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 Encyclopedia of Physical Science and Technology  En006G-249  June 27, 2001  14:7








              Fluid Dynamics (Chemical Engineering)                                                        53

              pressure head, −h s is the pump or shaft work head, h f is           f = f/4.               (66)

              the friction head, and  z is the potential or ground head.
                                                                Care should always be exercised in using friction factors
                                                                derived from a chart, table, or correlating equation to de-
                b. Friction head. In order to solve problems using
                                                                terminewhichtypeoffrictionfactorisbeingobtained.The
              Eq. (63), additional information is required regarding the
                                                                Darcy–Weisbach form is gradually supplanting the Fan-
              nature of the friction head loss term −h f . This information
                                                                ning form as a consequence of most modern textbooks on
              can be obtained by empirical correlation of experimental
                                                                fluid mechanics being written by either civil or mechanical
              data, by theoretical solution of the field equations, or a
                                                                engineers. Figure 3 is the widely accepted correlation for
              combination of both. It is customary to express the friction
                                                                f for Newtonian fluids. This is called the Moody diagram.
              head loss term as a proportionality with the dimensionless
                                                                In it f is correlated as a function of the two dimensionless
              length of the pipe L/D and the velocity head in the pipe
                2
               v  /2g,                                          variables ε/D and Re = D v ρ/µ, where ε is a relative
                                                                roughness factor expressed as an average depth of pit or
                                         2
                                    L  v                        height of protrusion on the wall of a rough pipe and Re is
                              h f = f     ,             (65)
                                    D 2g                        called the Reynolds number. Re is a dynamic similarity pa-
              where f is called a friction factor. The problem is thus  rameter. This means that two flows having the same value
              reduced to finding a functional relation between the di-  of Re are dynamically similar to one another. All vari-
              mensionless factor f and whatever variables with which  ables in two pipes therefore scale in similar proportion to
              it may be found to correlate. In practice, two definitions  their Re values. The Moody diagram does not work for
              of the friction factor are in common use. The expression  non-Newtonian fluids. In this case other methods, to be
              given in Eq. (65) is the Darcy–Weisbach form common  discussed below, must be employed.
              to civil and mechanical engineering usage. An alternative
              form, commonly used by chemical engineers in the older  c. Pump or work head. The pump head term in
              literature, is the Fanning friction factor,       Eq. (63) is given by h s = ˆw s /g and represents the head







































                     FIGURE 3A Moody diagram for Newtonian pipe flow. [Adapted from Moody, L. F. (1944). Trans. ASME 66, 671–
                     684.]
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