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Flow Rate Calculator

Find the flow rate through a pipe or channel.

How it is calculated

The tool applies the continuity relation Q = A × v. A is the cross-sectional area of the pipe or channel in square metres (m²) and v is the mean flow velocity in metres per second (m/s). Q is the volumetric flow in cubic metres per second (m³/s), shown to five decimals, and the same value multiplied by 1,000 in litres per second (L/s).

The area must not be negative. A negative velocity is accepted and simply gives a negative flow, meaning flow in the opposite direction. The area is the flow cross-section, so for a circular pipe use A = π × d² / 4 with the inside diameter, and for a part-full pipe only the wetted area.

Worked example

A pipe with an inside diameter of 100 mm has an area of π × 0.1² / 4 ≈ 0.00785 m². Water moves at 2 m/s. Then Q = 0.00785 × 2 = 0.01570 m³/s. Multiplying by 1,000 gives 15.70 L/s, which is about 942 litres per minute.

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Common mistakes

  • Entering the pipe diameter in the area field. The field needs area; compute π × d² / 4 first, with d in metres.
  • Using millimetres or square centimetres. The area must be in m², so a 100 mm pipe is 0.1 m, not 100.
  • Using the outside diameter of a pipe instead of the inside. Wall thickness reduces the flow area.
  • Entering velocity in km/h or ft/s. The field is metres per second.
  • Using the peak velocity at the centre of the pipe. The formula needs the mean velocity across the section, which is lower.

About this calculator

Volumetric flow rate follows the continuity equation Q = A · v — cross-sectional area of the pipe or channel multiplied by the average flow velocity — giving the volume passing a given point per unit time. It's the fundamental relationship behind how fluid engineers size pipes: for a fixed flow rate, a narrower pipe forces a higher velocity, and a wider one slows the flow.

Civil and mechanical engineers use flow rate calculations for plumbing and pipe sizing, HVAC engineers apply it to duct design for adequate airflow, hydrologists use it to describe river and stream discharge, and irrigation engineers size channels and pipes to deliver the right water volume to fields. Enter the cross-sectional area and velocity to find the flow rate.

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