Fluid Flow Calculator
Computes volumetric flow rate, dynamic pressure, and total Bernoulli head for fluid moving through a pipe. Use it when sizing pumps, analysing pipe systems, or solving fluid mechanics problems.
Last updated: October 2026
Result
15.71 L/s
Formula below · 2 sources (openstax.org, app.jove.com) · Updated Oct 2026
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About this calculator
This calculator applies two basic results of fluid mechanics for an incompressible fluid.
Flow rate
The volume passing per second is the pipe's cross-section times the average speed: Q = A × v = π(d/2)² × v. A 0.1 m pipe at 2 m/s carries 0.0157 m³/s, shown as 15.71 L/s (1 m³/s = 1,000 L/s).
Dynamic pressure
The kinetic energy per unit volume, ½ρv², in pascals. Water at 2 m/s has 2,000 Pa; air at the same speed only 2.45 Pa.
Pressure required
Bernoulli's equation, P + ½ρv² + ρgh = constant along a streamline, gives the pressure a pump must add to raise the pressure by ΔP, accelerate fluid from rest to v and lift it by Δh: ΔP + ½ρv² + ρgΔh, with g = 9.81 m/s².
Bernoulli's equation ignores friction. Real pipes lose extra pressure to wall friction and fittings (Darcy–Weisbach), so treat the last output as a minimum.
How to use
Consider water (ρ = 1000 kg/m³) flowing at v = 2 m/s through a pipe of diameter d = 0.1 m, with a height rise of Δh = 3 m and a pressure difference of ΔP = 5000 Pa. Flow rate Q = π × (0.05)² × 2 ≈ 0.01571 m³/s. Dynamic pressure = ½ × 1000 × 4 = 2000 Pa. Hydrostatic term = 1000 × 9.81 × 3 = 29,430 Pa. Pressure required = 5000 + 2000 + 29,430 = 36,430 Pa (≈ 36.4 kPa). Choose each output in turn to see 15.71 L/s (0.01571 m³/s), 2,000 Pa and 36,430 Pa.
Frequently asked questions
What does Bernoulli's equation tell you about fluid flow in a pipe?
It says that for steady, incompressible flow without friction, pressure energy, kinetic energy and potential energy per unit volume add up to a constant along a streamline: P + ½ρv² + ρgh. Where a pipe narrows and the fluid speeds up, the pressure drops, which is how Venturi meters work. Real flows lose some energy to friction, which is added as a head-loss term.
How do you calculate volumetric flow rate from pipe diameter and velocity?
Q = A × v, with A = π(d/2)² for a round pipe. A 0.2 m pipe at 3 m/s gives π × 0.1² × 3 = 0.0942 m³/s, or 94.2 L/s. By continuity the same flow passes every cross-section, so where the pipe narrows the speed rises.
What is dynamic pressure and how is it different from static pressure?
Static pressure is the pressure exerted by a fluid at rest or perpendicular to flow — it is what a pressure gauge measures. Dynamic pressure is ½ρv², the pressure associated with the fluid's kinetic energy; it only manifests when the flow is brought to rest (e.g., at a stagnation point). Total pressure = static + dynamic pressure, and this sum is conserved along a streamline in ideal flow. Pitot tubes used on aircraft measure total pressure and subtract static pressure to infer airspeed using exactly this relationship.
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