Homework 3
Fluid Mechanics CE 3502 Fall, 2008
(1) Water strikes a block as shown and is deflected 30°.
The flow rate of the water
is 1.50 kg/s, and the mass of the block is 1.30 kg.
The coefficient of static
friction between the block and the surface is 0.100 (friction force / normal force).
If the force parallel to the surface exceeds the frictional force, the block will move.
Find the maximum initial velocity (V) such that the block will not slip.
Neglect the
weight of the water.
Find: maximum initial water velocity (V) such that the block will not slip.
Solution:
Use conservation of momentum for the stationary control volume with control
surface as shown:
Force / Free body diagram
Momentum diagram
W
block
F
normal
F
friction
30°
V
m
&
V
m
&
Conservation of momentum in the x
‐
direction:
(
)
(
)
∑
∑
∫
∑
−
+
ρ
=
CS
IN
x
CS
OUT
x
CV
x
x
v
m
v
m
V
d
v
F
&
&
For the one inlet and outlet, as shown, V
IN
= V
OUT
, so given the information in the drawing: v
x,IN
= V, and v
x,OUT
= Vcos30°
There is no accumulation in the control volume, so
(
)
(
)
(
)
(
)
V
2
3
1
s
/
kg
50
.
1
F
V
s
/
kg
50
.
1
2
3
V
s
/
kg
50
.
1
0
F
friction
friction
−
=
⇒
−
+
=
−
Conservation of momentum in the y
‐
direction:
(
)
(
)
∑
∑
∫
∑
−
+
ρ
=
CS
IN
y
CS
OUT
y
CV
y
y
v
m
v
m
V
d
v
F
&
&
v
y,IN
= 0, and v
y,OUT
= Vsin30°, and there is no accumulation in the control volume, so
(
)
(
)
(
)
(
)
(
)
(
)
N
75
.
12
V
s
/
kg
.75
0
s
/
m
81
.
9
kg
30
.
1
V
s
/
kg
.75
0
F
2
/
1
V
s
/
kg
50
.
1
0
W
F
2
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 Fall '08
 KimberlyHill
 Force, Friction, diagram Momentum diagram

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