
11.190
59.0
3.145
18.543
3.470
16.765
5.334
10.806
60.0
3.191
18.265
3.592
16.155
5.525
10.424
61.0
3.237
18.000
3.660
15.857
5.731
10.048
62.0
63.0
3.285
3.334
17.723
17.457
3.727
3.797
15.561
15.270
5.950
6.185
9.675
9.304
64.0
3.383
17.195
3.868
14.983
6.438
8.935
65.0
3.433
16.937
3.941
14.698
6.710
8.571
w.
Le
arn
En
gin
e
eri
ng
.i n
M
γ = 1.67
ww
ω (M)
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Prandtl–Meyer Functions and Mach Angles
133
TABLE 9.2
Mach numbers and Mach angles as functions of ω (M)
ω (M)
γ = 1.3
γ = 1.4
α
M
α
66.0
67.0
68.0
69.0
70.0
3.484
3.536
3.588
3.642
3.697
16.682
16.430
16.182
15.937
15.694
4.016
4.094
4.173
4.255
4.340
71.0
72.0
73.0
74.0
75.0
3.753
3.810
3.868
3.927
3.987
15.455
15.219
14.985
14.754
14.525
4.426
4.515
4.608
4.703
4.801
M
α
14.417
14.140
13.965
13.593
13.325
7.000
7.323
7.670
8.050
8.468
8.209
7.850
7.490
7.135
6.782
13.059
12.800
12.535
12.277
12.021
8.928
9.440
10.010
10.651
11.378
6.430
6.081
5.733
5.387
5.043
ww
w.
Le
arn
En
gin
e
eri
ng
.i n
M
γ = 1.67
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Gas Tables for Compressible Flow Calculations
134
TABLE 10.1
Approximate velocities and Mach numbers of air at p = 1.0133 bar
t = 25°C (T = 298.15 K and ρ = 1.183 kg/m3 ; a = 347.07 m/s)
Dynamic head
(mm W.G.)
Velocity (c)
m/s
Mach number
(M)
0.00
4.07
5.76
7.05
8.14
9.10
0.000
0.0117
0.0166
0.0203
0.0235
0.0262
10
15
20
25
30
12.87
15.76
18.20
20.35
22.29
0.0371
0.0454
0.0525
0.0586
0.0643
24.08
25.74
27.30
28.78
30.18
0.0694
0.0742
0.0787
0.0829
0.0270
31.53
32.81
34.05
35.25
36.40
0.0908
0.0945
0.0981
0.1015
0.1049
85
90
95
100
37.52
38.61
39.67
40.70
0.1081
0.1113
0.1143
0.1173
200
300
400
500
600
57.56
70.49
81.40
91.00
99.69
0.1658
0.2032
0.2346
0.2623
0.2873
En
gin
e
eri
ng
.i n
0
1
2
3
4
5
w.
Le
ww
60
65
70
75
80
arn
35
40
45
50
55
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Approximate Velocities and Mach Numbers of Air
135
TABLE 10.2
Approximate velocities and Mach numbers of air at p = 1.0133 bar
t = 25°C (T = 298.15 K and ρ = 1.183 kg/m3 ; a = 347.07 m/s)
Velocity (c)
m/s
Mach number
(M)
50
60
70
80
106.06
116.19
125.50
134.16
0.306
0.335
0.362
0.387
90
100
110
120
142.30
150.00
157.30
164.32
0.410
0.432
0.453
0.474
171.03
177.48
183.71
189.74
0.493
0.511
0.529
0.547
195.50
201.25
206.76
212.13
0.564
0.580
0.596
0.611
237.17
259.81
280.62
300.00
318.17
335.47
0.683
0.748
0.808
6.865
0.917
0.966
En
gin
e
eri
ng
.i n
Dynamic head
(mm Hg)
130
140
150
160
w.
Le
ww
250
300
350
400
450
500
arn
170
180
190
200
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Gas Tables for Compressible Flow Calculations
136
TABLE 10.3
Mach numbers as functions of pressure ratios (γγ = 1.4)
M
p/p0
M
1.00
0.99
0.98
0.97
0.96
0.95
0.000
0.120
0.170
0.209
0.242
0.272
0.74
0.73
0.72
0.71
0.70
0.670
0.686
0.702
0.717
0.732
0.94
0.93
0.92
0.91
0.90
0.298
0.324
0.347
0.370
0.391
0.69
0.68
0.67
0.66
0.65
0.748
0.763
0.778
0.794
0.809
0.89
0.88
0.87
0.86
0.85
0.411
0.431
0.451
0.469
0.488
0.64
0.63
0.62
0.61
0.60
0.825
0.840
0.855
0.871
0.886
0.505
0.523
0.540
0.557
0.574
0.59
0.58
0.57
0.56
0.55
0.902
0.918
0.933
0.949
0.965
0.590
0.607
0.623
0.639
0.655
0.54
0.53
0.52
0.51
0.50
0.981
0.997
1.014
1.030
1.046
En
gin
e
arn
ww
0.79
0.78
0.77
0.76
0.75
w.
Le
0.84
0.83
0.82
0.81
0.80
eri
ng
.i n
p/p0
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Pressure Ratios and Mach Numbers of Air
137
TABLE 10.3
Mach numbers as functions of pressure ratios (γγ = 1.4)
M
p/p0
M
0.49
0.48
0.47
0.46
0.45
1.063
1.080
1.097
1.114
1.132
0.24
0.23
0.22
0.21
0.20
1.587
1.615
1.645
1.676
1.709
0.44
0.43
0.42
0.41
0.40
1.150
1.168
1.186
1.204
1.223
0.19
0.18
0.17
0.16
0.15
1.742
1.778
1.815
1.855
1.897
0.39
0.38
0.37
0.36
0.35
1.242
1.262
1.282
1.302
1.322
0.14
0.13
0.12
0.11
0.10
1.941
1.989
2.040
2.096
2.157
1.344
1.365
1.387
1.410
1.433
0.09
0.08
0.07
0.06
0.05
2.225
2.300
2.385
2.484
2.601
1.457
1.481
1.506
1.532
1.560
0.04
0.03
0.02
0.01
0.00
2.746
2.935
3.208
3.693
∞
En
gin
e
arn
ww
0.29
0.28
0.27
0.26
0.25
w.
Le
0.34
0.33
0.32
0.31
0.30
eri
ng
.i n
p/p0
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Gas Tables for Compressible Flow Calculations
138
TABLE 11
Manometer inclinations required for the desired magnification of the deflection
Inclination from the horizontal
α = (sin−1 h/1) degrees
2
3
4
5
6
7
8
9
10
30
19.47
14.47
11.53
9.59
8.21
7.18
6.38
5.74
ww
w.
Le
arn
En
gin
e
eri
ng
.i n
Magnification required
(1/h)
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Static Pressure Drop in Gas Pipe Lines
139
TABLE 12.1
Static pressure drop (pr = outlet pressure/inlet pressure) in gas pipe lines
(Isothermal flow, f = 0.002 − 0.005, γ = 1.3, M1 = 0.02)
L/D
Static pressure ratio, pr = p2 /p1
f = 0.0025
f = 0.0030
10
50
100
250
400
0.9999
0.9998
0.9997
0.9995
0.9992
0.9999
0.9998
0.9997
0.9993
0.9989
0.9999
0.9998
0.9996
0.9992
0.9987
500
600
700
800
900
0.9989
0.9987
0.9985
0.9983
0.9981
0.9986
0.9984
0.9981
0.9979
0.9976
1000
2000
3000
4000
5000
0.9979
0.9958
0.9937
0.9916
0.9895
6000
7000
8000
8500
9000
0.9874
0.9853
0.9832
0.9821
0.9811
1 × 104
1.5 × 104
2.0 × 104
2.5 × 104
3 × 104
f = 0.0040
f = 0.0050
0.9999
0.9998
0.9996
0.9991
0.9985
0.9999
0.9997
0.9995
0.9989
0.9983
0.9999
0.9997
0.9995
0.9987
0.9979
0.9984
0.9981
0.9978
0.9975
0.9971
0.9982
0.9978
0.9975
0.9970
0.9967
0.9979
0.9975
0.9970
0.9967
0.9962
0.9974
0.9968
0.9963
0.9958
0.9953
0.9973
0.9947
0.9921
0.9895
0.9869
0.9968
0.9937
0.9905
0.9874
0.9842
0.9963
0.9927
0.9890
0.9853
0.9816
0.9958
0.9916
0.9874
0.9832
0.9789
0.9947
0.9895
0.9842
0.9789
0.9736
0.9842
0.9816
0.9789
0.9776
0.9763
0.9811
0.9779
0.9747
0.9731
0.9715
0.9779
0.9742
0.9704
0.9685
0.9667
0.9747
0.9704
0.9661
0.9639
0.9618
0.9683
0.9629
0.9575
0.9548
0.9520
0.9789
0.9683
0.9575
0.9465
0.9355
0.9736
0.9602
0.9465
0.9327
0.9186
0.9683
0.9520
0.9355
0.9187
0.9015
0.9629
0.9438
0.9243
0.9044
0.8841
0.9575
0.9355
0.9130
0.8899
0.8662
0.9466
0.9187
0.8899
0.8602
0.8294
4 × 104
5 × 104
6 × 104
7 × 104
8 × 104
0.9130
0.8899
0.8663
0.8419
0.8168
0.8899
0.8602
0.8295
0.7975
0.7642
0.8663
0.8295
0.7909
0.7505
0.7077
0.8419
0.7975
0.7505
0.7003
0.6462
0.8168
0.7642
0.7077
0.6462
0.5783
0.7642
0.6928
0.6132
0.5215
0.4099
1 × 105
2 × 105
0.7642
0.4098
0.6928
–
0.6132
–
0.5215
–
0.4099
–
–
–
En
gin
e
arn
w.
Le
ww
f = 0.0035
eri
ng
.i n
f = 0.0020
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Gas Tables for Compressible Flow Calculations
140
TABLE 12.2
Static pressure drop (pr = outlet pressure/linlet pressure) in gas pipe lines
(Isothermal flow, f = 0.002 − 0.005, γ = 1.4, M1 = 0.02)
L/D
Static pressure ratio, pr = p2 /p1
f = 0.0025
f = 0.0030
10
50
100
250
400
0.9999
0.9998
0.9997
0.9994
0.9991
0.9999
0.9998
0.9997
0.9993
0.9988
0.9999
0.9998
0.9996
0.9991
0.9986
500
600
700
800
900
0.9988
0.9986
0.9984
0.9982
0.9979
0.9986
0.9983
0.9980
0.9977
0.9975
1000
2000
3000
4000
5000
0.9977
0.9955
0.9932
0.9910
0.9887
6000
7000
8000
8500
9000
0.9864
0.9842
0.9819
0.9808
0.9796
1 × 104
1.5 × 104
2 × 104
2.5 × 104
3 × 104
f = 0.0040
f = 0.0050
0.9999
0.9998
0.9996
0.9990
0.9984
0.9999
0.9997
0.9995
0.9988
0.9982
0.9999
0.9997
0.9994
0.9986
0.9977
0.9983
0.9979
0.9976
0.9973
0.9969
0.9980
0.9976
0.9972
0.9968
0.9964
0.9977
0.9973
0.9968
0.9964
0.9959
0.9972
0.9966
0.9960
0.9955
0.9949
0.9972
0.9943
0.9915
0.9887
0.9859
0.9966
0.9932
0.9898
0.9864
0.9830
0.9961
0.9921
0.9882
0.9842
0.9802
0.9955
0.9910
0.9864
0.9819
0.9773
0.9944
0.9887
0.9830
0.9773
0.9716
0.9830
0.9802
0.9773
0.9759
0.9744
0.9796
0.9762
0.9727
0.9710
0.9692
0.9762
0.9721
0.9681
0.9661
0.9640
0.9727
0.9681
0.9635
0.9611
0.9588
0.9658
0.9600
0.9541
0.9512
0.9482
0.9773
0.9658
0.9541
0.9423
0.9304
0.9716
0.9571
0.9423
0.9273
0.9121
0.9658
0.9482
0.9303
0.9121
0.8935
0.9600
0.9393
0.9182
0.8967
0.8745
0.9541
0.9303
0.9059
0.8809
0.8551
0.9423
0.9121
0.8809
0.8485
0.8150
4 × 104
5 × 104
6 × 104
7 × 104
8 × 104
0.9060
0.8809
0.8551
0.8285
0.8010
0.8809
0.8485
0.8149
0.7797
0.7429
0.8551
0.8149
0.7725
0.7277
0.6800
0.8285
0.7797
0.7277
0.6717
0.6106
0.8010
0.7430
0.6800
0.6106
0.5322
0.7430
0.6633
0.5727
0.4648
0.3225
1 × 105
2 × 105
0.7429
0.3225
0.6633
–
0.5727
–
0.4648
–
0.3225
–
En
gin
e
arn
w.
Le
ww
f = 0.0035
eri
ng
.i n
f = 0.0020
–
–
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Isentropic Compressor Power
141
TABLE 13.1
Isentropic compressor power in kW (cp =1.0 kJ/kg K, T1 = 300 K, γ = 1.3)
m = mass flow rate in kg/s
1.5
2.0
3.0
4.0
5.0
1.1
1.2
1.3
1.4
1.5
6.671
12.891
18.724
24.221
29.425
10.007
19.337
28.086
36.332
44.137
13.342
25.782
37.448
48.443
58.850
20.014
38.673
56.172
72.664
88.274
26.685
51.564
74.896
96.886
117.700
33.356
64.455
93.620
121.107
147.123
1.6
1.7
1.8
1.9
2.0
34.367
39.078
43.580
47.894
52.036
51.551
58.617
65.370
71.840
78.054
68.735
78.156
87.160
95.787
104.072
103.102
117.234
130.740
143.681
156.108
137.470
156.312
174.320
191.574
208.144
171.837
195.390
217.900
239.468
260.180
2.1
2.2
2.3
2.4
2.5
56.022
59.864
63.575
67.163
70.638
84.033
89.796
95.362
100.744
105.957
112.044
119.729
127.149
134.326
141.276
168.065
179.593
190.724
201.489
211.914
224.087
239.457
254.299
268.652
282.552
280.109
299.321
317.873
335.815
353.190
2.6
2.7
2.8
2.9
3.0
74.008
77.279
80.459
83.552
86.564
111.011
115.919
120.688
125.328
129.846
148.015
154.558
160.917
167.104
173.128
222.023
231.837
241.376
250.656
259.693
296.031
309.116
321.835
334.208
346.257
370.038
386.396
402.293
417.760
432.822
3.5
4.0
4.5
5.0
5.5
100.563
113.098
124.479
134.926
144.598
150.844
169.646
186.719
202.389
216.897
201.125
226.195
248.959
269.852
289.196
301.688
339.293
373.438
404.779
433.794
402.250
452.390
497.917
539.705
578.391
502.813
565.488
622.397
674.631
722.990
6.0
7.0
8.0
9.0
10.0
153.615
170.041
184.751
198.107
210.365
230.423
255.062
277.126
297.160
315.548
307.230
340.083
369.501
396.213
420.731
460.845
510.124
554.252
594.320
631.096
614.460
680.165
739.002
792.426
841.462
768.075
850.207
923.753
990.533
1051.827
w.
Le
arn
En
gin
e
eri
ng
.i n
1.0
ww
pr = p2 /p1
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Gas Tables for Compressible Flow Calculations
142
TABLE 13.2
Isentropic compressor power in kW (cp =1.0 kJ/kg K, T1 = 300 K, γ = 1.4)
m = mass flow rate in kg/s
1.5
2.0
3.0
4.0
5.0
1.1
1.2
1.3
1.4
1.5
8.281
16.041
23.351
30.271
36.845
12.422
24.061
35.027
45.406
55.268
16.563
32.082
46.703
60.541
73.690
24.844
48.123
70.054
90.812
110.536
33.124
64.164
93.406
121.083
147.381
41.406
80.205
116.757
151.353
184.227
1.6
1.7
1.8
1.9
2.0
43.114
49.109
54.856
60.380
65.700
64.671
73.663
82.285
90.571
98.551
86.228
98.217
109.713
120.761
131.401
129.342
147.326
164.569
181.141
197.101
172.456
196.434
219.425
241.522
262.802
215.570
245.543
274.282
301.902
328.502
2.1
2.2
2.3
2.4
2.5
70.834
75.795
80.598
85.254
89.774
106.251
113.693
120.898
127.882
134.661
141.668
151.591
161.197
170.509
179.548
212.501
227.386
241.795
255.763
269.322
283.335
303.181
322.393
341.018
359.095
354.169
378.977
402.992
426.272
448.869
2.6
2.7
2.8
2.9
3.0
94.166
98.439
102.600
106.657
110.615
141.249
147.659
153.901
159.986
165.922
188.332
196.878
205.201
213.314
221.230
282.498
295.317
307.801
319.971
331.845
376.664
393.756
410.402
426.628
442.460
470.830
492.195
513.002
533.286
553.075
3.5
4.0
4.5
5.0
5.5
129.103
145.789
161.046
175.135
188.251
193.654
218.684
241.569
262.702
282.376
258.206
291.579
322.092
350.270
376.501
387.309
437.368
483.137
525.405
564.7521
516.412
583.158
644.183
700.540
753.003
645.515
728.947
805.229
875.675
941.253
6.0
7.0
8.0
9.0
10.0
200.540
223.077
243.418
262.016
279.190
300.810
334.616
365.127
393.023
418.785
401.081
446.154
486.836
524.031
558.381
601.621
669.232
730.254
786.047
837.570
802.161
892.309
973.672
1048.062
1116.761
1002.702
1115.386
1217.090
1310.078
1395.951
w.
Le
arn
En
gin
e
eri
ng
.i n
1.0
ww
pr = p2 /p1
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Pumping Power for Fans and Blowers
143
TABLE 14
Approximate values of pumping power (kW) for fans and blowers
∆p = Pressure rise in millimeters W.G.
1
2
0.0015
0.0030
0.0045
0.0060
0.0075
0.0030
0.0060
0.0091
0.0121
0.0151
1.0
1.2
1.4
1.6
1.8
0.0151
0.0181
0.0211
0.0241
0.0272
0.0302
0.0362
0.0423
0.0483
0.0543
2.0
2.5
3.0
3.5
4.0
0.0302
0.0377
0.0453
0.0528
0.0604
5.0
10.0
20.0
50.0
100
0.0755
0.1509
0.3018
0.7546
1.5092
1000
1500
2000
2500
3000
5
0.0060
0.0121
0.0181
0.0241
0.0302
0.0075
0.0151
0.0226
0.0302
0.0377
0.0453
0.0543
0.0634
0.0724
0.0815
0.0604
0.0724
0.0845
0.0966
0.1087
0.0755
0.0906
0.1056
0.1207
0.1358
0.0604
0.0755
0.0906
0.1056
0.1207
0.0906
0.1132
0.1358
0.1585
0.1811
0.1207
0.1509
0.1811
0.2111
0.2415
0.1509
0.1886
0.2264
0.2641
0.3018
0.1509
0.3018
0.6037
1.5092
3.0184
0.2264
0.4528
0.9055
2.2638
4.5276
0.3018
0.6037
1.2073
3.0184
6.0367
0.3773
0.7546
1.5092
3.7730
7.5460
2.2638
3.0184
6.0367
9.0551
12.0735
4.5276
6.0367
12.0735
18.1102
24.1469
6.7913
9.0551
18.1102
27.1653
36.2204
9.0551
12.0735
24.1469
36.2204
48.2939
11.3189
15.0918
30.1837
45.2755
60.3673
15.0918
22.6378
30.1837
37.7296
45.2755
30.1837
45.2755
60.3673
75.4592
90.5510
45.2755
67.9133
90.5510
113.1888
135.8265
60.3673
90.5510
120.7347
150.9183
181.1020
75.4592
113.1888
150.9183
188.6479
226.3775
arn
w.
Le
ww
150
200
400
600
800
4
0.0045
0.0091
0.0136
0.0181
0.0226
En
gin
e
0.1
0.2
0.3
0.4
0.5
3
eri
ng
.i n
Q (m 3 /s )
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Gas Tables for Compressible Flow Calculations
144
TABLE 14
Approximate values of pumping power (kW) for fans and blowers
∆p = Pressure rise in millimeters W.G.
10
20
0.0151
0.0302
0.0453
0.0604
0.0755
0.0302
0.0604
0.0906
0.1207
0.1509
1.0
1.2
1.4
1.6
1.8
0.1509
0.1811
0.2113
0.2415
0.2717
0.3018
0.3622
0.4226
0.4829
0.5433
2.0
2.5
3.0
3.5
4.0
0.3018
0.3773
0.4528
0.5282
0.6037
5.0
10.0
20.0
50.0
100
0.7546
1.5092
3.0184
7.5459
15.0918
1000
1500
2000
2500
3000
50
0.0604
0.1207
0.1811
0.2415
0.3018
0.0755
0.1509
0.2264
0.3018
0.3773
0.4528
0.5433
0.6339
0.7244
0.8150
0.6037
0.7244
0.8451
0.9659
1.0866
0.7546
0.9055
1.0564
1.2073
1.3583
0.6037
0.7546
0.9055
1.0564
1.2073
0.9055
1.1319
1.3583
1.5846
1.8110
1.2073
1.5092
1.8110
2.1129
2.4147
1.5092
1.8865
2.2638
2.6411
3.0184
1.5092
3.0184
6.0367
15.0918
30.1837
2.2638
4.5276
9.0551
22.6378
45.2755
3.0184
6.0367
12.0735
30.1837
60.3673
3.7730
7.5459
15.0918
37.7296
75.4592
22.6378
30.1837
60.3673
90.5510
120.7347
45.2755
60.3673
120.7347
181.1020
241.4693
67.9133
90.5510
181.1020
271.6530
362.2040
90.5510
120.7347
241.4693
362.2040
482.9387
113.1888
150.9183
301.8367
452.7550
603.6733
150.9183
226.3775
301.8367
377.2958
452.7550
301.8367
452.7550
603.6733
754.5917
905.5100
452.7550
679.1325
905.5100
1131.8876
1358.2650
603.6733
905.5100
1207.3467
1509.1833
1811.0200
754.5917
1131.8876
1509.1833
1886.4792
2263.7751
arn
w.
Le
ww
150
200
400
600
800
40
0.0453
0.0906
0.1358
0.1811
0.2264
En
gin
e
0.1
0.2
0.3
0.4
0.5
30
eri
ng
.i n
Q (m 3 /s )
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Pumping Power for Fans and Blowers
145
TABLE 14
Approximate values of pumping power (kW) for fans and blowers
∆p = Pressure rise in millimeters W.G.
100
200
0.1509
0.3018
0.4528
0.6037
0.7546
0.3018
0.6037
0.9055
1.2073
1.5092
1.0
1.2
1.4
1.6
1.8
1.5092
1.8110
2.1129
2.4147
2.7165
3.0184
3.6220
4.2257
4.8294
5.4331
2.0
2.5
3.0
3.5
4.0
3.0184
3.7730
4.5276
5.2821
6.0367
5.0
10.0
20.0
50.0
100
7.5459
15.0918
30.1837
75.4592
150.9183
1000
1500
2000
2500
3000
500
0.6037
1.2073
1.8110
2.4147
3.0184
0.7546
1.5092
2.2638
3.0184
3.7730
4.5276
5.4331
6.3386
7.2441
8.1496
6.0367
7.2441
8.4514
9.6588
10.8661
7.5459
9.0551
10.5643
12.0735
13.5827
6.0367
7.5459
9.0551
10.5643
12.0735
9.0551
11.3189
13.5827
15.8464
18.1102
12.0735
15.0918
18.1102
21.1286
24.1469
15.0918
18.8648
22.6378
26.4107
30.1837
15.0918
30.1837
60.3673
150.9183
301.8367
22.6378
45.2755
90.5510
226.3775
452.7550
30.1837
60.3673
120.7347
301.8367
603.6733
37.7296
75.4592
150.9183
377.2958
754.5917
226.3775
301.8367
603.6733
905.5100
1207.3467
452.7550
603.6733
1207.3467
1811.0200
2414.6934
679.1325
905.5100
1811.0200
2716.5300
3622.0400
905.5100
1207.3467
2414.6934
3622.0400
4829.3867
1131.8876
1509.1833
3018.3667
4527.5503
6036.7334
1509.1833
2263.7751
3018.3667
3772.9585
4527.5503
3018.3667
4527.5503
6036.7334
7545.9170
9055.1006
4527.5503
6791.3252
9055.1006
11318.8750
13582.6504
6036.7334
9055.1006
12073.4668
15091.8340
18110.2012
arn
w.
Le
ww
150
200
400
600
800
400
0.4528
0.9055
1.3583
1.8110
2.2638
En
gin
e
0.1
0.2
0.3
0.4
0.5
300
eri
ng
.i n
Q (m 3 /s )
7.546 MW
11.319 MW
15.092 MW
18.865 MW
22.638 MW
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Gas Tables for Compressible Flow Calculations
146
TABLE 14
Approximate values of pumping power (kW) for fans and blowers
∆p = Pressure rise in millimeters W.G.
600
700
0.1
0.2
0.3
0.4
0.5
0.9055
1.8110
2.7165
3.6220
4.5276
1.0564
2.1129
3.1693
4.2257
5.2821
1.0
1.2
1.4
1.6
1.8
9.0551
10.8661
12.6771
14.4882
16.2992
10.5643
12.6771
14.7900
16.9029
19.0157
2.0
2.5
3.0
3.5
4.0
18.1102
22.6378
27.1653
31.6929
36.2204
5.0
10.0
20.0
50.0
100
45.2755
90.5510
181.1020
452.7550
905.5100
1000
1500
2000
2500
3000
1000
1500
1.5092
3.0184
4.5276
6.0367
7.5459
2.2638
4.5276
6.7913
9.0551
11.3189
12.0735
14.4882
16.9029
19.3175
21.7322
15.0918
18.1102
21.1286
24.1469
27.1653
22.6380
27.1653
31.6930
36.2204
40.7480
21.1286
26.4107
31.6929
36.9750
42.2571
24.1469
30.1837
36.2204
42.2571
48.2939
30.1837
37.7296
45.2755
52.8214
60.3673
45.2755
56.5944
67.9133
79.2321
90.5510
52.8214
105.6428
211.2857
528.2142
1056.4283
60.3673
120.7347
241.4693
603.6733
1207.3467
75.4592
150.9183
301.8367
754.5917
1509.1833
113.1888
226.3780
452.7550
1131.8876
2263.7751
1358.2650
1811.0200
3622.0400
5433.0601
7244.0801
1584.6426
2112.8567
4225.7134
6338.5703
8451.4268
1811.0200
2414.6934
4829.3867
7244.0801
9658.7734
2263.7751
3018.3667
6036.7334
9055.1006
12073.4668
3395.6626
4527.5503
9055.1006
13582.6504
18110.2012
9055.1006
13582.6504
18110.2012
22637.7500
27165.3008
10564.2832
15846.4258
21128.5664
26410.7090
31692.8516
12073.4668
18110.2012
24146.9336
30183.6680
36220.4023
w.
Le
arn
En
gin
e
1.2073
2.4147
3.6220
4.8294
6.0367
ww
150
200
400
600
800
800
eri
ng
.i n
Q (m 3 /s )
15.091 MW
22.637 MW
30.184 MW
37.729 MW
45.275 MW
22.637 MW
33.957 MW
45.275 MW
56.594 MW
67.913 MW
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S.I. Metric and British Units
147
TABLE 15.1
S.I, Metric and British units
Principal dimensions and units
S.I.
Metric
British
Length
Mass
Time
Temperature
Area
Volume
Density
Force
Torque
Velocity
Acceleration
Pressure
Work and energy
Heat
Specific heat
Power
Specific entropy
Dynamic viscosity
L
M
T
θ
L2
L3
M/L3
ML/T2
ML2/T2
L/T
L/T2
M/LT2
ML2/T2
ML2/T2
L2/T2θ
ML2/T3
L2/T2θ
M/LT
m
kgm
sec
°K
m2
m3
kgm/m3
kgf
m kgf
m/sec
m/s2
kgf/m2
kgf m
cal
cal/kgm °K
kgf m/s
cal/kgm °K
kgf-sec/m2
ft
lbm
sec
°R
ft2
ft3
Ibm/ft3
lbf
ft lbf
ft/sec
ft/sec2
lbf/ft2
ft lbf
Btu
Btu/lbm °R
ft lbf/sec
Btu/lbm °R
lbf-sec/ft2
Kinematic viscosity
Weight
L2/T
ML/T2
m
kg
s
K
m2
m3
kg/m3
N = kg m/s2
mN
m/s
m/s2
Pa = N/m2
J = Nm
Joule = J
J/kg K
Nm/s, J/s
J/kg K
Ns/m2
kg/ms
m2/s
N = kg m/s2
m2/sec
kgf
ft2/sec
lbf
arn
En
gin
e
eri
ng
.i n
Dimensions
ww
w.
Le
Quantity
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Gas Tables for Compressible Flow Calculations
148
TABLE 15.2
Conversion of units
=
=
=
=
=
=
=
3.28 ft
0.3937 in
0.6215 mile
30.48 cm
2.54 cm
1.609 km
6076 ft = 1.853 km
Area
1 m2
1 cm2
1 ft2
1 in2
=
=
=
=
10.765 ft2
0.155 in2
0.0929 m2
6.452 cm2
=
=
=
1 m bar
=
=
1 mm W.G. =
1 torr
=
=
1 atmosphere =
=
=
Density
1 kg/m3
1 lbm/ft3
arn
En
gin
e
Volume
1 m3
= 1000 litres = 35.315 ft2
1 litre = 1000 cc = 0.001 m3 = 0.0353 ft3
1 cc
= 0.061 in3
3
1 ft
= 0.0283 m3 = 28.328 litres
3
1 in
= 16.387 cm3
1 gallon (British) = 8 pints = 4.546 litres
= 0.160 ft3 = 277.3 in3
1 pint = 568.25 cc
Pressure
1 bar
Temperature
F − 32
1.8
= 1.8 °C + 32
= 273.15 + °C = Kelvins (in S.I. Units)
= 459.4 + °F = 1.8 °K
o
°F
°K
°R
=
ww
°C
w.
Le
Mass
1 kgm = 2.204 lbm
1 lbm
= 0.4537 kgm
1 metric ton (tonne) = 0.984 ton
Force
1N
= 105 dynes = 0.102 kgf = 0.2248 lbf
1 kgf
= 9.807 N = 2.204 lbf
1 metric ton = 1000 kgf
1 lbf
= 4.448 N = 0.4537 kgf
Velocity
1 m/s
1 km/hr
1 mile/hr
1 ft/sec
1 knot
=
=
=
=
=
3.28 ft/sec
0.621 mile/hr
1.609 km/hr
0.305 m/s
1.689 ft/sec = 0.515 m/s
105 N/m2 = 105 Pa = 100 kN/m2
0.1 MN/m2 = 1.0197 kgf/cm2
14.504 lbf/in2
10-3 bar = 100 N/m2 = 100 Pa
10.2 mm W.G.
1 kgf/m2 = 9.807 N/m2 = 0.098 m bar
1 mm Hg = 13.6 mm W.G. = 133.38N/m2
1.334 m bar
1.013 bar = 1.033 kgf/cm2
14.696 lbf/in2 = 29.921 in Hg
760 mm Hg = 10.336 m W.G.
eri
ng
.i n
Length
1m
1 cm
1 km
1 ft
1 in
1 mile
1 nautical mile
= 0.0624 lbm/ft3
= 16.025 kg/m3
Work and Energy
1 Nm
= 1 Joule = 107 ergs
= 0.102 kgf m = 0.7374 ft lbf
1 kgf m = 9.807 Nm = 7.229 ft lbf
1 ft lbf
= 0.1383 kgf m = 1.356 Nm = 1.356 J
Heat
1 kJ
1 k cal
1 Btu
Power
1 Nm/s
1 kW
= 1000 J = 0.2388 k cal = 0.9478 Btu
= 427 kgf m = 4.187 kJ = 3.968 Btu
= 778 ft lbf = 1.055 kJ = 0.252 k cal
= 1 J/s = 1 watt
= 0.102 kgf m/sec = 0.7375 ft lb/sec
= 1000 J/s = 102 kgf m/sec = 737.5 ft lbf/sec
= 1.36 metric H.P. = 1.34 H.P. (FPS)
1 metric H.P. = 75 kgf m/sec = 0.735 kW = 0.985 H.P.
1 H.P. (FPS) = 550 ft lb/sec = 1.015 metric H.P.
= 0.746 kW
Dynamic Viscosity
1 Ns/m2
= 1 kg/ms = 0.102 kgf/m2
= 0.0209 lbf sec/ft2 = 10 poise
1 lbf sec/ft = 47.847 Ns/m2
Kinematic Viscosity
1 m2/s = 10.76 ft2/sec = 104 cm2/sec = 104 Stokes
1 ft2/sec = 0.0929 m2/s
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