Pipe Flow — Velocity & Pressure Drop Calculator

The Calculation, Explained

The Darcy–Weisbach equation

Pressure drop in a pipe is dynamic pressure, multiplied by everything that resists the flow:

f is the Darcy friction factor — read historically from the Moody chart, computed here with the Haaland equation, an explicit approximation of the Colebrook relation good to about ±1%:

In laminar flow (Re < 2,300) roughness is irrelevant and f = 64/Re exactly. ΣK gathers the fittings: a fully open gate valve ≈ 0.15, a standard elbow ≈ 0.9, a swing check valve ≈ 2.5, entrance 0.5, exit 1.0 — a throttled control valve can dwarf all of them and should be taken from its own Cv data.

Assumptions and applicability

• Incompressible (liquid) flow: density constant along the line. For long gas lines with large Δp relative to line pressure, integrate in segments or use a compressible-flow method.
• Fully developed flow in a circular pipe of the stated internal diameter — use the real ID (schedule matters), not the nominal bore on the drawing title.
• Roughness grows up: commercial steel starts near 0.045 mm but corrosion and scaling can multiply effective roughness several-fold over a plant's life. When an old line "mysteriously" loses pressure, this is usually the confession.
• Practical water velocities in plant piping sit near 1–3 m/s: below that you are buying pipe you do not need; above it, noise, erosion-corrosion and water hammer start charging rent.

References

Crane Technical Paper 410 — Flow of Fluids (K values and practice); Haaland (1983) explicit friction relation; Colebrook (1939).

Companion: Orifice / DP Flow Calculator for when the restriction is deliberate.