Fluid Flow Rate & Continuity Calculator
Find the volumetric flow rate through a pipe from its diameter and flow speed, and use the continuity equation to get the speed in a second, narrower section.
How it works
Q = A·v, A = π·(d ÷ 2)² · Continuity: A1·v1 = A2·v2 ⇒ v2 = A1·v1 ÷ A2
Volumetric flow rate is the cross-sectional area of the pipe times the average flow speed, Q = A·v. For an incompressible fluid, mass is conserved, so the flow rate is the same everywhere along the pipe: A1·v1 = A2·v2. That is why a fluid speeds up when a pipe narrows — halving the diameter quarters the area, so the speed must quadruple to carry the same flow. This is the principle behind nozzles and the pinched end of a garden hose.
Worked example
Water moves at 2 m/s through a 0.05 m pipe. Area = π·(0.025)² = 0.001963 m², so Q = 0.001963 × 2 = 0.003927 m³/s ≈ 3.93 L/s. Where the pipe narrows to 0.025 m (area 0.000491 m²), the speed rises to 0.003927 ÷ 0.000491 = 8 m/s.
Sources: Continuity equation — Wikipedia
Frequently asked questions
What is the continuity equation?
For an incompressible fluid it states A1·v1 = A2·v2 — the product of cross-sectional area and flow speed is constant along a pipe. It expresses conservation of mass: whatever volume enters one section per second must leave the next.
Why does water speed up in a narrower pipe?
Because the same volume per second must pass through a smaller area. Since area scales with the square of the diameter, halving the diameter cuts the area to a quarter and multiplies the speed by four.
How do I convert m³/s to litres per second?
Multiply by 1000, since one cubic metre is 1000 litres. So 0.004 m³/s is 4 L/s. For litres per minute, multiply L/s by 60.
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This calculator is for educational purposes. Double-check important results before acting on them.