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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.]