Answer to Question #234073 in Mechanical Engineering for Randal Rodriguez

Question

10. If a pump discharges 90 GPM of water whose specific weight is 61.5 lb f /ft 3 (g = 31.95 ft/s 2 ), find a) mass

flow rate (lb m /min), b) time to fill a spherical tank 8 ft in diameter.

Answer 1

a)

There are $7.48 ft^3$ in a gallon

Therefore, the volume flow rate can be expressed as $\frac{75 gallon/min}{7.48 gallon /ft^3}= 10.03 ft^3/min$

We can multiply that by the density of 62.4 lbm/ft^3

Mass flow rate = 626 LBM/min

b)

$Time = \frac{Volume}{Flowrate}\\ =\frac{\pi}{4}*\frac{L}{10.03}ft^3/min\\ = 94.0 minutes$