How this instrument works
Volumetric flow rate counts how much fluid crosses some chosen surface each second. Picture one metre-long plug of liquid inside a pipe of section A: it holds A cubic metres, and travelling at speed v it clears that surface in 1⁄v seconds, so A·v cubic metres pass every second. No more derivation exists than that — geometry with the clock attached — which is why one identical product describes water in mains, air down ducts, and grain along conveyor belts.
Rome sold water by width of pipe alone. Householders bought calices of stated bore, and Frontinus, appointed water commissioner in 97 CE, grumbled through De aquaeductu about fraud that arrangement invited without quite owning the tool to stop it. That tool arrived in 1628, when Benedetto Castelli — one of Galileo's students — published Della misura dell'acque correnti and stated plainly that what any channel delivers depends on its section and on how fast water runs through it, never on section by itself. Hydraulics has been two-variable work ever since.
Two assumptions hide inside this tidy product. First, v must be mean speed across the whole section, not whatever some probe reads mid-stream: wall friction bends velocity into that familiar bulging profile, and in fully developed laminar flow the centreline runs exactly twice average. Second, your fluid needs to be near enough incompressible for volume to mean something fixed. Squeeze or warm any gas and identical kilograms occupy some different count of cubic metres, which is why compressor data separates actual from standard conditions, and why mass flow ρ·A·v is what genuinely stays conserved down the duct.
- Enter Pipe cross-section area. Round bore? Use A = π·d²⁄4 — 100 mm of bore gives 7854 mm² — and the menu accepts mm², cm², m², in² or ft².
- Enter Flow speed as an average over that whole section, not one centreline reading. Metres per second, km/h and ft/s all convert.
- Read Volumetric flow rate, switching its unit to l/s, l/min, m³/h or gpm — whichever your meter face or pump curve happens to use.
- Sanity-check your speed: water in closed pipework is normally designed between about 0.6 and 3 m/s, quiet enough to live with and brisk enough to keep silt moving.
Worked example — box culvert running full
One stormwater box culvert measures 2.0 m wide by 1.0 m deep and is running full, with water clocked at 3 m/s by floating debris over 20 m of measured channel. Put 2 into Pipe cross-section area and 3 into Flow speed: Volumetric flow rate returns Q = 2 × 3 = 6 m³/s, exact by inspection.
Six cubic metres per second deserves translating. Flip that output unit and it reads 6000 l/s, 21,600 m³/h, or roughly 95,100 US gallons per minute — enough to fill one 50-metre competition pool in just under seven minutes. Halve your culvert's depth and, were water still moving at 3 m/s, you would carry precisely half as much; real channels run slower when shallower, so losses compound rather than scale.
Questions
What units does volumetric flow rate come in?
Cubic metres per second is coherent SI, though an outsized unit: 1 m³/s equals 1000 l/s, so plumbing and pump work usually gets quoted in l/s, l/min or m³/h. American practice prefers gallons per minute, where 1 m³/s comes to 15,850 US gpm. Watch which gallon, since the imperial gallon holds 4.546 l against 3.785 l for its US cousin — pumps badged 100 gpm in London shift 20% more than ones badged 100 gpm in Chicago. Hydrologists keep their own dialect and say cumec for m³/s, cusec for ft³/s.
Should I use centreline velocity or an average?
Average over your whole section, always. Q = A·v is shorthand for integrating velocity across area, and one probe reading is not that integral. Friction drags near-wall fluid to rest, so profiles bulge in mid-stream: laminar flow puts its centreline at exactly twice mean, turbulent pipe flow roughly 20% above. Drop one pitot tube down the pipe's middle, multiply by area, and you overstate discharge — far and away this formula's commonest misuse. Traverse several points instead, or in open channels sample at 0.6 of depth, where velocity sits close to average.
Does Q = A·v work for air and other gases?
At any single station, yes — area times mean speed still gives cubic metres passing per second. What breaks is comparing two stations. Gas density shifts with pressure and temperature, so ducts carrying constant mass show rising volumetric flow as pressure falls along their length. Fan and compressor catalogues therefore separate actual cubic feet per minute from standard cubic feet per minute, referred to one fixed reference state. Where mass governs — combustion air, process gas, rocket thrust — reach for ṁ = ρ·A·v and leave volume aside.
Why does water speed up when the pipe narrows?
Because identical volume must squeeze through some smaller opening each second. For incompressible fluid with no leaks, Q holds constant along the run, giving A₁v₁ = A₂v₂: halve area and speed doubles. Your thumb over the hose end makes that equation visible. It also underpins the Venturi meter, which infers discharge from pressure drop accompanying that speed-up — faster fluid, lower static pressure, exactly as Bernoulli's relation predicts.
How do I work out cross-section area for round pipe?
A = π·d²⁄4, using internal bore — never outside diameter, never nominal size. For 100 mm bore: π × 0.1² ⁄ 4 = 0.00785 m², or 7854 mm². Two traps wait here. Nominal pipe designations are trade labels rather than dimensions, so pull real bore from manufacturers' tables. And if your pipe is not running full — one part-filled drain, say — enter wetted cross-section occupied by liquid, not the whole circle.
What flow speed should I be designing for?
Water in closed pipework conventionally sits between roughly 0.6 and 3 m/s. Under about 0.6 m/s, silt and debris settle out. Past about 3 m/s the run turns noisy, friction loss climbs steeply since it grows with something near velocity squared, and erosion-corrosion begins eating elbows and copper. Gases tolerate much more, with compressed air mains commonly run at 6 to 9 m/s. Treat these as habits of practice rather than physics: this instrument returns an honest answer for any speed you type.