Hazen-Williams Equation for Pipe Friction and Pressure Drop

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Hazen-Williams formula:

V = k C R0.63 S0.54

Where:

Full flow circular pipes Hazen-Williams
R = D / 4

By Continuity
Q = V A

V = fluid velocity, m/s (ft/s),
C = factor for relative roughness Hazen-Williams coefficient
R = hydraulic pipe radius, m (ft),
S = Slope of the energy linie (head loss divided by pipe length),
k = conversion factor for unit system

k = 0.849 for units of m/sec
k = 1.318 for units of ft/sec


Flow round pipe

Imperial Units
Q = 0.432 C D 2.63 S0.54
Where
Q = ft3 / sec
S = ft

SI Units
Q = 0.278 C D 2.63 S0.54
Where
Q = m3 / sec
S = m


SI Units Head loss formula

hf = S L

or

hf = L ( Q / ( 0.278 C D 2.63 ) ( 1 / 0.54)

Where:

hf = head loss height

The Hazen-Williams formula is empirically derived and is limited to use with fluids that have a kinematic viscosity of approximately 1.12 x 10-6 m2 /s (1.22 x 10-5 ft2 /s), which corresponds to water at 15.6 C (60 F), and for turbulent flow. Deviations from these conditions can lead to significant error. The Hazen-Williams coefficient, C, is independent of the Reynolds number. The Pipe Roughness Coefficient Chart provides values of C for various pipe materials.

The Chezy-Manning equation is occasionally applied to full pipe flow. The use of this equation requires turbulent flow and an accurate estimate of the Manning factor, n, which varies by material and increases with increasing pipe size. Pipe Roughness Coefficient Chart provides values of n for various pipe materials. The Chezy-Manning equation is:

Chezy-Manning equation

where:

hL = head loss, m (ft)
V = fluid velocity, m/s (ft/s)
n = Manning factor
a = empirical constant, 1.0 for SI units (2.22 for IP units)

Reference:

Robert Pitt, University of Alabama
Shirley Clark, Penn State Harrisburg