Poiseuille’s equation relates the volumetric flow rate Q (volume per time unit) to the
pressure differential ΔP that drives the flow:
Q = (πr^4)/(8η) x (ΔP/L)
Here η is the viscosity of the fluid and the tube has length L and radius r. A fire brigade
needs to triple its hose length to be able to serve a new neighborhood where the fire
hydrants will be further from each other. The old hoses had a radius of r=3 cm.
(a) Determine the new hose radius required to maintain the same volume flow rate as
the original hoses.
(b) What must the minimum water pressure at the fire hydrant be to ensure a flow
rate of 300 gallons per minute through a 300 foot long new hose? The viscosity of
water at room temperature is approximately 1.
10-3 Pascal second.