Science of Water : Concepts and Applications

Water Hydraulics 71
The Darcy–Weisbach formula as such was meant to apply to the fl ow of any fl uid and into
this friction factor was incorporated the degree of roughness and an element called the Reynolds
number, which was based on the viscosity of the fl uid and the degree of turbulence of fl ow.
The Darcy–Weisbach formula is used primarily for determining head loss calculations in pipes.
For making this determination in open channels, the Manning equation was developed during the
later part of the 19 th century. Later, this equation was used for both open channels and closed
conduits.
In the early 1900s, a more practical equation, the Hazen–Williams equation, was developed for
use in making calculations related to water pipes and wastewater force mains:
Q0.435CD S
2.63 0.54
where
Q = fl ow rate, ft 3 /s
C = coeffi cient of roughness (C decreases with roughness)
D = hydraulic radius R, ft
S = slope of energy grade line, ft/ft
C FACTOR
(3.22)
C factor, as used in the Hazen–Williams formula, designates the coeffi cient of roughness. C does
not vary appreciably with velocity, and by comparing pipe types and ages, it includes only the concept
of roughness, ignoring fl uid viscosity and Reynolds number.
Based on experience (experimentation), accepted tables of C factors have been established for
pipe (see Table 3.3). Generally, C factor decreases by one with each year of pipe age. Flow for a
newly designed system is often calculated with a C factor of 100, based on averaging it over the life
of the pipe system.
√ Note: A high C factor means a smooth pipe. A low C factor means a rough pipe.
√ Note: An alternate to calculating the Hazen–Williams formula, called an alignment chart,
has become quite popular for fi eldwork. The alignment chart can be used with reasonable
accuracy.
SLOPE
Slope is defi ned as the head loss per foot. In open channels, where the water fl ows by gravity, slope
is the amount of incline of the pipe, and is calculated as feet of drop per foot of pipe length (ft/ft).
Slope is designed to be just enough to overcome frictional losses, so that the velocity remains constant,
the water keeps fl owing, and solids will not settle in the conduit. In piped systems, where pressure
loss for every foot of pipe is experienced, slope is not provided by slanting the pipe but instead
by pressure added to overcome friction.
MINOR HEAD LOSS
In addition to the head loss caused by friction between the fl uid and the pipe wall, losses also
are caused by turbulence created by obstructions (i.e., valves and fi ttings of all types) in the line,
changes in direction, and changes in fl ow area.
√ Note: In practice, if minor head loss is less than 5% of the total head loss, it is usually
ignored.