Pipe-flow pressure loss

Understand it in 30 seconds

A longer or narrower pipe, or a higher flow velocity, generally produces a larger pressure loss. Fluid viscosity and wall shear dissipate part of the mechanical energy supplied by a pump.

For a horizontal, constant-diameter straight pipe, the Darcy–Weisbach equation gives the pressure loss $\Delta p$ . First determine mean velocity $V$ and Reynolds number, then select the Darcy friction factor $f$ from the flow regime and relative roughness.

What is lost inside a pipe?

Viscous wall shear opposes the flow. The fluid continually does work against this shear, converting macroscopic mechanical energy into thermal internal energy. In fully developed flow through a horizontal, constant-diameter pipe, mean velocity is unchanged while static pressure falls from $p_1$ to $p_2$ .

Loss does not mean that mass or total energy disappears. It means that mechanical energy available for useful work is irreversibly degraded by viscous dissipation.

The Darcy–Weisbach equation

Straight-pipe friction can be written in pressure form, Equation (1), or head form, Equation (2) [1,2]. $L/D$ is the pipe length-to-diameter ratio, $\rho V^2/2$ is the dynamic pressure and the Darcy friction factor $f$ represents wall resistance.

The $f$ used here is the Darcy friction factor. Some references use the Fanning friction factor, whose numerical value is one quarter of the Darcy factor, so verify the definition before substitution.

Eq. (1)Straight-pipe pressure loss

\Delta p=f\frac{L}{D}\frac{\rho V^2}{2}

Eq. (2)Straight-pipe head loss

h_{\mathrm f}=f\frac{L}{D}\frac{V^2}{2g}

Eq. (3)Pressure loss and head loss

\Delta p=\rho g h_{\mathrm f}

Symbols and units

Use the same length unit for inside diameter and pipe length. The calculator uses SI units and unit symbols are set upright [4].

Symbols and SI units for pipe-flow pressure loss
Symbol	Meaning	SI unit
$\Delta p$	Straight-pipe pressure loss	$\mathrm{Pa}$
$h_{\mathrm f}$	Straight-pipe head loss	$\mathrm m$
$f$	Darcy friction factor	—
$L$	Straight-pipe length	$\mathrm m$
$D$	Inside pipe diameter	$\mathrm m$
$V$	Cross-sectional mean velocity	$\mathrm{m/s}$
$\rho$	Fluid density	$\mathrm{kg/m^3}$
$g$	Gravitational acceleration	$\mathrm{m/s^2}$
$K$	Minor-loss coefficient	—

How to determine the friction factor

The Darcy friction factor $f$ is not a universal constant. It depends on pipe Reynolds number $\mathrm{Re}_D$ and relative roughness $\varepsilon/D$ [1–3]. For fully developed laminar flow in a circular pipe, use Equation (4).

For turbulent flow, obtain $f$ from a Moody chart or a relation such as Colebrook–White. Transitional flow is sensitive to disturbances and inlet conditions; do not simply join the laminar and turbulent formulas for design.

Eq. (4)Darcy friction factor for circular-pipe laminar flow

f=\frac{64}{\mathrm{Re}_D}

Fully developed laminar flow in a circular pipe.

Eq. (5)Colebrook–White equation

\frac{1}{\sqrt f}=-2\log_{10}\!\left(\frac{\varepsilon}{3.7D}+\frac{2.51}{\mathrm{Re}_D\sqrt f}\right)

Fully developed turbulent flow; solve iteratively for f.

Laminar: $f=64/\mathrm{Re}_D$ ; viscous effects dominate over surface roughness.
Turbulent: $f$ depends on both $\mathrm{Re}_D$ and $\varepsilon/D$ .
Check the convention: Confirm whether a source reports the Darcy or Fanning friction factor.

Minor losses from bends, valves and entrances

Bends, valves, expansions, contractions, entrances and exits cause separation and mixing in addition to straight-pipe friction. With a coefficient $K$ for each component, the losses can be added as in Equation (6).

$K$ depends on geometry, opening, Reynolds number and the reference velocity. When using a standard or manufacturer's value, check which cross-section defines that velocity.

Eq. (6)Straight-pipe and minor losses

\Delta p_{\mathrm{total}}=\left(f\frac{L}{D}+\sum K\right)\frac{\rho V^2}{2}

Worked example: water in a horizontal pipe

Water of density $\rho=1000\ \mathrm{kg/m^3}$ flows through a horizontal straight pipe of length $L=20\ \mathrm m$ and inside diameter $D=0.050\ \mathrm m$ at mean velocity $V=1.5\ \mathrm{m/s}$ . Take the Darcy friction factor as $f=0.025$ and find the straight-pipe pressure and head losses.

Equation (1) gives 11.25 kPa. With $g=9.80665\ \mathrm{m/s^2}$ , Equation (3) gives a head loss of about 1.15 m. Thus this straight section alone dissipates mechanical energy equivalent to approximately 1.15 m of water column.

Eq. (7)Pressure loss

\Delta p=0.025\frac{20}{0.050}\frac{1000(1.5)^2}{2}=11250\ \mathrm{Pa}

Eq. (8)Head loss

h_{\mathrm f}=\frac{11250}{(1000)(9.80665)}\approx1.15\ \mathrm m

Calculator

Enter density, pipe length, inside diameter, mean velocity and the Darcy friction factor to calculate straight-pipe pressure and head losses. Determine the friction factor separately from a Moody chart or an appropriate correlation.

CALCULATOR

Calculate straight-pipe pressure loss

Density ρ

kg/m³

Pipe length L

m

Inside diameter D

m

Mean velocity V

m/s

Darcy friction factor f

—

Pressure loss Δp11.25kPa

Head loss h_f1.147m

Straight-pipe loss from the Darcy–Weisbach equation. Minor losses, elevation changes and pump work are not included.

Conditions and limits

The equations here use cross-sectional mean quantities for steady flow in a constant-diameter straight pipe. Large density changes in high-speed gases, non-Newtonian fluids, two-phase flow, pulsating flow and short developing regions require additional models.

A measured pressure difference may include elevation change, velocity change and pump or turbine work as well as friction. Do not identify every pressure difference as pipe friction; organize all terms with the extended Bernoulli equation.

Common mistakes

Before calculating, mark the friction-factor convention, inside diameter, velocity and loss boundary on a diagram.

Use outside diameter: Use the flow passage's inside diameter $D$ .
Mix Darcy and Fanning factors: Both may be denoted $f$ , but their values differ by a factor of four.
Ignore fittings: Add minor losses for valves, bends, entrances and exits.
Confuse velocity with flow rate: Convert volumetric flow $Q$ to mean velocity with $V=Q/A$ .
Treat every pressure difference as friction: Account for elevation, area change and machine work in the full energy equation.

Applications and related topics

Pipe loss underlies pump head, pipe diameter, operating cost, flow control and differential-pressure measurements. A smaller diameter can reduce material cost but raises velocity, pressure loss and pumping power.

Review density, pressure and viscosity, continuity, the Bernoulli equation, Reynolds number and flow regimes. The next step is to find a pump operating point from the intersection of pump and system curves.

Prerequisites: Density, pressure & viscosity; continuity; Bernoulli equation; Reynolds number
Next: Pumps and piping systems, system curves and operating points

References

Sources accessed 20 August 2026. Independent expert review has not yet been completed.