Darcy-Weisbach Head Loss

\[h_f=f\frac{L}{D}\frac{v^2}{2g}\]

Variables

hfhead loss due to friction (m)

fDarcy friction factor (-)

Lpipe length (m)

Dinternal pipe diameter (m)

vaverage fluid velocity (m/s)

ggravitational acceleration (m/s²)

Description

What is this formula?

The Darcy-Weisbach equation calculates the hydraulic head loss caused by friction as water flows through a pipe. It is one of the most widely used equations in hydraulic engineering and irrigation system design.

When to use it

Use this formula when designing or analyzing irrigation pipelines, pumping systems, water distribution networks, and agricultural hydraulic installations where friction losses must be estimated accurately.

Example

A PVC irrigation pipe has:

L = 200 m

D = 0.10 m

v = 1.5 m/s

f = 0.020

g = 9.81 m/s²

Formula:

hf = f·L·v² / (2·g·D)

Substitution:

hf = (0.020 × 200 × 1.5²) / (2 × 9.81 × 0.10)

hf = 4.59 m

Result:

The friction head loss is approximately 4.59 m of water column.

Applications

- Irrigation system design

- Agricultural pumping stations

- Drip irrigation networks

- Sprinkler irrigation systems

- Water conveyance pipelines

- Hydraulic energy loss calculations