Pipe Flow and Pressure Drop Calculator

Pressure drop, velocity and Reynolds number for flow through a round pipe, with fittings, valves, elevation and a pressure drop against flow curve.

How it works

The pressure lost to friction in a straight pipe is given by the Darcy–Weisbach equation, and the loss in fittings and valves by a loss coefficient K applied to the dynamic pressure.

Δp = f × (L ÷ d) × ρ v² ÷ 2 + K × ρ v² ÷ 2 + ρ g Δz

The friction factor depends on the Reynolds number Re = ρ v d ÷ μ and the relative roughness ε ÷ d. Below Re = 2 300 the flow is laminar and f = 64 ÷ Re. Above 4 000 it is turbulent and f comes from the Colebrook–White equation, which the calculator solves by iteration: 1 ÷ √f = −2 log10(ε ÷ 3.7 d + 2.51 ÷ (Re √f)). Between 2 300 and 4 000 the flow is unstable and the result is uncertain. The theory is on Structures and Strength of Materials for the stresses and in the coming fluids guides; the pipe sizes are standard schedule 40 steel.

The curve under the results shows how the pressure drop changes with flow, from zero to twice the flow entered: friction grows roughly as the square of the flow, and the elevation term is constant.

Worked example

Water at 20 °C (ρ = 998.2 kg/m³, μ = 1.002 mPa·s) flows at 10 L/s through 100 m of 3 in (DN80) schedule 40 commercial steel pipe, inside diameter 77.9 mm, rising 5 m, with four 90° elbows, one open gate valve and a sharp entrance and exit.

  • Area = π × 0.0779² ÷ 4 = 0.00477 m², so v = 0.010 ÷ 0.00477 = 2.098 m/s.
  • Re = 998.2 × 2.098 × 0.0779 ÷ 0.001002 = 162 826: turbulent. Relative roughness 0.045 ÷ 77.9 = 0.000578, and Colebrook gives f = 0.0196.
  • Dynamic pressure ρ v² ÷ 2 = 2 197 Pa. Friction loss = 0.0196 × (100 ÷ 0.0779) × 2 197 = 55.2 kPa.
  • Fittings: K = 4 × 0.9 + 0.2 + 1.5 = 5.3, giving 11.6 kPa. Elevation: 998.2 × 9.80665 × 5 = 48.9 kPa.
  • Total = 115.8 kPa (1.16 bar, 11.8 m of water head). The velocity of 2.1 m/s is within the usual 0.5 to 3 m/s for water.

Things to know

The loss coefficients K are typical values for threaded or flanged fittings at high Reynolds number: manufacturers publish exact values (or a flow coefficient Cv) for valves, and K rises for small pipes and slow flow.

The roughness values are for new, clean pipe. Scale, corrosion and age can raise the roughness several times over the life of a system: design with a margin of 10 to 25 percent.

The calculator treats the fluid as incompressible. For gases it is valid only while the pressure drop stays small compared with the absolute pressure; use compressible-flow methods for long gas lines.

Fluid properties depend on temperature. The values for water are from standard tables; for other fluids use the supplier’s data and enter density and viscosity directly.

The pipe sizes are standard steel schedule 40 inside diameters. Copper, plastic and stainless pipe have different wall thicknesses: choose “Other” and enter the real inside diameter.

Velocity limits are rules of thumb: 0.5 to 3 m/s for water in general, lower on the suction side of pumps, and lower still where noise or erosion matters.

Common questions

What is the Darcy friction factor?

A dimensionless number that gives the pressure drop of turbulent or laminar flow in a pipe. It depends on the Reynolds number and the relative roughness of the pipe wall. It is four times the Fanning friction factor, which some textbooks use.

How do I choose a pipe size?

Pick the smallest size whose velocity is within the usual limit (for water 1 to 3 m/s) and whose pressure drop is acceptable, then compare the cost of a larger pipe against the energy to pump through the smaller one over its life.

Why does the pressure drop change so much with a small change in pipe size?

For a fixed flow the velocity goes as 1 ÷ d² and the friction loss as roughly 1 ÷ d⁵. A pipe one size larger can cut the friction loss to less than half.

What does K mean?

The loss coefficient of a fitting: the number of dynamic pressures (ρ v² ÷ 2) lost across it. Add up the K of all fittings and multiply by the dynamic pressure.

Can I use this for non-round ducts?

Approximately, using the hydraulic diameter 4 A ÷ P as the diameter. Enter it as the inside diameter with “Other”.

Sources

  • Crane Co., Flow of Fluids Through Valves, Fittings and Pipe, Technical Paper No. 410 (K values, roughness).
  • Colebrook, C. F. (1939), “Turbulent flow in pipes”, Journal of the Institution of Civil Engineers 11; Moody, L. F. (1944), Transactions of the ASME 66.
  • White, F. M., Fluid Mechanics, McGraw-Hill; ASME B36.10M (steel pipe dimensions).

Last reviewed: November 2, 2026