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                                          Chapter 5
                                                   Water Hydraulics, Transmission, and Appurtenances
                                    in the Hazen–Williams formula is the estimate of C in the
                                                                                       different conduit materials and age of conduit
                                    absence of measurements of loss of head and discharge or
                                    velocity. Values of C vary for different conduit materials and
                                                                                                                            Age
                                    their relative deterioration in service. They vary somewhat
                                                                                                                     New
                                                                                                                               Uncertain
                                    also with size and shape. The values listed in Table 5.1 reflect
                                                                                       Conduit material
                                    more or less general experience.
                                                                                                                     130
                                                                                                                                 100
                                                                                       Cast iron pipe, coated (inside and
                                        For purposes of comparison, the size of a noncircular
                                                                                        outside)
                                    conduit can be stated in terms of the diameter of a circular
                                                                                                                        a
                                                                                                                     130
                                                                                       Cast iron pipe, lined with cement
                                                                                                                                 130
                                    conduit of equal carrying capacity. For identical values of C
                                                                                        or bituminous enamel
                                    and s, multiplication of Eq. (5.32) by the conduit area a and
                                                                                       Steel, riveted joints, coated
                                                                                                                     110
                                    equating the resulting expression to Eq. (5.35), the diameter
                                                                                       Steel, welded joints, coated
                                                                                                                                 100
                                                                                                                     140
                                                                                                                        a
                                                                                                                     140
                                                                                                                                 130
                                                                                       Steel, welded joints, lined with
                                    of the equivalent conduit becomes                  Table 5.1  Values of the Hazen–Williams coefficient, C,for 90 a a
                                                                                        cement or bituminous enamel
                                                     D = 1.53 a 0.38 0.24      (5.38)  Concrete                      140         130 a
                                                                r
                                        Equation (5.38) is applicable to both the US customary  Wood stave           130         130
                                                                                       Cement-asbestos and plastic pipe  140     130
                                    system and the SI system. The units for the above equation
                                                    2
                                                         2
                                    are D (ft or m), a (ft or m ), and r (ft or m).    a For use with the nominal diameter, that is, the diameter of unlined pipe.
                                      EXAMPLE 5.30 METRIC OPEN CHANNEL EQUATIONS
                                      Compare the US customary system’s open channel equations with the SI system’s equations.
                                      Solution:
                                      Chezy formula, in terms of the US customary units, is presented below:
                                                                                      √
                                                                                 v = C rs                                     (5.18a)
                                      where v = average velocity, ft/s; C = coefficient, dimensionless; r = hydraulic radius, ft; and s = slope of water surface or energy
                                      gradient, dimensionless.
                                          The equivalent Chezy formula using the SI system is
                                                                                        √
                                                                               v = 0.552 C rs                                 (5.18b)
                                      where v = average velocity, m/s; C = coefficient, dimensionless; r = hydraulic radius, m; and s = slope of water surface or energy
                                      gradient, dimensionless.
                                          Substituting Eq. (5.22) into Eq. (5.18a), one obtains the Manning’s US customary equation:
                                                                                 1.486  0.67  0.5
                                                                             v =     (r)  (s)                                  (5.25)
                                                                                  n
                                          Its equivalent SI equation is
                                                                                  1   0.67  0.5
                                                                              v =   (r)  (s)                                   (5.26)
                                                                                  n
                                      where v = average velocity, m/s; C = coefficient, dimensionless; r = hydraulic radius, m; and s = slope of water surface or energy
                                      gradient, dimensionless.
                                      EXAMPLE 5.31 ROUGHNESS COEFFICIENT
                                      Discuss the applications of the roughness coefficient. What is the roughness coefficient for an average cement-lined open channel?
                                      Solution:
                                      The following are the average values of the roughness coefficient n, for use in the application of the Kutter’s and Manning’s equations:
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