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The pipe flow rate formula, from area to GPM

How Q = A times v works for a round pipe, why inside diameter matters, and how to convert cubic metres per second into L/min and gallons per minute.

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Continuity: why Q equals area times velocity

Volumetric flow rate measures how much fluid passes a point each second. For an incompressible liquid in a pipe running full, that volume equals the pipe's cross-sectional area multiplied by how fast the fluid moves, written Q = A x v. Picture a cylinder of water advancing down the pipe: in one second it advances a distance equal to the velocity, sweeping out a volume of area times that distance. This is the continuity principle, and it is why narrowing a pipe forces the same flow to speed up.

Finding the area of a round pipe

A round pipe has a circular bore, so its area is A = pi x (D / 2) squared, where D is the inside diameter. Because the radius is squared, the area grows with the square of the diameter: doubling the diameter quadruples the area and, at the same velocity, quadruples the flow. That sensitivity is why using the inside diameter rather than the nominal or outside size matters so much. A 100 mm bore gives an area of about 0.007854 square metres, and at 3 m/s that carries roughly 0.023562 cubic metres per second.

Solving for velocity when you know the flow

The same equation runs backwards. If you already know the volumetric flow rate, perhaps from a meter reading, you can find the average velocity by dividing the flow by the area, v = Q / A. This is useful for checking whether a pipe is sized well, since velocities that are too high cause noise, erosion and pressure loss, while very low velocities can let sediment settle. A common design guideline keeps water velocity in the low single digits of metres per second.

Converting to litres per minute and gallons per minute

SI flow rate in cubic metres per second is precise but hard to picture, so engineers convert it to everyday units. Multiply by 60000 to get litres per minute, since a cubic metre is 1000 litres and a minute is 60 seconds. Multiply by 15850.323 to get US gallons per minute. A flow of 0.023562 m3/s therefore equals about 1413.72 litres per minute or 373.46 US gallons per minute, the same physical flow expressed three ways.

Frequently asked questions

Does the formula assume the pipe is full?

Yes. Q = A x v uses the full circular area, so it applies to a pressurised pipe flowing completely full. A partly filled pipe, such as a gravity drain, has a smaller wetted area and needs an open-channel calculation instead.

Is the velocity here an average or a peak?

It is the average velocity across the cross-section. Real pipe flow is faster in the centre and slower near the walls, but the average velocity is what pairs with the full area to give the correct volumetric flow rate.

Why is a US gallon used rather than an imperial gallon?

The 15850.323 factor converts to US liquid gallons, which are smaller than imperial gallons. If you need imperial GPM, convert litres per minute instead, since one imperial gallon is about 4.546 litres.