Pipe velocity & flow
Fluid velocity in a pipe from the flow and the inside diameter — with the rule-of-thumb limits (roughly 7 ft/s on suction, 10 on discharge) that keep erosion, noise, and water hammer in check.
Fluid velocity in a round pipe · from flow & inside diameter
v = 0.4085 · gpm / d² (d = inside dia, in)
What this gives you
This is the average velocity of a liquid moving through a round pipe, worked out from the volumetric flow and the pipe's inside diameter. It's the number you use to check whether a line is sized sensibly: too slow and solids settle out or you've overspent on pipe; too fast and you invite erosion, noise, and water hammer. For water in US units the shortcut is v = 0.4085 × gpm ÷ d², where d is the inside diameter in inches and v comes out in feet per second.
Where the 0.4085 comes from
Velocity is just flow divided by area: v = Q ÷ A. Take one gallon per minute, convert it to cubic feet per second, divide by a pipe area written in square inches, carry the unit factors, and the constant collapses to 0.4085. So you only ever need two numbers — the flow in gpm and the real bore in inches. Use the actual inside diameter, not the nominal pipe size: a nominal 4" Schedule 40 pipe measures about 4.026" inside, and thick-wall or lined pipe runs smaller still, which pushes velocity up fast because it goes as the square of the diameter.
To make that easy, the Nominal pipe size picker drops in the real Schedule 40 bore for common sizes — pick 4" and it fills 4.026" and locks the field so you can't fat-finger it; choose Custom ID to type an exact bore for lined, thick-wall, or tubing runs. Working in SI? Switch the Flow units to m³/h and the tool converts internally (1 m³/h = 4.4029 gpm) before applying the 0.4085 constant, so the velocity still comes out in ft/s.
Field note — suction vs. discharge, and why 7 and 10 matter
The limits most piping and pump guides settle on are roughly 7 ft/s on the suction side and 10 ft/s on discharge. Suction lines are kept slow to protect NPSH and keep the pump out of cavitation; discharge lines can run faster because the pump is pushing. Creep past those numbers and friction loss climbs with the square of velocity, elbows and control valves start to erode, and a fast-moving column turns into a water-hammer problem the instant a valve slams. Treat the flag here as a first screen, not a substitute for a full hydraulic calc on a critical line.
Worked example
Push 100 gpm through a 4" line: velocity is 0.4085 × 100 ÷ 4² = 40.85 ÷ 16 = about 2.55 ft/s, with a cross-section of π÷4 × 4² = 12.57 in². That sits comfortably under 7 ft/s, so it's fine on a suction line. Take the same 100 gpm down to a 2" pipe and velocity jumps to about 10.2 ft/s — the diameter halved, so velocity went up four-fold, and now you're right at the discharge limit.