An evaporative cooling unit needs to pump 100 litres of air per second through a pipe of radius 10 cm and length 10 m. How much of a pressure difference must be applied to the air to produce this flow rate? The viscosity of air is 1.8x10-5 Pa s.
A) 4.6x10-9 Pa
B) 1.44 Pa
C) 0.46 Pa
D) 460 Pa
E) 0.057 Pa
ANS

Question

Quizplus · Accepted Answer

Using Poiseuille's law, we have:

Q = (pi*r^4 / 8*eta*L) * ∆P

Where Q is the flow rate, r is the radius of the pipe, eta is the viscosity of air, L is the length of the pipe, and ∆P is the pressure difference.

Rearranging for ∆P, we get:

∆P = (8*eta*L*Q) / (pi*r^4)

Substituting the given values, we get:

∆P = (8*1.8x10^-5 * 10 * 100) / (pi*0.1^4)

∆P ≈ 0.46 Pa

An Evaporative Cooling Unit Needs to Pump 100 Litres of Air