Friction Loss Methods

Last updated: October 30, 2023

The Friction loss methods available are:

Chezy's Equation
Kutter's Equation
Colebrook-White Equation
Hazen-Williams Equation
Darcy-Weisbach Equation
Manning's Equation

Of these, two - the Colebrook-White Equation and the Manning's Equation - are of interest to UK Engineers.

Colebrook-White Equation

The Colebrook-White equation is used to iteratively calculate for the Darcy-Weisbach friction factor:

Free Surface:

Full Flow (Closed Circuit):

Where:

f = Friction factor (unitless)
k = Darcy-Weisbach roughness height (m, ft.)
Re = Reynolds Number (unitless)
R = Hydraulic radius (m, ft.)
D = Pipe diameter (m, ft.)

Darcy-Weisbach Equation

Because of non-empirical origins, the Darcy-Weisbach equation is viewed by many engineers as the most accurate method for modeling friction losses. It most commonly takes the following form:

Where:

h_L = Headloss (m)
f = Darcy-Weisbach friction factor (unitless)
D = Pipe diameter (m)
L = Pipe length (m)
V = Flow velocity (m/s)
g =Gravitational acceleration constant (m/s²)

For section geometries that are not circular, this equation is adapted by relating a circular section's full-flow hydraulic radius to its diameter:

D = 4R

Where:

R = Hydraulic radius (m)
D = Diameter (m)

This can then be arranged to the form:

Where:

Q - Discharge (m³/s)
A = Flow Area (m²)
R = Hydraulic radius (m)
S = Friction slope (m/m)
f = Darcy-Weisbach friction factor (unitless)
g = Gravitational acceleration constant (m/s²)

The Kinematic Viscosity is used in determining the friction coefficient in the Darcy-Weisbach Friction Method. The value for this is set in the Calculation Options, and depends on the water temperature. Temperatures of 10 or 15 degrees are normally used.

Manning's Equation

Where:

Q - Discharge (m³/s)
k = Constant (1.00m^1/3/s)
n = Manning's roughness (unitless)
A = Flow Area (m²)
R = Hydraulic radius (m)
S = Friction slope (m/m)