Darcy-Weisbach Equation Calculator

The Darcy-Weisbach equation relates the pressure drop in a pipe to the fluid's flow velocity, density, pipe dimensions, and a friction factor. It is expressed as ΔP = f × (L/D) × (ρv²/2), where f is the Darcy friction factor, L is pipe length, D is diameter, ρ is fluid density, and v is flow velocity. It is the most widely used equation for calculating major (friction) losses in pipe flow.

To calculate pressure drop, you need the Darcy friction factor (f), pipe length (L), pipe diameter (D), fluid density (ρ), and flow velocity (v). Plug these values into the formula ΔP = f × (L/D) × (ρv²/2). The result is the pressure loss in Pascals due to friction along the pipe section.

Head loss (hf) is the pressure drop expressed as an equivalent height of fluid column, calculated as hf = ΔP / (ρ × g), where g is gravitational acceleration (9.81 m/s²). It is commonly used in hydraulics to describe energy losses in pipe systems and is measured in metres (m).

For laminar flow (Re < 2300), the friction factor is simply f = 64/Re. For turbulent flow, it is determined using the Moody diagram or the Colebrook-White equation, which accounts for pipe roughness and Reynolds number. Typical values range from about 0.01 for smooth pipes to 0.05 or higher for rough pipes.

Pressure drop is influenced by pipe length (longer pipes = more loss), pipe diameter (smaller diameter = more loss), flow velocity (higher velocity = more loss), fluid density, and the friction factor (which itself depends on surface roughness and flow regime). Fittings and bends cause additional minor losses not captured by this equation.

The Reynolds number (Re = v × D / ν) is a dimensionless value that characterises the flow regime. Re < 2300 indicates laminar flow, Re between 2300 and 4000 is transitional, and Re > 4000 indicates turbulent flow. The flow regime determines which method to use for calculating the friction factor, which directly impacts pressure drop results.

The Darcy-Weisbach equation is valid for fully developed, steady-state, incompressible flow in straight circular pipes. It applies to liquids like water and oil, and to gases at low Mach numbers where compressibility effects are negligible. For highly compressible gas flow or non-Newtonian fluids, specialised equations are required.

Relative roughness is the ratio of the pipe's absolute surface roughness (ε) to its internal diameter (D), expressed as ε/D. Higher relative roughness increases the friction factor in turbulent flow, which in turn increases pressure drop. Smooth pipes (like drawn tubing) have very low relative roughness values, while older steel or cast iron pipes have higher values.