Problem 3.53
Given:
Geometry of plane gate
Find:
[3]
Minimum weight to keep it closed
L=3m
h
y
L/2
dF
W
w=2m
Solution:
FR
dp
dh
p dA
or, use computing equations
g
MO
FR
Basic equation
pc A
y'
0
Ixx
yc
A yc
Assumptions: static fluid; = constant; patm on ot
Problem *4.122
[3]
CS (moves
at speed U)
y
x
Rx
Ry
Given:
Water jet striking moving vane
Find:
Force needed to hold vane to speed U = 5 m/s
Solution:
Basic equations: Momentum flux in x and y directions
Assumptions: 1) Steady flow 2) Incompressible flow 3
Problem 6.52
[2]
h1 =
H=
(h2)
Given:
Flow through tank-pipe system
Find:
Velocity in pipe; Rate of discharge
Solution:
Basic equation
2
p
V
2
gz
p
const
g h
Q
VA
Assumptions: 1) Incompressible flow 2) Inviscid 3) Steady 4) Along a streamline
Hence, apply
Problem 2.9
Given:
Velocity field
Find:
[2]
Equation for streamline through (1,3)
Solution:
y
A
dy
dx
2
For streamlines
v
u
x
So, separating variables
dy
y
Integrating
ln ( y)
The solution is
y
Cx
which is the equation of a straight line.
For the streamli
MAE 2315
Fluid Dynamics
Fall 2014
Potential Flows
Basic Potential Flows
Uniform Flow
2-D, Incompressible, Irrotational
Cylindrical coordinates
(r , ) Ur cos( )
(r , ) Ur sin( )
Cartesian coordinates
( x, y ) U x cos( ) y sin( )
( x, y ) U y cos( ) x
Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#1 Solutions
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Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#2 Solutions
1
2
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4
Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#3 Solutions
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5
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Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#4 Solutions
1
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3
4
5
Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#5 Solutions
1
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4
5
Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#6 Solutions
1
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3
4
5
Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#7 Solutions
1
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3
4
5
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Rutgers, The State University of New Jersey School of Engineering
Department of Mechanical and Aerospace Engineering
14:650:312 Fluid Mechanics- Fall 2014
HW#8 Solutions
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