CHEG 232-Fluid
Mechanics
Lecture 8
DR. MARYAM K HAL EEL
RESPEC TI V E MATERIAL F RO M TH E TEXTB O O K : PG. 183 – 194
Turbulent Flow
Turbulent Flow in Smooth Pipe
Turbulent Flow in Smooth Pipe
Turbulent Flow in Rough Pipe
Moody Plot
As ԑ/D increases, f becomes a
constant independent of
density, viscosity, velocity,
diameter
Friction Factor
Example
Read the value of the friction factor form for R=10^5 and ԑ/D=0.0002 and compare that value to
the value from the following equation
+ 10! = 0.001375 1 + 20000 +
,
.
! ≈ 0.0047
//1
The Three Friction Factor Problems
300
Commercial steel
What is the gauge pressure in tank A
required to produce this flow rate?
Apply B.E. (negligible velocities, no change in elevation, no
shaft work), assume constant density
∆"
= −ℱ
#
How can we get ℱ ? This is 6 times the velocity at 50
gal/min
#'4
This makes the
' = 6 ∗ 2.17.//1 = 13 .//1
3=
= 6 ∗ 1028 = 6168 > 4000
flow turbulent
5
: 0.0018 ;<
=
= 0.0006
4
3.068 ;<
. ≈ 0.0091
This is 21 times the pressure drop
for laminar flow at 50 gal/min
Apply B.E. (negligible velocities, ∆"=0, no shaft work), assume
constant density
∆* , ∆ #$ = −ℱ = −4)
+ 2
/ 0.0018 45 1 6
=
= 0.00046
+
0.1 6 39.37 45
/ 10=
) = 0.001375 1 + 20000 +
+
>
?/A
For turbulent flow f is between
0.0042 and 0.008
1- Assume f
2- Calculate V
3- Calculate f
∆ #$ = −4)
2 unknowns: V and f
Either solve the 2 equations
using a computer or solve by
trial and error
∆B D E
C -
) = 0.001375 1 +
F
20000 C
+
?GH
I
4- Repeat steps 2 and 3 until successive values of f match
?/A
You can use goal
seek in excel
Example
We want to transport 500 ft^3/min of air horizontally from our air conditioner to an outbuilding
800 ft away. The air is at 40 F and a pressure of 0.1 psig. At the outbuilding the pressure is to be
0 psig. We will use a circular sheet metal duct, which has a roughness of 0.00006 in. Find the
required duct D.
Apply B.E. from the inlet to the outlet (negligible velocities, no change in
elevation, no shaft work), assume constant density approximation (good
assumption for gases at low velocities)
3 unknowns: D, V and f
Either solve the 3 equations
using a computer or solve by
trial and error
Assume ideal gas (calculate density at the average pressure)
489:
?@#
?@F
∗
29
;<
?@F
?@FG?
ABC
=
=
=
0.08
∘
∘
3= 10.73 ?@# #H 2 /(ABC ?@FG? 3) ∗ 500 3
#H 2
14.75
1- Assume D
!
2- Calculate
"
3- Calculate V
4- Calculate R
5- Calculate f
456
7
!
-./
# = 0.001375 1 + 20000 +
3=
"
0
-/2
(or read it from Moody’s plot)
6- Calculate ΔP
7- Repeat steps 1 to 7 until we get ΔP=0.1 psi
You can use goal
seek in excel