Darcy-Weisbach Pressure Drop Calculator

Q: What is the Darcy friction factor and how do I find it for my pipe?

The Darcy friction factor (f) is a dimensionless number that quantifies the resistance to flow caused by pipe wall roughness and fluid viscosity. For laminar flow (Reynolds number below 2300), it is calculated exactly as f = 64/Re. For turbulent flow you use the Moody chart or the implicit Colebrook-White equation, which depends on both the Reynolds number and the pipe's relative roughness (roughness height divided by diameter). Many engineers use the explicit Swamee-Jain approximation for quick estimates in turbulent conditions.

Q: How does pipe diameter affect pressure drop in the Darcy-Weisbach equation?

Pipe diameter has a very strong inverse effect on pressure drop. For a fixed volumetric flow rate, increasing the diameter reduces velocity (Q = Av, so v ∝ 1/D²), and since ΔP depends on v², doubling the diameter reduces velocity by a factor of 4 and dynamic pressure by 16. Combined with the L/D term, doubling diameter reduces ΔP by a factor of roughly 32. This is why engineers often upsize pipes slightly to achieve large reductions in energy consumption.

Q: When should I use the Darcy-Weisbach equation instead of the Hazen-Williams formula?

The Darcy-Weisbach equation is the physically rigorous choice and works for any Newtonian fluid, any flow velocity, and any pipe material, making it the standard in engineering design. The Hazen-Williams formula is an empirical approximation valid only for water at typical municipal supply velocities and temperatures. Use Darcy-Weisbach when working with non-water fluids (oils, chemicals), high-velocity flows, or when precision is required for pump sizing. Darcy-Weisbach is also preferred in computational fluid dynamics and when using the Moody chart to account for pipe roughness.

Calculates pressure drop along a pipe section using the Darcy-Weisbach equation. Used by engineers designing water supply, HVAC, and industrial piping systems to size pipes and pumps correctly.

Last updated: September 2026

Friction Factor

Pipe Length (m)

Pipe Diameter (m)

Flow Velocity (m/s)

Fluid Density (kg/m³)

Pressure Drop

40,000 Pa

Formula below · 2 sources (asme.org, Wikipedia) · Updated Sep 2026

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About this calculator

The Darcy-Weisbach equation is the most widely accepted method for calculating frictional pressure loss in full pipe flow. The formula is: ΔP = f × (L / D) × (ρ × v² / 2), where f is the dimensionless Darcy friction factor, L is pipe length (m), D is pipe diameter (m), ρ is fluid density (kg/m³), and v is mean flow velocity (m/s). The term ρv²/2 represents the dynamic pressure of the fluid. The friction factor f depends on the flow regime: for laminar flow (Re < 2300), f = 64/Re; for turbulent flow it is found from the Moody chart or Colebrook equation. A larger diameter pipe dramatically reduces pressure drop because D appears in the denominator and velocity squared appears in the numerator — doubling diameter roughly cuts ΔP by a factor of 32 for the same flow rate.

How to use

Suppose water (density 1000 kg/m³) flows at 2 m/s through a 50 m steel pipe with an inner diameter of 0.1 m and a Darcy friction factor of 0.02. Plug into the formula: ΔP = 0.02 × (50 / 0.1) × (1000 × 2² / 2). Step 1: L/D = 50 / 0.1 = 500. Step 2: dynamic pressure = 1000 × 4 / 2 = 2000 Pa. Step 3: ΔP = 0.02 × 500 × 2000 = 20,000 Pa (20 kPa). Enter these five values into the calculator and it returns the pressure drop instantly, saving manual arithmetic. With the default inputs (100 m of 0.1 m pipe) the same flow loses 0.02 × (100 / 0.1) × 2,000 = 40,000 Pa (40 kPa).

Frequently asked questions

What is the Darcy friction factor and how do I find it for my pipe?

The Darcy friction factor (f) is a dimensionless number that quantifies the resistance to flow caused by pipe wall roughness and fluid viscosity. For laminar flow (Reynolds number below 2300), it is calculated exactly as f = 64/Re. For turbulent flow you use the Moody chart or the implicit Colebrook-White equation, which depends on both the Reynolds number and the pipe's relative roughness (roughness height divided by diameter). Many engineers use the explicit Swamee-Jain approximation for quick estimates in turbulent conditions.

How does pipe diameter affect pressure drop in the Darcy-Weisbach equation?

Pipe diameter has a very strong inverse effect on pressure drop. For a fixed volumetric flow rate, increasing the diameter reduces velocity (Q = Av, so v ∝ 1/D²), and since ΔP depends on v², doubling the diameter reduces velocity by a factor of 4 and dynamic pressure by 16. Combined with the L/D term, doubling diameter reduces ΔP by a factor of roughly 32. This is why engineers often upsize pipes slightly to achieve large reductions in energy consumption.

When should I use the Darcy-Weisbach equation instead of the Hazen-Williams formula?

The Darcy-Weisbach equation is the physically rigorous choice and works for any Newtonian fluid, any flow velocity, and any pipe material, making it the standard in engineering design. The Hazen-Williams formula is an empirical approximation valid only for water at typical municipal supply velocities and temperatures. Use Darcy-Weisbach when working with non-water fluids (oils, chemicals), high-velocity flows, or when precision is required for pump sizing. Darcy-Weisbach is also preferred in computational fluid dynamics and when using the Moody chart to account for pipe roughness.

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Sources & references

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