You need to fill a football with air to play with it. You know that your pump expels air at speed of 8.2 ft/s. The needle of your pump has a radius of 4.5 millimeters. What is the volume flow rate of the air being pumped into the football?
Answers
Given : pump expels air at speed of 8.2 ft/s. pump has a radius of 4.5 millimeters.
To find : volume flow rate of the air being pumped into the football
Solution:
Volume of Pump = Cross section Area * length
=> V = πr² * x
volume flow rate of the air being pumped into the football
=> dV/dt = d ( πr² * x )/dt
=> dV/dt = πr² dx/dt
dx/dt = speed = 8.2 ft/s.
r = radius = 4.5 mm = 4.5/304.8 ft
=> dV/dt = π (4.5/304.8)² * 8.2
=> dV/dt = 0.0056 ft³/s
volume flow rate of the air being pumped into the football 0.0056 ft³/s
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