Pipe Sizing by Flow Rate and Velocity

Sizing basis

Velocity, then pressure drop

Typical liquid target

6 – 8 ft/s

Pump suction target

2 – 4 ft/s

Capacity formula

Q = 3.117 × A × v

The sizing equation

Flow rate, area and velocity are related by continuity. In the units the work is actually done in:

Q (US gpm) = 3.117 × A (in²) × v (ft/s)
A (in²) = Q / (3.117 × v)  ·  v (ft/s) = Q / (3.117 × A)

The constant is not magic: it converts in²·ft/s to US gallons per minute — multiply by 12 for inches per second, by 60 for minutes, and divide by 231 cubic inches per gallon.

Worked example

Size a line for 400 gpm of cooling water on a pump discharge, target velocity 8 ft/s.

1. Required area: A = 400 / (3.117 × 8) = 16.04 in²
2. Required bore: d = √(4A/π) = 4.52 in
3. The smallest Schedule 40 size meeting that is NPS 5, bore 5.047 in (128.2 mm), area 20.01 in².
4. Actual velocity at 400 gpm in NPS 5 Sch 40: v = 400 / (3.117 × 20.01) = 6.4 ft/s — below the target, because the standard size is larger than the exact requirement.

Note that NPS 5 is one of the sizes many piping specifications exclude from their standard size list. Where that applies, the next permitted size is taken instead — which is the usual reason a line ends up larger than the calculation strictly requires.

Always round up to the next standard size. Rounding down raises velocity, and pressure drop rises with roughly the square of velocity — so a half-size saving on pipe can cost far more in pump power over the life of the line.

Design velocity by service

These are common engineering practice, not code requirements. Project specifications and the fluid's own erosion behaviour override them.

Flow capacity, Schedule 40

Capacity at four common design velocities for every Schedule 40 size through NPS 24, computed from the published bore.

Dimensions are given in inches, with the millimetre equivalent beneath in grey.

Computed from the ASME B36.10M bore. For another schedule, scale by the ratio of flow areas — see the size pages for each schedule's bore.

Erosional velocity

For two-phase and gas service, API RP 14E gives an erosional velocity limit that is widely used as a check:

V_e = C / √ρ  ·  ρ in lb/ft³, V_e in ft/s

C is commonly taken as 100 for continuous service in carbon steel and 125 for intermittent service, with higher values for corrosion-resistant alloys and clean, non-corrosive fluids. The correlation is empirical and has been criticised as conservative for clean service and unconservative where sand is present — treat it as a screening check, not a design basis.

When pressure drop governs instead

Velocity sizing works because on a short line the velocity limit is reached before the pressure drop budget is. On long runs the reverse is true, and the line must be sized on the Darcy-Weisbach loss against the available head. As a rule of thumb, anything over a few hundred feet should be checked on pressure drop, and anything feeding a pump or a control valve should be checked regardless of length.