Problem 4.71
[Difficulty: 3]
Given:
Water tank attached to mass
Find:
Whether tank starts moving; Mass to just hold in place
Solution:
Basic equation: Momentum flux in x direction for the tank
Assumptions:
1) Steady flow
2) Incompressible flow 3) Atmospheric pressure at exit 4) Uniform flow
Hence
R
x
V cos
θ
( )
⋅
ρ
⋅
V A
⋅
(
)
⋅
=
ρ
V
2
⋅
π
D
2
⋅
4
⋅
cos
θ
( )
⋅
=
We need to find V.
We could use the Bernoulli equation, but here it is known that
V
2 g
⋅
h
⋅
=
where h = 2 m is the
height of fluid in the tank
V
2
9.81
×
m
s
2
⋅
2
×
m
⋅
=
V
6.26
m
s
=
Hence
R
x
1000
kg
m
3
⋅
6.26
m
s
⋅
⎛
⎜
⎝
⎞
⎠
2
×
π
4
×
0.05 m
⋅
(
)
2
×
cos 60 deg
⋅
(
)
×
=
R
x
38.5 N
=
This force is equal to the tension T in the wire
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 Fall '07
 Lear
 Fluid Mechanics, Force, Friction, Mass, Flux, fmax, 2 kg

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