Question

Question 5 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?

Answer 1

➮ Question :-

$⟹$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?

➮ Given :-

$⟶$pump expels air at speed of 8.2 ft/s.  

$⟶$radius of the pump = 4.5 millimeters.

➮ To find :-

$⟶$ volume flow rate of the air being pumped into the football

➮ Solution:-

→ Volume of  Pump = Cross section Area  × length

$\boxed{\sf V  = πr² ×  x }$

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

hence, volume flow rate of the air being pumped into the football 0.0056  ft³/s