A 3ftdiameter duct is used to carry ventilating air into a v

A 3-ft-diameter duct is used to carry ventilating air into a vehicular tunnel at a rate of 9000 ft^3/min. Tests show that the pressure drop is 1.5 in. of water per 1500 ft of duct. What is the value of the friction factor for this duct and the approximate size of the equivalent roughness of the surface of the duct?

Solution

Solution:

Q = 9000 ft3/min = 150 ft3/s

D = 3 ft

Pressure drop is given as 1.5 in per 1500 ft for water

Pressure is given by = density x height x gravity

= 62.43 x 0.125 x 32.2

this pressure will be same for air as well

62.43 x 0.125 x 32.2 = (density x height )air x gravity

(height)air = 102 ft

friction factor can be calculated using formula

h = f L Q^2/(3 D^5)

f = 0.02

Roughness is given by

1/sqrt(4f) = 2log₁₀(D/2k) + 1.74

pluging values of f & D, k comes out to be

k = 0.013