Page 376 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 305

4.87
p D 4.727L C Q C 1.85
Z c Z d (12.33)
w D C C C
(12.34)
Q A Q B Q C
where p pressure at D; and w unit weight of liquid.
D

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:
S slope of the energy grade line, m/m (ft/ft)
h head loss, m (ft)
f
L length of pipeline, m (ft)
f coefficient of friction
3
3
Q flow rate, m /s (ft /s)
D diameter of pipe, m (ft)
n coefficient of roughness, Manning formula
C coefficient of roughness, Hazen-Williams formula
Darcy-Weisbach:

h f 8fQ 2
S (12.35)
2
L
gD 5
Manning:
Q 2
S 10.3n 2 (SI units) (12.36)
D 16 3
Q 2
S 4.66n 2 (U.S. customary units) (12.37)
D 16 3
Hazen-Williams:

10.7Q 1.85
S (SI units) (12.38)
C 1.85 D 4.87
4.73Q 1.85
S (U.S. customary units) (12.39)
C 1.85 D 4.87

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