Fluid Mechanics

Darcy–Weisbach Pressure Drop

The Darcy–Weisbach equation estimates the pressure loss caused by wall friction in a straight pipe.

Δ P_{f} = f_{D} \frac{L}{D} \frac{ρ v ˉ ^{2}}{2}

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Source & review

Difficulty

Intermediate

Read time

4 min

Prerequisites

Consistent SI units, algebra, and the physical assumptions listed below

Review statusNeeds review

Source

Teng-Jui Lin — Equation Sheets

Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.

Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Converted Fanning head loss to Darcy pressure loss using f_D = 4 f_F and ΔP_f = ρ g h_f.

Definition

Understanding the core concept

The Darcy–Weisbach equation estimates the pressure loss caused by wall friction in a straight pipe. The Darcy friction factor contains the effect of flow regime and roughness, while length and diameter account for geometry.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$Δ P_{f}$	Frictional pressure drop	$Pa$
$f_{D}$	Darcy friction factor	$1$
$L$	Pipe length	$m$
$D$	Internal pipe diameter	$m$
$ρ$	Fluid density	$kg/ m^{3}$
$v ˉ$	Bulk mean speed	$m/s$

Real-World Applications

Where this formula is used in practice

Pipe sizing

Estimate frictional pressure losses for a proposed line.

Pump selection

Calculate the straight-pipe portion of a system pressure requirement.

Worked Example

Step-by-step calculation with real numbers

Problem

Water flows at 2 m/s through a 20 m pipe with diameter 0.05 m. Using density 1000 kg/m³ and Darcy factor 0.025, find the frictional pressure loss.

Given

f_{D} = 0.025, L = 20 m

D = 0.05 m

ρ = 1000 kg/ m^{3}, v ˉ = 2 m/s

Solution

Δ P_{f} = f_{D} \frac{L}{D} \frac{ρ v ˉ ^{2}}{2}

Δ P_{f} = 0.025 \frac{20}{0.05} \frac{1000 ( 2 ) ^{2}}{2}

Final Answer

Δ P_{f} = 20000 Pa

Formula Guide

Info

DifficultyIntermediate

Read Time4 min

PrerequisitesConsistent SI units, algebra, and the physical assumptions listed below

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

Teng-Jui Lin — Equation Sheets

Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.

Assumptions

• Use steady, fully developed, approximately incompressible flow in a straight circular pipe.
• Use the Darcy factor, which is four times the Fanning factor; fittings, elevation, and acceleration require separate terms.
• The friction factor must be selected for the actual Reynolds number and relative roughness.

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