Fluid Mechanics
Basic

Volumetric Flow Rate

Volume of fluid passing per unit time.

Formula

Q=AvQ = Av

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Variables

AArea
vSpeed

How it works

This formula says that the volume of fluid moving past a point each second depends on two things: how wide the passage is and how fast the fluid is moving. If you imagine a tube or channel, the fluid in a short time interval occupies a length equal to speed × time, so the volume moved is area × length = A × v × t; dividing by time gives Q = Av. This works when the flow is steady and the speed is roughly uniform across the cross-section.

When to use it

Use this when you want to find how much liquid or gas passes through a pipe, hose, river section, or nozzle per second. It is common in hydraulics, plumbing, ventilation, and basic physics problems involving flow in a uniform channel.

Worked example, step by step

A garden hose has a cross-sectional area of 0.0008 m^2 and water flows through it at 3.5 m/s. Q = Av Q = 0.0008 × 3.5 Q = 0.0028 m^3/s So the volumetric flow rate is 0.0028 cubic metres per second.

Common mistakes to avoid

  • Using the diameter instead of the cross-sectional area
  • Forgetting to convert units so area is in m^2 and speed is in m/s
  • Confusing volumetric flow rate with mass flow rate

Did You Know?

Doubling a pipe's radius multiplies its flow capacity by sixteen, thanks to fourth-power dependence in smooth flow.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026