Darcy Weisbach Calculator

Enter pipe length, diameter, flow velocity, and friction factor to find the friction head loss and pressure drop using the Darcy-Weisbach equation, h_f = f(L/D)(V²/2g).

Quick Facts

Head loss formula
h_f = f × (L/D) × (V²/2g)
Friction loss expressed as an equivalent height of fluid.
Pressure drop
ΔP = ρ × g × h_f
Converts head loss into a pressure using fluid density.
Reynolds number
Re = V × D / ν
Re < 2,300 is laminar; Re > 4,000 is turbulent.
Typical friction factor
f ≈ 0.02-0.06
Common range for turbulent flow in commercial pipes, per the Moody chart.

Your Results

Calculated
Head Loss (h_f)
-
f × (L/D) × V²/2g, in pipe-length units
Pressure Drop (ΔP)
-
ρ × g × head loss, in kPa
Reynolds Number (Re)
-
V × D / ν — flow regime indicator
Flow Rate (Q)
-
V × cross-sectional area, in L/s

Ready

Enter pipe dimensions, flow velocity, and friction factor, then press Calculate.

Formula and Method for the Darcy-Weisbach Equation

The Darcy-Weisbach equation is the standard fluid-mechanics formula for the friction head loss that occurs when a fluid flows through a pipe: h_f = f × (L/D) × (V²/2g), where f is the dimensionless Darcy friction factor, L is the pipe length, D is the internal diameter, V is the average flow velocity, and g is gravitational acceleration (9.80665 m/s²). Unlike the empirical Hazen-Williams formula, Darcy-Weisbach is dimensionally consistent and applies to any Newtonian fluid — water, air, oil, or gas — across both laminar and turbulent flow.

How the calculation works

Enter the flow velocity, pipe diameter, pipe length, and the Darcy friction factor. The calculator converts every value to SI units (m/s, m) and applies h_f = f(L/D)(V²/2g) to get head loss, then multiplies by fluid density and g to get the pressure drop, ΔP = ρgh_f (equivalently ΔP = f(L/D)(ρV²/2)). It also computes the Reynolds number, Re = VD/ν, from the velocity, diameter, and the fluid's kinematic viscosity, and the volumetric flow rate, Q = V × πD²/4, from velocity and pipe cross-section.

Choosing a friction factor and checking the flow regime

The friction factor f is not a fixed constant — it depends on the Reynolds number and, in turbulent flow, on the pipe's relative roughness (ε/D). For laminar flow (Re below about 2,300), f = 64/Re exactly. For turbulent flow (Re above about 4,000), f is read from a Moody chart or solved from the implicit Colebrook-White equation; the explicit Swamee-Jain formula is a common approximation. This calculator lets you enter f directly — from a Moody chart, a manufacturer spec, or a prior calculation — and reports the Reynolds number alongside the result so you can confirm your chosen f actually matches the flow regime you have.

Real-world applications

  • Sizing water supply, irrigation, and fire-sprinkler piping so friction losses stay within pump capacity.
  • Calculating pressure drop across HVAC ductwork and refrigerant lines during system design.
  • Determining the total dynamic head a pump must overcome, combining elevation change with Darcy-Weisbach friction losses.
  • Checking oil and gas pipeline pressure drop over long transmission runs.

Frequently Asked Questions

What is the Darcy-Weisbach equation?
The Darcy-Weisbach equation calculates the head loss (or pressure drop) caused by friction as fluid flows through a pipe: h_f = f × (L/D) × (V²/2g), where f is the dimensionless Darcy friction factor, L is pipe length, D is internal diameter, V is average flow velocity, and g is gravitational acceleration. It is the standard method used in fluid mechanics and works for both laminar and turbulent flow.
How do I find the Darcy friction factor f?
For laminar flow (Reynolds number below about 2,300), f = 64/Re. For turbulent flow, f is read from a Moody chart or solved from the Colebrook-White equation using the Reynolds number and the pipe's relative roughness, with the explicit Swamee-Jain formula as a common shortcut. This calculator asks you to enter f directly and reports the Reynolds number so you can check that your chosen f matches the flow regime.
What's the difference between head loss and pressure drop?
Head loss (h_f) expresses the friction loss as an equivalent height of the flowing fluid, in meters or feet. Pressure drop (ΔP = ρ × g × h_f) expresses the same loss as a pressure, in pascals or psi. They describe the same physical loss of energy — head loss is common in open-channel and gravity-fed systems, while pressure drop is common when sizing pumps.
Does the Darcy-Weisbach equation work for gases as well as liquids?
Yes, as long as the flow can be treated as incompressible — meaning the pressure drop is small relative to the absolute pressure (typically under about 10-20%) and the Mach number is low. For larger pressure drops in compressible gas flow, you need compressible-flow relations instead, since gas density changes significantly along the pipe.

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