A fan produces an air curtain to separate a loading dock from a cold storage room. The air curtain is a jet of air 10 ft wide, 0.5 ft thick moving with speed v = 30 ft/s the loss associated with this flow is (Kl)V^2/2 where Kl=5 how much power must the fan supply to the air to produce this flow?

The power the fan must supply to the air to produce this flow is 1.74 hp

Explanation:

Given;

Thickness of air curtain, h = 0.5 ft

Width of air curtain, w = 10 ft

speed of air flow, v = 30 ft/s

Area of flow, A = 0.5 x 10 = 5 ft²

volumetric flow rate, Q = A x v = 5 x 30 = 150 ft³/s

Energy loss associated with this flow = (Kl)V²/2

Given;

KI = 5

Energy loss associated with this flow = 5 x (30)²/2

                                                              = 2250 ft²/s²

Volumetric flow rate, Q = 2250 ft²/s² x 0.5 ft = 1125 ft³/s²

P = ΔpQ

At a constant pressure drop;

Therefore, the power the fan must supply to the air to produce this flow is 1.74 hp

option number c is the right answer.