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 lb_{m}/min. Assume the density of water is 1000
kg/m^{3}
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 crosssectional area for flow. 














Diagram: 















Given: 
V 
24 
gal/min 



D 
4 
in 



r 
64.4 
lb_{m}/ft^{3} 




0.333 
ft 


























Find: 
a.) 
m 
??? 
lb_{m}/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 ft^{3}/min. 
















Eqn 2 


V 
3.208 
ft^{3}/min 















Now, we plug values
into Eqn 1 to get : 


m 
206.6 
lb_{m}/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 
ft^{2} 





















v 
0.6127 
ft/s 














Verify: 
We cannot verify the
constant density assumption. 














Answers : 
a.) 
m 
207 
lb_{m}/min 

b.) 
v 
0.613 
ft/s 













































































































