E4.11 Relative Roughness Unknown Case

Example 4.11: Five hundred cubic feet per minute of water are pumped through a horizontal pipe that has 10 in ID and is 645 ft long. Pump work is 50 ft·lb_f/lb. Determine the surface roughness of the pipe. Use the following information:

Temperature of the water is 60 °F; Density of water = 62.36 lb/ft³

Viscosity of water = 7.56 ´ 10^-4 lb/(ft·s)

Solution

Velocity of water, V:

Volumetric flow rate, q = 500 ft³/min = 8.33 ft³/s

Inside diameter of pipe, d = 0.833 ft

Assume that pump work is equivalent to the frictional head (h_f ):

Friction factor, f (Equation 4.11):

Reynolds number, Re (Equation 4.12)

Relative roughness, ε/d (Figure 4.3) = 0.0006

Absolute roughness, ε = 0.0005 ft.