Problem 4.70
[Difficulty: 4]
CS
x
y
R
x
V
W
Given:
Water flowing into tank
Find:
Mass flow rates estimated by students.
Explain discrepancy
Solution:
Basic equation: Momentum flux in y direction
Assumptions:
1) Steady flow
2) Incompressible flow 3) Atmospheric pressure throughout 4) Uniform flow
For the first student
m
1
ρ
V
⋅
t
=
where m
1
represents mass flow rate (software cannot render a dot above it!)
m
1
1000
kg
m
3
⋅
3
×
m
3
⋅
1
60 s
⋅
×
=
m
1
50.0
kg
s
=
For the second student
m
2
M
t
=
where m
2
represents mass flow rate
m
2
3150 kg
⋅
1
60 s
⋅
×
=
m
2
52.5
kg
s
=
There is a discrepancy because the second student is measuring instantaneous weight PLUS the force generated as the pipe flow
momentum is "killed".
There is a discrepancy because the second student is measuring instantaneous weight PLUS the force generated as the pipe flow
momentum is "killed".
To analyse this we first need to find the speed at which the water stream enters the tank, 10 m below the
pipe exit.
This would be a good place to use the Bernoulli equation, but this problem is in the set before Bernoulli is covered.
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 Fall '07
 Lear
 Fluid Dynamics, Fluid Mechanics, Force, Mass, Flux, kg, Mass flow rate, Vpipe

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