Pipe flow rate (Q = A * V) and continuity nozzle velocity formulas

Area, mean velocity and conserved volumetric flow

Cross-sectional area of a circular pipe scales with the SQUARE of diameter: Area = PI() * (D / 2)^2. Multiplying Area (m^2) by Fluid Velocity V (m/s) gives Volumetric Flow Q in m^3/s—and multiplying by 1,000 converts m^3/s into Liters/second!

For incompressible fluids (Continuity Equation A1*V1 = A2*V2), PI()/4 cancels out cleanly: Exit Velocity V2 = V1 * (D1 / D2)^2! Narrowing a 0.10 m (100 mm) pipe flowing at 2.0 m/s into a 0.05 m (50 mm) nozzle boosts jet velocity 4x to 8.0 m/s!

V is the cross-section’s mean velocity. The continuity comparison assumes steady incompressible flow with no leakage or branches. Both diameters are positive internal diameters in metres.

A smaller nozzle requires a higher mean velocity only if the same flow is maintained. Changing a real nozzle can change flow through pressure losses and pump behavior; this calculation does not predict the resulting operating flow or pressure.

Doubling diameter quadruples flow only when mean velocity is held fixed. For gases with appreciable density changes, use mass continuity rather than assuming constant volumetric flow.

Volumetric flow rate (L/s) and continuity nozzle velocity formulas

Always use INSIDE pipe diameter (ID), not nominal outside diameter, for accurate hydraulic flow.

=ROUND(PI() * ((A2 / 2) ^ 2) * B2 * 1000, 3)

Continuity Equation exit velocity V2 through reducer/nozzle diameter C2

Velocity scales inversely with the square of diameter ratio: V1 * (D1 / D2)^2.

=IF(OR(A2<=0,C2<=0),"Use positive diameters",ROUND(B2 * ((A2 / C2) ^ 2), 4))

Further reading

• Microsoft Support — PI function