Water Conveyance Loss and Designing Conveyance System - Practices of Irrigation and On-farm Water Management - page 28

V 2
2 g ,

f L
D

h f = (1.20)

where

h f = head loss due to friction (m)

f = friction factor (or Darcy's friction coefficient)

L = length of pipe (m)

V = velocity of flow (m/s)

acceleration due to gravity (m/s 2 ) 9.81 m/s 2 g = =

=

D inner diameter of the pipe (m)

Darcy introduced the concept of relative roughness, where the ratio of the internal
roughness of a pipe to the internal diameter of the pipe affect friction factor for
turbulent flow.

Colebrook-White Equation

The Colebrook-White equation for calculating friction factor is

2log 10 e

1
√ f =

9.35
R e √ f

1.14 −

D +

(1.21)

where

f = friction factor

e = internal roughness of the pipe

D = inner diameter of pipe work

To find out “f”, iteration (trial and error) is required. A value of 0.02 can be
assumed as a first step.

The Moody Chart

In 1944, L. F. Moody plotted the data obtained from the Colebrook equation, which
is designated as “The Moody Chart” (Fig. 1.12 ) . From this chart, the user can find
the friction factor for turbulent flow condition with reasonable accuracy.

Fanning's Friction Factor

Fanning, after many experiments, provided data for friction factors, but with
hydraulic radius concept. For full pipe flow, hydraulic radius, R

= 1/4th of the

diameter of the pipe (i.e., R = D /4). Thus, the head loss equation becomes

4 f f LV 2
2 gD

h f = (1.22)