The quantity used to measure the roughness of the pipe is called the relative roughness, which
equals the average height of surface irregularities (e) divided by the pipe diameter (D).
The value of the friction factor is usually obtained from the Moody Chart (Figure B-1 of
Appendix B). The Moody Chart can be used to determine the friction factor based on the
Reynolds number and the relative roughness.
Determine the friction factor (f) for fluid flow in a pipe that has a Reynolds number of
40,000 and a relative roughness of 0.01.
Using the Moody Chart, a Reynolds number of 40,000 intersects the curve corresponding
to a relative roughness of 0.01 at a friction factor of 0.04.
The frictional head loss can be calculated using a mathematical relationship that is known as
Darcys equation for head loss. The equation takes two distinct forms. The first form of Darcys
equation determines the losses in the system associated with the length of the pipe.
D 2 g
f = friction factor (unitless)
L = length of pipe (ft)
D = diameter of pipe (ft)
v = fluid velocity (ft/sec)
g = gravitational acceleration (ft/sec2)
Darcys Head Loss Equation
A pipe 100 feet long and 20 inches in diameter contains water at 200°F flowing at a mass
flow rate of 700 lbm/sec. The water has a density of 60 lbm/ft3 and a viscosity of 1.978
x 10-7 lbf-sec/ft2. The relative roughness of the pipe is 0.00008. Calculate the head loss
for the pipe.