Flow Rate Calculator

Volumetric flow rate is cross-sectional area times average velocity:

$Q = A v \qquad A = \frac{\pi d^2}{4}$

Symbols and SI units:

• $Q$ — volumetric flow rate, cubic metres per second (m³/s)
• $A$ — internal cross-sectional area, square metres (m²)
• $v$ — mean velocity across the section, metres per second (m/s)
• $d$ — internal pipe diameter, metres (m)

Rearranged, $v = Q/A$ — the form used to check whether a chosen pipe size gives an acceptable velocity.

Mass flow rate follows from the density $\rho$ in kg/m³:

$\dot{m} = \rho Q = \rho A v \quad [\text{kg/s}]$

The assumption people forget: $d$ is the bore, not the nominal size or the outside diameter. A DN100 steel pipe is nominally 100 mm but its actual bore depends on wall thickness, and $Q$ scales with $d^2$, so a 5% diameter error is a 10% flow error.

Flow is quoted in a dozen units; convert to m³/s before substituting.

Typical design velocities for water in pipework are roughly $1$–$3$ m/s: below that, solids settle and the pipe is oversized; above it, noise, erosion and pressure loss climb steeply. Treat those figures as orientation only — the velocity limit for a real installation comes from the governing design standard or the pipe manufacturer's data, not from a rule of thumb.

The assumption people forget: $Q = Av$ uses the mean velocity. Real pipe flow has a velocity profile — near zero at the wall, maximum at the centre — and $Q = Av$ is correct only because $v$ is defined as the area-averaged value. It also assumes a full pipe and steady flow; a partly full gravity drain needs open-channel hydraulics instead.

• Using the radius where the diameter belongs — $A = \pi d^2/4$ and $A = \pi r^2$ are the same thing; using $\pi d^2$ overstates area fourfold.
• Leaving diameters in millimetres — $100$ mm is $0.100$ m. In millimetres the area comes out in mm² and the flow rate is off by $10^6$.
• Using nominal or outside diameter — always the internal bore.
• Confusing mass and volume flow — $\dot{m} = \rho Q$; the two differ by a factor of roughly $1000$ for water in SI units.
• Applying a liquid density to a gas — gas density changes with pressure and temperature, so a compressible-flow treatment is needed once the pressure drop is significant.
• Assuming pressure alone sets flow — flow depends on the pressure drop along the whole system, including fittings and elevation.