Example Problem with Complete Solution

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