Flow velocity, Reynolds number, friction factor and pressure drop for a fluid flowing in a pipe, using the Darcy-Weisbach equation.
Page last changed 2026-10-19 · based on n/a — standard engineering relationships, no single governing revision
Quick Answer
Pressure drop follows ΔP = f · (L/D) · ρv²/2. Both the velocity and the friction factor are needed, and the regime matters: flow below Re ≈ 2,300 is laminar, above 4,000 turbulent. Pressure drop rises with roughly the square of flow rate in turbulent flow.
Pipe Pressure Drop (Darcy-Weisbach)
The Formulas Used
Velocity: v = 0.4085 · Q ÷ D² (Q in US gpm, D in inches, v in ft/s) Reynolds number: Re = ρ·v·D ÷ µ Laminar below 2,300, turbulent above 4,000 Darcy-Weisbach: ΔP = f · (L ÷ D) · ρ·v² ÷ 2 Swamee-Jain friction factor: f = 0.25 ÷ [log₁₀(ε/3.7D + 5.74/Re0.9)]²
Why Pressure Drop Rises With the Square of Flow
In turbulent flow — which is almost every practical pipe flow — the friction factor is nearly constant, so pressure drop is proportional to v², and therefore to Q². Doubling the flow rate quadruples the pressure drop, and the pump power needed rises with the cube of flow for the same system.
That is the single most useful fact for troubleshooting: if a system delivers less flow than expected, the cause is usually a restriction, and the symptom is that the pump is operating far to the left of its curve. It is also why doubling the pipe diameter is so effective — velocity falls by a factor of four for the same flow, and pressure drop falls by roughly a factor of sixteen (the velocity-squared term dominates over the diameter term in f·L/D).
Frequently Asked Questions
How do I calculate pressure drop in a pipe?
Use Darcy-Weisbach: ΔP = f·(L/D)·ρv²/2. You need the flow velocity, the Reynolds number to establish the regime, and the friction factor. For turbulent flow in commercial pipe, the Swamee-Jain approximation gives the friction factor without iterating on the Moody chart.
Why does pressure drop increase with the square of flow?
Because in turbulent flow the friction factor is nearly constant, so the pressure drop is proportional to velocity squared. Doubling the flow rate quadruples the drop, and the pump power required rises eightfold if the system curve is dominated by friction.
What Reynolds number counts as turbulent?
Below about 2,300 the flow is laminar, above 4,000 it is fully turbulent, and between the two it is transitional and unpredictable. Almost all practical pipe flow is turbulent — water at 3 ft/s in a 2 in pipe is already at Re ≈ 47,000.
Does pipe roughness matter?
In fully turbulent flow, yes. The calculator uses a roughness of 0.00015 ft, typical of commercial steel. Drawn copper and plastic are smoother and lose less; old galvanised or concrete pipe is rougher and can lose substantially more. In laminar flow roughness has almost no effect.
What does this calculator not include?
Fittings, valves, bends and elevation change. Fittings are usually handled by adding equivalent lengths to the pipe length, and elevation by adding the static head separately. A system with many fittings can have more loss in them than in the straight pipe.
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