CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 305

(12.33)

(12.34)

wherepDpressure at D; and wunit weight of liquid.

Comparison of the Darcy-Weisbach, Manning,
and Hazen-Williams Formulas*

Because the Darcy-Weisbach, Manning, and Hazen-Williams equations are all
used frequently in practice, it is important to know their similarities and differ-
ences. They can be compared more easily if each is solved for the slope of the
energy grade line, Fig. 12.15, using this nomenclature:

Sslope of the energy grade line, m/m (ft/ft)

hfhead loss, m (ft)

Llength of pipeline, m (ft)

fcoefficient of friction

Qflow rate, m^3 /s (ft^3 /s)

Ddiameter of pipe, m (ft)

ncoefficient of roughness, Manning formula

Ccoefficient of roughness, Hazen-Williams formula

Darcy-Weisbach:

(12.35)

Manning:

(SI units) (12.36)

(U.S. customary units) (12.37)

Hazen-Williams:

(SI units) (12.38)

S (U.S. customary units) (12.39)

4.73Q1.85

C1.85D4.87

S

10.7Q1.85

C1.85D4.87

S4.66n^2

Q^2

D^16 ^3

S10.3n^2

Q^2

D^16 ^3

S

hf

L



8 fQ^2



2 gD^5

QAQBQC

ZcZd

pD

w



4.727LC

D4.87C 

QC

CC

1.85

*Metcalf & Eddy, Inc.—Wastewater Engineering,McGraw-Hill.