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.
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. The total Bernoulli sum computed here is: Q + ½ρv² + ρ × 9.81 × Δh + ΔP/ρ. Each term represents flow rate, dynamic pressure, hydrostatic head, and pressure head respectively. 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 head = 5000 / 1000 = 5 Pa/kg. Total Bernoulli sum ≈ 0.01571 + 2000 + 29,430 + 5 ≈ 31,435 (mixed units as per formula output).
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.