Flow rate formula
Volumetric flow rate is how much fluid passes a point each second, equal to the pipe cross-sectional area times the flow velocity. It is the starting point for pipe sizing, pump selection, and flow measurement.
Variables
| Q | Volumetric flow rate | m³/s |
| A | Cross-sectional area | m² |
| v | Average velocity | m/s |
Rearranged
A = Q / v
Worked example
Water flows at 2 m/s through a pipe with a cross-section of 0.005 m².
Multiply area by velocity: 0.005 × 2 = 0.01.
Flow rate ties velocity and pipe size together: for a fixed flow, a smaller pipe forces a higher velocity. The continuity equation says the flow rate is the same all along a pipe, so where the bore narrows the fluid must speed up. Mass flow is simply density times Q.
Sizing the pipe or checking the regime?
Use the Reynolds Number Calculator, or see the Pipe Volume Calculator.
The continuity equation
For an incompressible fluid the volume flow rate is constant along a pipe, so area times velocity at one point equals area times velocity at another. Where the pipe narrows, the velocity rises in proportion. This is the rule behind nozzles speeding up a jet and behind the pressure changes that Bernoulli then predicts.
Volumetric vs mass flow
Volumetric flow, in cubic metres per second, measures the space the fluid occupies; mass flow, in kilograms per second, measures the matter moved and equals density times the volume flow. For liquids the two track closely, but for gases, whose density changes with pressure and temperature, the distinction matters a great deal.
FAQ
What is the flow rate formula?
Volumetric flow rate equals cross-sectional area times velocity, Q = A times v, in cubic metres per second.
What is the continuity equation?
It states that area times velocity is constant along a pipe for an incompressible fluid, so a narrower section means a faster flow.
How do I find mass flow rate?
Multiply the volumetric flow rate by the fluid density. Mass flow equals rho times Q, in kilograms per second.