Formula and Method for Flow Rate
Flow rate describes how much fluid moves past a point per unit time. The volumetric flow rate through a pipe or duct follows the continuity equation: Q = A × v, where A is the cross-sectional area the fluid flows through and v is the average velocity across that area. For a circular pipe of inside diameter d, the area is A = π(d/2)². Multiply the volumetric flow rate by the fluid's density (ρ) to get the mass flow rate: ṁ = ρ × Q. This calculator converts your diameter and velocity to consistent SI units, computes the pipe's cross-sectional area, and reports the flow rate in several common units.
How the calculation works
Enter the pipe's inside diameter and choose its unit, then enter the average fluid velocity and choose its unit. The calculator converts both to meters and meters per second, computes the circular cross-sectional area A = π(d/2)², and multiplies by velocity to get Q = A × v in cubic meters per second. That base value is then converted to liters per minute (× 60,000) and US gallons per minute (× 15,850.32). If you supply a fluid density, the tool also reports the mass flow rate ṁ = ρQ in kilograms per second — water at 20°C has a density of about 998 kg/m³, while air at sea level is about 1.2 kg/m³.
Common mistakes and practical notes
- Diameter vs. radius: pipe sizes are usually quoted as diameter, not radius — halve the diameter before squaring, which this calculator does automatically.
- Average velocity, not peak: real velocity profiles are not flat. In laminar flow the centerline velocity is about twice the cross-sectional average; in turbulent flow it is closer to 1.2 times the average. Use the true average, not a single point measurement, for an accurate Q.
- Compressible fluids: for gases at high pressure or velocity, density changes along the pipe and this simple formula becomes an approximation — use compressible-flow relations for those cases.
- Nominal vs. actual pipe diameter: a nominal pipe size (e.g., "2-inch pipe") often differs from the actual inside diameter — check the schedule or spec sheet for the true bore before calculating.
Real-world applications
- HVAC duct and pump sizing uses Q = A × v to confirm a duct or pipe can carry the required air or water volume without excessive velocity — and the pressure drop that comes with it.
- Irrigation and plumbing design sizes pipes so flow rate meets fixture or field demand in GPM or L/min.
- Process and chemical engineering converts between volumetric and mass flow rate when metering fuels or other fluids by weight.
- Open-channel and stormwater calculations apply the same Q = A × v principle using the wetted cross-sectional area of a channel.