Solution:
The CV encloses the inlet and outlet and is just inside the walls of the tube.
We don’t need to establish a relation between umax and Uo by integration, because the
results for these two profiles are given in the text. Note that Uo
uav at section (2). Now
use these results as needed for the balance of forces:
R
2
2
)
22
x1
2
d
r
a
g
2
2
o
o
o
2
0
F(
pp
)
RF
u
(
u
2
r
d
r
)
U
(R
U
)
R
U
(
1
We simply insert the appropriate momentumflux factors
from p. 136 of the text:
(a)
Laminar:
. (a)
Ans
2
drag
1
2
o
p
p
)
R
(
1
/
3
)
R
U
Turbulent,
1.020:
F
(p
p ) R
0.02
R U
(b)
2
. (b)
Ans
2
drag
1
2
o
P3.54
For the pipeflow reducing section
of Fig. P3.54, D1
8 cm, D2
5 cm, and p2
1 atm. All fluids are at 20°C. If V1
5
m/s and the manometer reading is
h
58
cm, estimate the total horizontal force
resisted by the flange bolts.
Fig. P3.54
Solution:
Let the CV cut through the bolts and through section 2. For the given
manometer reading, we may compute the upstream pressure:
12
m
e
r
cw
a
t
e
r
p
p
(
)h
(132800 9790)(0.58 m)
71300 Pa (gage)
Now apply conservation of mass to determine the exit velocity:
2
2
Q
Q , or
(5 m/s)( /4)(0.08 m)
V ( /4)(0.05) , solve for V
12.8 m/s
)
,
Finally, write the balance of horizontal forces:
x
bolts
1,gage
1
2
1
FF
p
A
m
(
V
V
bolts
or: F
(71300)
(0.08)
(998)
(0.08) (5.0)[12.8 5.0]
.
44
Ans
163 N
P3.55
In Fig. P3.55 the jet strikes a vane which moves to the right at constant velocity
Vc
on
a frictionless cart. Compute (a) the force
Fx
required to restrain the cart and (b) the power
P
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View Full DocumentP3.57
Water flows through the duct in Fig. P3.57, which is 50 cm wide and 1 m deep
into the paper. Gate BC completely closes the duct when
90°. Assuming one
dimensional flow, for what angle
will the force of the exit jet on the plate be 3 kN?
Solution:
The steady flow equation applied to the duct, Q1
Q2, gives the jet velocity
as V2
V1(1 – sin
). Then for a force summation for a control volume around the jet’s
impingement area,
Fig.
P3.57
2
11
1
1
(s
i
n
)
(
)
(
1s
i
n
xj
j
FF
m
V
h
h
D
V
2
)
2
2
(998)(0.5)(1)(1.2)
sin
1
sin
1
3000
hDV
Ans.
F
49.5
P3.58
The water tank in Fig. P3.58
stands on a frictionless cart and feeds a jet
of diameter 4 cm and velocity 8 m/s, which
is deflected 60° by a vane. Compute the
tension in the supporting cable.
Solution:
The CV should surround the
tank and wheels and cut through the cable
and the exit water jet. Then the horizontal
force balance is
Fig. P3.58
22
x
cable
out out
j
j
F
T
m
u
( AV )V cos
998
(0.04) (8) cos60
.
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 Spring '11
 Dong
 Force, Fig, Jet, p1 p2

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