CIVIL ENGINEERING FORMULAS

302 CHAPTER TWELVE

Darcy–Weisbach Formula

One of the most widely used equations for pipe flow, the Darcy–Weisbach for-
mula satisfies the condition described in the preceding section and is valid for
laminar or turbulent flow in all fluids:

(12.20)

wherehfhead loss due to friction, ft (m)
ffriction factor (see an engineering handbook)
Llength of pipe, ft (m)
Ddiameter of pipe, ft (m)
Vvelocity of fluid, ft/s (m/s)
gacceleration due to gravity, 32.2 ft/s^2 (9.81 m/s^2 )

It employs the Moody diagram for evaluating the friction factor f. (Moody, L. F.,
“Friction Factors for Pipe Flow,” Transactions of the American Society of
Mechanical Engineers, November 1944.)
Because the preceding equation is dimensionally homogeneous, it can be used
with any consistent set of units without changing the value of the friction factor.
Roughness values $, ft (m), for use with the Moody diagram to determine
the Darcy–Weisbach friction factor fare listed in engineering handbooks.
The following formulas were derived for head loss in waterworks design
and give good results for water-transmission and -distribution calculations.
They contain a factor that depends on the surface roughness of the pipe mater-
ial. The accuracy of these formulas is greatly affected by the selection of the
roughness factor, which requires experience in its choice.

Chezy Formula

This equation holds for head loss in conduits and gives reasonably good results
for high Reynolds numbers:

VCRS (12.21)

hff

L

D

V^2

2 g

Vmax

FIGURE 12.6 Velocity distribution for turbulent flow

in a circular pipe is more nearly uniform than that for

laminar flow.