Page 203 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch05_154-193.qxd 8/2/10 9:44 PM Page 165

5.2 Fluid Transport 165
As written by the authors, the Hazen-Williams formula is

s
v Cr 0.63 0.54 (0.001 0.04 )
v 1.318 Cr 0.63 0.54 (U.S. Customary Units) (5.32)
s
v 0.849 Cr 0.63 0.54 (SI units) (5.33)
s
where C is a coefficient known as the Hazen-Williams coefficient, and the factor
(0.001 0.04 ) 1.318 makes C conform in general magnitude with established values of a
similar coefficient in the more-than-a-century-older Chezy formula.
For circular conduits, the Hazen-Williams formulation can take one of the following forms:

v 0.115 Cd 0.63 0.54 (U.S. Customary Units) (5.34)
s
s
v 0.550 CD 0.63 0.54 (U.S. Customary Units)
v 0.3545 CD 0.63 0.54 (SI units)
s
h 5.47 (v>C) 1.85 L>d 1.17 (U.S. Customary Units) (5.35)
f
h f 3.02 (v>C) 1.85 L>D 1.17 (U.S. Customary Units)
h 6.81 (v>C) 1.85 L>D 1.17 (SI Units)
f
Q gpd 405 Cd 2.63 0.54 (U.S. Customary Units) (5.36)
s
s
Q MGD 0.279 CD 2.63 0.54 (U.S. Customary Units)
s
Q 3 0.432 CD 2.63 0.54 (U.S. Customary Units)
ft >s
s
Q m >s 0.278 CD 2.63 0.54 (SI Units)
3
5
h 1.50 10 (Q gpd >C) 1.85 L>d 4.87 (U.S. Customary Units) (5.37)
f
h 10.6 (Q MGD >C) 1.85 L>D 4.87 (U.S. Customary Units)
f
h 4.72 (Q 3 >C) 1.85 L>D 4.87 (U.S. Customary Units)
ft >s
f
h 10.67 (Q m >s >C) 1.85 L>D 4.87 (SI Units)
3
f
h KQ 1.85 (U.S. Customary Units or SI Units)
f
Note that in this Hazen-Williams relationship, the head loss is proportional to the flow
raised to the power of 1.85, whereas in Darcy-Weisbach relationship (Eq. 5.10b) the head
loss is proportional to the square of the flow.
Solutions of Eqs. 5.32 and 5.34 through 5.37 for Q, v, r, D, d, s, h , L, or C requires
f
the use of logarithms, a log-log slide rule, tables, a diagram with logarithmic scales (see
Figs. 5.5a and 5.5b), an alignment chart (Fig. 5.6 and Appendix 14) or a computer
program. The use of the Hazen-Williams pipe flow diagram (Fig. 5.5) is explained in
Fig. 5.5c. The weakest element in the Hazen-Williams formula is the estimate of C in
the absence of measurements of loss of head and discharge or velocity. Values of C vary
for different conduit materials and their relative deterioration in service. They vary
somewhat also with size and shape. The values listed in Table 5.1 reflect more or less
general experience.
For purposes of comparison, the size of a noncircular conduit can be stated in terms of
the diameter of a circular conduit of equal carrying capacity. For identical values of C and
s, multiplication of Eq. 5.32 by the conduit area a and equating the resulting expression to
Eq. 5.35, the diameter of the equivalent conduit becomes

r
D 1.53 a 0.38 0.24 (5.38)
Equation 5.38 is applicable to both the U.S. customary system and the SI system. The units
2
2
for the above equation are D (ft or m), a (ft or m ), and r (ft or m).