Water is
flowing through a pipe
with an inside diameter
of 4 inches. The volumetric flow rate is 24 GPM (gallons
per minute). Determine ... |
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a.) The mass flow rate in lbm/min. Assume the density of water is 1000
kg/m3
b.) The average velocity of the water in the pipe in ft/s. |
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Read : |
This is a
straightforward application of the relationships between mass and volumetric flow rates, density
or specific volume, velocity and cross-sectional area for flow. |
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Diagram: |
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Given: |
V |
24 |
gal/min |
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D |
4 |
in |
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r |
64.4 |
lbm/ft3 |
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0.333 |
ft |
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Find: |
a.) |
m |
??? |
lbm/min |
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b.) |
v |
??? |
ft/s |
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Assumptions: |
1 - |
The density of the water is uniform and constant. |
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Equations
/ Data / Solve: |
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Part a.) |
The key relationship
for this part of the problem is : |
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Eqn 1 |
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Before we can use Eqn 1, we need to convert the units on the volumetric flow rate to ft3/min. |
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Eqn 2 |
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V |
3.208 |
ft3/min |
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Now, we plug values
into Eqn 1 to get : |
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m |
206.6 |
lbm/min |
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Part b.) |
The key relationship
for this part of the problem is : |
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Eqn 3 |
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We can solve Eqn 3 for the average water velocity,
v : |
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Eqn 4 |
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Where : |
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Plugging values into Eqns 4 & 5 yields : |
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A |
0.08727 |
ft2 |
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v |
0.6127 |
ft/s |
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Verify: |
We cannot verify the
constant density assumption. |
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Answers : |
a.) |
m |
207 |
lbm/min |
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b.) |
v |
0.613 |
ft/s |
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