4.0775
m
40,000
Pa
40
kPa
4.0775
m/100 m
40
kPa/100 m
0.015708
m³/s
56.549
m³/h
4.0775
m
40,000
Pa
40
kPa
4.0775
m/100 m
40
kPa/100 m
0.015708
m³/s
56.549
m³/h
The Friction Loss Calculator determines the head loss and pressure drop caused by fluid friction inside a pipe using the Darcy-Weisbach equation, the most widely used formula in pipe-flow hydraulics. Every piping system — from municipal water mains to industrial process lines — experiences energy loss due to viscous shear at the pipe wall, and accurately predicting this loss is essential for pump sizing, system design, and energy optimization.
The Darcy-Weisbach equation expresses the head loss as: $$h_f = \frac{f \, L \, v^2}{2 g D}$$ where f is the Darcy friction factor, L is pipe length, v is mean flow velocity, g is gravity, and D is pipe diameter. The corresponding pressure drop is $$\Delta p = \rho g h_f$$.
The friction factor f depends on the Reynolds number and pipe roughness. For laminar flow (Re < 2300), f = 64/Re exactly. For turbulent flow, use the Moody chart or the Colebrook-White equation. This calculator takes f as input so you can use any source for the friction factor, making it universally applicable to any fluid and pipe material.
The Darcy-Weisbach equation is derived from dimensional analysis and the momentum balance on a control volume of fluid in a pipe:
$$h_f = f \frac{L}{D} \frac{v^2}{2g}$$
Here, $$\frac{v^2}{2g}$$ is the velocity head — the kinetic-energy equivalent height. The factor $$\frac{L}{D}$$ captures the geometric aspect ratio, and f encapsulates all viscous and roughness effects.
Pressure drop follows from the hydrostatic relation: $$\Delta p = \rho g h_f = f \frac{L}{D} \frac{\rho v^2}{2}$$
Common Darcy friction factor values: laminar flow f ≈ 0.03–0.06; smooth turbulent pipes f ≈ 0.01–0.03; rough pipes f ≈ 0.03–0.08.
A larger head loss means more pump energy is consumed overcoming friction. Head loss increases with the square of velocity, so doubling flow speed quadruples friction loss. Larger diameter dramatically reduces loss (inversely proportional to D), which is why upsizing pipes is one of the most effective strategies to reduce pumping costs. The pressure drop in Pascals lets you directly compare against pump specifications.
Inputs
Results
A 100 m long, 100 mm pipe carrying water at 2 m/s with f = 0.02 produces ~4.08 m of head loss (40 kPa pressure drop).
Inputs
Results
A 500 m oil line (D = 200 mm, f = 0.035) at 1.5 m/s loses ~10 m of head. The higher friction factor reflects the rougher pipe or higher viscosity regime.
The Darcy friction factor (also called the Moody friction factor) is a dimensionless number that quantifies the resistance to flow in a pipe. It depends on the Reynolds number and the relative roughness (ε/D) of the pipe wall. For laminar flow, f = 64/Re; for turbulent flow, it is determined from the Moody chart or the Colebrook-White equation.
The Darcy friction factor is exactly four times the Fanning friction factor: f_Darcy = 4 × f_Fanning. The Darcy-Weisbach equation uses the Darcy factor. Always check which convention your source uses to avoid a factor-of-four error.
Yes. The Darcy-Weisbach equation works for any Newtonian fluid, including gases, provided the flow is incompressible (Mach number < 0.3). For compressible gas flow at higher speeds, modified equations or the Fanno flow model are needed.
Minor (local) losses from fittings, valves, and bends are expressed as K × v²/(2g). In long pipelines, friction losses dominate; in compact systems with many fittings, minor losses can be significant or even dominant.
In turbulent flow, the shear stress at the pipe wall is roughly proportional to v². Since the Darcy-Weisbach equation is derived from wall shear stress, the quadratic velocity dependence carries through. This is why reducing flow velocity is an effective way to cut energy consumption.
The most effective strategies are: increase pipe diameter (hf ∝ 1/D), reduce pipe length and minimize bends, use smoother pipe materials (lower roughness ε), and reduce flow velocity. In practice, pipe diameter is the strongest lever.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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