EQUATIONS
A
↓ ->Vol
RELATIONS
v
-
>
of
body
velocity
Streamwise - Normal Accel
as
2
VE,
=
an=-
IR
Force Balance
( Iv y
+
viscosity
[M]
Invisid
M
=.
=
Kinematic
neg viscosity
Pressure Gradient
p
I
=kg
=
Stationary
-
-
Normal
steady,
to
inviscid,
Incompressible flow
=
-
C
S
Distribution
of pressure
RR
-
Variation
-
2k Pz
=
n
Stationary, Incompressible
zocos
= -
+
Force
-
Force Balance
Location of
p
Hydrostatic
=
+
1
=
0)
+
Force
(n
=
Continuity Equation
A,Vi=
AzV2,
Xc
Normal, steady,
2z
c,(Algs)
=
(Flow Rate)
Q1 Q2
=
+
yaA
N
Broyant Force
Es 2F,
Yc
-
Incompressible, Inviscid
Plane surface
=
=
=
streamline for
Fluid
Fr UhcA
XR
CAIng5)
vz C,
+
Pressure Gradient
S
-
BV
+
=
Hydrostatic
YR
c,(angs)
Bernoulli Equation
Pa.s
=
Pi
or
=
=
+
=
Viscosity
v
(U) 2
Pressure
No
U
=
E
->
Streamline, inviscid
-
F
I
=
IE
+
Equation
E H c,
+
=
vol
body
of
A
Total Head
=
(Along
montion
Islug
32.1141bM
=
P
85
streamline
along strl
zV
=
-
AVEs
Conservation
t
Pressure
Mass
of
cdt+Jast.dA
P21P,
0
=
D2/P1
expE-[9(ze-z,1]/RTo
=
in
=
-
((((zz z,1)/Pi)
-
of
4
+
Quet,in+Wshaft,
Find
is
A
=
=
Mass
-
Incomp
Energy
=
Average Velocity
Conservation of
1
(2+ (,(k
SQ SAV
=
comp
=
Conservation
Mass Flowrate
Ratio
* gz)p.SA
+
net in
[hou-hin+mtvin-g(Zort-Zin)]
Steady
Imont- [iin 0
=
Conservation of Mass
-
Control Volume
Sct=Jw.dA
Conservation of Mass
-
o
=
Deforming
⑪=S**:Jew.
Volume
dA
=
es
Force->
Change
in
Linear Momentum
Fluid w/const
Jedt+ScsYs.ndA=IF
Force->
Change
in
Linear Momentum
ScsWeW.ndA= IE
Shaft Torque from Force
I((xE]:Isnaft
-
Gas, density
density
--
incomp
changes--comp
CV
Mass Flowrate
Through
Control Surface
J.P.REA=I rou-2min
Differential
Analysis
of Fluid
vorticity
Flow
I zw
=
Rotation
Dialation Rate
Rate increase
per
Rate of
Rate
I
strain
shearing
Deformation
or
Angular
of
+
=
5v
=
=
-
wz
(-
=
conservation of Mass
Steady
IE
state
=
Cylindrical
Stream Functions
a
volume
unit volume
Wx=g eee
Polar Coordinates
IF
E
2
Steady
State
->
0
=
-x
Equations
Velocity components
of
Motion
BernoulliEquation
++
z
=
+
For
Velocity
Ev w =
potential
n
vr
=
4vov2 =
=
+
+
inviscid flow
shearing
=
I (re)
Euler's Equations of Motion
=
stress -
o
Uniform Flow
u
Ucosx
=
v vsinx
=
2
=
=
=
b v(xcosx
=
+
=
-
ysinx)
4 v(ycos2 -xsinx)
=
Source- Sink
m
->
rol flow
per unit
rate
(2Ar)Ur M,
=
+
m,
V
Nr
source
2
=
-
r,
2
M,
No
0
=
sink
=2r
=
-
vo t
=
length
e
=
0
-
=
deer
Vortex
Yr
Vo
p
4
vr 0
=
(irc: T 2πk
=
=
kQ
=
=
-
k
k2r
=
Combined Vortex
Vo
ar
=
Above
Doublet
r
r
ro
>
ro->
central
to
Sourcet Sink
:Rico
k
Get ais
vergin
el
an
=
core
Half
Body
↓=
UrcosO+
4
UrsinO
=
Nr
+O
2
Ur UCOSO +m/z
=
Lur
Vo=- USinQ
Distance from source
Rankine Ovals
to
stagnation point:b
2F,
=
U=2
s
Flow around
4 Ur(1-2)
=
a
cylinder
sin
4 Ur(r-cost
=
Ursin O- (A-0r)
↑=
&=UrCosO- (Inr-Intel
Navier Stokes
Laminar Flow
Equations
Between two
Fixed plates
u
(yz
=
=
n2)
-
=
9
Lorette Flow
Dimensional Scales
1:200
icl
Dimensional
=
n-r
L
-
model:1
I
=
20
Analysis Modeling
of i terms
#
=
FLT
P
Ref dimensions
# of variables
proto:
MLT
FL-3
M23 +
L
D
L
FL- 4T2
P
M
FL-2T
v
LT-1
⑨
↳3 T-1
ML 3
-
M2 T
-
-
LT
L3T
-
9
LT-2
LT- 2
+
T
T
v22
-1
+
1
1
L
L
U FL-3
-
L
2
h
-
M22
22
+
-
1
+
e
1
3
200
Viscous Flow
in
Pipes
Reynolds' Number
Re
Re
DVD
=-
a
<2100
Friction
Op
Factor
fe
=
Flowrate
mean
Energy
velocity
Considerations
( +
(
)
z,
+
-
Zet
+
=hu
n=
haminor-hamajor
4000
[ReS
TurbulentTransit
Laminar
Velocity
2100
Re >4000
was
g
minor Loss
huminor
=
KnE