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: September 2026
Formula below · 2 sources (NIST, Wikipedia) · Updated Sep 2026
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About this calculator
This calculator combines the continuity equation and Bernoulli's principle. Volumetric flow rate Q = A × v = π(d/2)² × v, where d is pipe diameter and v is fluid velocity. Bernoulli's equation states that along a streamline: P + ½ρv² + ρgh = constant, where P is pressure (Pa), ρ is fluid density (kg/m³), g = 9.81 m/s², and h is height. Pick what to calculate: the flow rate Q (shown in litres per second; 1 m³/s = 1,000 L/s); the dynamic pressure ½ρv² (Pa); or the pressure a pump must supply to deliver a pressure rise ΔP, accelerate the fluid from rest to v and lift it Δh: ΔP + ½ρv² + ρ·9.81·Δh (Pa, ignoring friction losses). Engineers use this to find pressure drops, design nozzles, and verify that flow conditions satisfy conservation of energy.
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?
Bernoulli's equation expresses conservation of energy for an ideal, incompressible, steady fluid flow: the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline. This means if a pipe narrows and fluid speeds up, the pressure must drop — the principle behind carburettors, venturi meters, and aerofoil lift. It is valid for inviscid (frictionless) flow; real-world applications add a friction loss term to account for viscosity.
How do you calculate volumetric flow rate from pipe diameter and velocity?
Volumetric flow rate Q = A × v, where A is the cross-sectional area of the pipe and v is the average fluid velocity. For a circular pipe, A = π(d/2)², so Q = π(d/2)² × v. For example, a 0.2 m diameter pipe with flow at 3 m/s gives Q = π × 0.01 × 3 ≈ 0.09425 m³/s. This is a fundamental result of the continuity equation, which states that mass flow must be conserved — if the pipe widens, velocity drops proportionally.
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.