Hydropower - Environmental Impacts of Renewable Energy - page 124

Calculating Major Head Loss
Darcy, Weisbach, and others developed the first practical equation used to determine
pipe friction in about 1850. The formula now known as the Darcy-Weisbach equa-
tion for circular pipes is

2

LV
Dg

hf

f =

(4.15)

2

In terms of the flow rate ( Q ), the equation becomes

2
25

f = 8

fLQ
gD

h (4.16)

π

where
h f = Head loss (ft).
f = Coefficient of friction.
L = Length of pipe (ft).
Q = Flow rate (ft 3 /s).
D = Diameter of pipe (ft).
g = Acceleration due to gravity (32.2 ft/s 2 ).

The Darcy-Weisbach formula was meant to apply to the flow of any fluid, and
into this friction factor was incorporated the degree of roughness and an element
called the Reynold's number , which is based on the viscosity of the fluid and the
degree of turbulence of flow. The Darcy-Weisbach formula is used primarily for
determining head loss calculations in pipes. For open channels, the Manning equa-
tion was developed during the later part of the 19th 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:

Q = 0.435 × C × D 2.63 × S 0.54 (4.17)

where
Q = Flow rate (ft 3 /s).
C = Coefficient of roughness ( C decreases with roughness).
D = Hydraulic radius R (ft).
S = Slope of energy grade line (ft/ft).

C Factor
The C factor, as used in the Hazen-Williams formula, designates the coefficient of
roughness. C does not vary appreciably with velocity, and by comparing pipe types
and ages it includes only the concept of roughness, ignoring fluid viscosity and