EGM 6812 – Fluid Mechanics 1 – Fall 2010
1/8
HW 3
3
rd
Homework
Problem 1:
A jet of water that is declined at an angle
is filling a moving water car.
The water car is
moving away from the jet at a constant velocity
U
and possesses a diameter
D
.
The liquid level
in the car is
()
ht
.
The jet has a diameter
d
and a uniform velocity
jet
U
.
A frictional force
F
is acting on the car.
Assume that the jet is always filling the car and ignore sloshing.
1.
Draw an appropriate control volume, explicitly stating unit normal vectors and flux areas.
2.
List your assumptions required to solve this problem.
3.
What are the pressure boundary conditions on your control volume?
4.
What is the time rate of change of the liquid level?
5.
What is the thrust force acting on the car by the jet of water?
6.
What is the frictional force acting on the car?
F
U
D
d
jet
U
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2/8
HW 3
Problem 2:
Given:
A vane with a turning angle
, is attached to a block which is sliding on a thin oil
flilm at a terminal velocity
,
T
U
, in the xdirection is shown below.
Water from a constantarea nozzle,
N
A
, flows over the vane with a known uniform
velocity,
N
V
, that is unchanged
as it flows over the vane.
The oil film possesses a viscosity
oil
and is of thickness
h
.
The frictional forces
from the film induce a net force
x
F
that opposes the block motion.
The block possesses a wetted surface area with the film of
B
A
.
Answers b) through d) should be expressed in terms of
N
A
,
2
A
,
N
V
,
x
F
,
oil
,
water
,
h
,
B
A
, and
(
note that all variables may not be needed for each answer).
Find:
a)
List the appropriate assumptions.
b)
Find an algebraic expression for
2
A
(be sure to draw a control volume).
c)
Assume a linear velocity profile in the gap between the sliding block and the solid
surface as a function of
T
U
and determine
x
F
d)
Starting with a momentum balance on the block, determine an algebraic expression
for
T
U
.
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 Fall '09
 RENWEIMEI
 Fluid Dynamics, Fluid Mechanics, Force, Dh, U T

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