Variables
Description
What is this formula?
The Darcy–Weisbach Flow Rate equation calculates the volumetric flow rate through a pipe when the allowable friction head loss is known.
It is obtained by combining the Darcy–Weisbach head loss equation with the continuity relationship between velocity and flow rate.
Unlike the traditional Darcy–Weisbach equation, which calculates head loss from a known flow velocity, this form directly estimates the flow capacity of a pipeline.
When to use it
Use this formula when:
- Designing water pipelines
- Sizing pumping systems
- Evaluating existing pipelines
- Determining maximum allowable flow rates
- Hydraulic design of industrial piping
Example
A water pipeline has:
D = 0.20 m
L = 150 m
f = 0.020
hf = 5.0 m
g = 9.81 m/s²
Formula:
Q = (πD²/4)√((2gDhf)/(fL))
Substitution:
Q = (π×0.20²/4)√((2×9.81×0.20×5)/(0.020×150))
Q = 0.198 m³/s
Result:
Q ≈ 0.198 m³/s
Q ≈ 198 L/s
Applications
- Water distribution systems
- Irrigation pipelines
- Industrial piping
- Pump station design
- Fire protection systems
- Hydraulic network analysis
Note
This equation assumes that the Darcy friction factor is already known. In practice, the friction factor depends on Reynolds number and pipe roughness and may need to be obtained from the Moody diagram or a separate friction-factor correlation. The equation assumes steady incompressible flow and neglects minor losses from fittings, valves, and bends.