Does pressure drop increase linearly with flow rate?

No, pressure drop increases roughly with the square of velocity (ΔP ∝ v²) in the turbulent regime, since v² appears directly in Darcy-Weisbach and f is only weakly dependent on velocity. In laminar flow, pressure drop is exactly proportional to velocity (ΔP ∝ v), since f = 64/Re makes the v² and 1/v terms partially cancel.

How much does pipe roughness affect pressure drop?

In fully turbulent flow, friction factor, and therefore pressure drop, can roughly double between a smooth drawn-tube pipe and a heavily corroded cast-iron pipe of the same diameter. In laminar flow, roughness has no effect at all, since f = 64/Re is independent of ε/D.

Do fittings and valves add to this pressure drop?

Yes, this calculator gives straight-pipe frictional loss only. Fittings, valves, and other components add additional "minor losses," commonly estimated either with an equivalent length added to L or with loss coefficients (K values) summed separately and added to the straight-pipe ΔP.

Is this the same as reading a Moody chart?

Yes, functionally, a Moody chart is a graphical plot of the same Colebrook equation this calculator solves numerically for the friction factor, given Reynolds number and relative roughness. Using this calculator gives the same result as an accurate chart read-off, without the interpolation error of reading between gridlines by eye.

Home/Calculators/Fluids/Pipe Pressure Drop

Darcy-Weisbach

Pipe Pressure Drop
Calculator

Compute frictional pressure drop from pipe and fluid data via Darcy-Weisbach, with full step-by-step solutions.

Formula

$\Delta P = f\left(\dfrac{L}{D}\right)\left(\dfrac{\rho v^2}{2}\right)$

Quick Answer

Frictional pressure drop in a pipe is given by the Darcy-Weisbach equation, ΔP = f(L/D)(ρv²/2), where f is the Darcy friction factor (64/Re for laminar flow, or the Colebrook/Swamee-Jain equations for turbulent flow). This calculator computes the Reynolds number and friction factor from your fluid and pipe data, then the resulting pressure drop.

Pipe Pressure Drop Calculator

$\Delta P = f\left(\dfrac{L}{D}\right)\left(\dfrac{\rho v^2}{2}\right)$

Velocity v (m/s)

Pipe Diameter D (m)

Pipe Length L (m)

Density ρ (kg/m³)

Viscosity μ (Pa·s)

Relative Roughness ε/D

How to Use the Pressure Drop Calculator

1
Enter fluid and pipe properties
Enter the fluid velocity, density, and viscosity, plus the pipe diameter and length.
2
Enter the relative roughness
Enter the pipe's relative roughness ε/D (used only if flow turns out to be turbulent).
3
Click Calculate
The calculator finds the Reynolds number, determines the flow regime, computes the Darcy friction factor, and applies Darcy-Weisbach.
4
Read the pressure drop
Read the frictional pressure drop ΔP, along with the intermediate Reynolds number and friction factor used.

Just need the friction factor itself? Use the Friction Factor Calculator, or see the full Fluid Mechanics topic guide.

What Is Pipe Pressure Drop?

As fluid moves through a pipe, friction between the fluid and the pipe wall (and within the fluid itself, in turbulent flow) steadily converts pressure into heat, causing the pressure to drop along the pipe's length. The Darcy-Weisbach equation is the standard way to quantify this loss for any fluid, in either laminar or turbulent flow.

This calculator finds the Reynolds number and Darcy friction factor from your fluid and pipe data (reusing the same laminar/Colebrook/Swamee-Jain logic as the friction factor calculator), then applies Darcy-Weisbach to get the pressure drop directly.

A gate valve and blow-off valve exposed along an above-ground water supply pipeline — This calculator gives straight-pipe loss only — a valve like this adds its own separate minor loss on top. Jet Lowe, National Park Service, Public domain, via Wikimedia Commons.

Derivation: The Darcy-Weisbach Equation

Darcy-Weisbach comes from a mechanical energy balance on the fluid in the pipe, expressing frictional head loss in terms of a dimensionless friction factor, the pipe's length-to-diameter ratio, and the fluid's kinetic energy per unit volume:

\Delta P = f\left(\dfrac{L}{D}\right)\left(\dfrac{\rho v^2}{2}\right)

The friction factor f itself depends on the flow regime: in laminar flow it comes from the exact Hagen-Poiseuille solution (f = 64/Re), and in turbulent flow it's found from the semi-empirical Colebrook equation (or its explicit Swamee-Jain approximation), which accounts for both Reynolds number and pipe roughness.

Pressure Drop vs Velocity

For this page's own pipe and fluid, here's the visible slope change at the laminar-turbulent crossover, not just the stated v vs v² ratio.

Same D = 0.1 m, L = 50 m, ε/D = 1.5×10⁻⁴ pipe as the worked example — note the visible kink where the curve crosses into turbulent flow (shaded transition band), the slope genuinely changes there.

When You Need This Calculation

Pump head and power sizing. Frictional pressure drop converts directly into head, which feeds into total dynamic head for pump power and NPSH calculations.
Pipe diameter selection. Choosing a pipe size for an acceptable pressure drop is an iterative calculation that runs this formula at each trial diameter.
Verifying a Moody chart reading. This calculator reproduces the same friction-factor result a Moody chart gives, numerically instead of graphically.

Worked Example

Water Through a Commercial Steel Pipe

Problem: Water (ρ = 998 kg/m³, μ = 0.001 Pa·s) flows at v = 2 m/s through a D = 0.1 m commercial steel pipe (ε/D = 0.00015) of length L = 50 m. Find the pressure drop.

Re = \dfrac{998 \times 2 \times 0.1}{0.001} = 199{,}600 \;\Rightarrow\; \text{turbulent}

f \approx 0.0158\ \text{(Colebrook)}

\Delta P = 0.0158 \times \dfrac{50}{0.1} \times \dfrac{998 \times 2^2}{2} \approx 15{,}760\ \text{Pa} \approx 15.8\ \text{kPa}

Answer: ΔP ≈ 15.8 kPa

Common Mistakes

Forgetting minor losses. This equation gives straight-pipe friction only, fittings, valves, and bends add additional pressure drop that must be added separately.
Using the wrong friction factor convention. Darcy-Weisbach needs the Darcy friction factor, not the Fanning friction factor (fDarcy = 4·fFanning), mixing them up gives a 4x error.
Ignoring the v² dependence. Pressure drop scales with the square of velocity in turbulent flow, doubling flow rate roughly quadruples the pressure drop, not doubles it.
Using inconsistent units. All quantities must be in SI units (m, m/s, kg/m³, Pa·s) for ΔP to come out directly in pascals.

Key Takeaways

ΔP = f(L/D)(ρv²/2), the Darcy-Weisbach equation for straight-pipe friction loss.
f comes from 64/Re (laminar) or Colebrook/Swamee-Jain (turbulent).
Pressure drop scales roughly with v² in turbulent flow, linearly with v in laminar flow.
Add minor losses (fittings, valves) separately, this covers straight pipe only.
Keep units consistent (SI) throughout for a result directly in pascals.

Frequently Asked Questions

Darcy-Weisbach, ΔP = f(L/D)(ρv²/2), is a fundamental, dimensionally consistent equation that works for any fluid and flow regime when paired with the correct friction factor. Hazen-Williams is an empirical correlation developed specifically for water in the turbulent regime and uses a roughness coefficient (C) instead of a friction factor, it is less general but faster to apply for water distribution systems.

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Derivation: The Darcy-Weisbach Equation

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Worked Example

Water Through a Commercial Steel Pipe

Common Mistakes

Key Takeaways

Frequently Asked Questions

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