Flow Rate Calculator — Continuity Equation & Fluid Velocity SolverQ = A × v · A₁V₁ = A₂V₂ · m³/s · L/s · m/s · cm² · Pipe Flow
Use this free Flow Rate Calculator to instantly solve any unknown variable in the fundamental continuity equation of fluid mechanics: Q = A × v — where Q is the volumetric flow rate in m³/s or litres per second (L/s), A is the cross-sectional area of the pipe or channel in m² or cm², and v is the mean fluid velocity in metres per second (m/s). Enter any two known flow parameters to automatically calculate the third, applying the full continuity equation A₁V₁ = A₂V₂ to analyze flow behaviour across pipe diameter changes, channel constrictions, and duct transitions. Results are available across all standard flow rate units: m³/s · L/s · m³/h · GPM (gallons per minute) · CFM (cubic feet per minute).
The Q = A × v flow rate equation is foundational across all disciplines of fluid mechanics and hydraulic engineering, applied daily in a wide range of civil, mechanical, and environmental engineering contexts: water supply pipe network design & sizing · HVAC duct flow rate & air velocity calculation · open channel flow & stormwater drainage design · venturi meter, orifice plate & flow nozzle analysis · pump selection, pipeline sizing & pressure drop calculation · irrigation system design & agricultural water flow planning · wastewater treatment & sewage flow rate analysis. This online fluid flow calculator is trusted by civil engineers, mechanical engineers, hydraulic engineers, HVAC designers, environmental engineers, and fluid dynamics students for fast, accurate pipe flow, duct flow, and open channel flow calculations based on Bernoulli's principle and conservation of mass in fluid systems.
⚠ Engineering Disclaimer: This flow rate calculator is intended for educational, academic, and estimation purposes only. Calculations assume steady-state, incompressible, one-dimensional laminar flow and do not account for turbulent flow conditions (Reynolds number Re > 4000), fluid viscosity and dynamic viscosity effects, pipe friction losses (Darcy-Weisbach equation), minor head losses at bends and fittings, compressible gas flow, or two-phase flow behavior. For safety-critical hydraulic systems, pressure pipeline design, or municipal water supply engineering, always verify results with a licensed civil or mechanical engineer following applicable IS, BS EN, ASME, and ISO hydraulic engineering standards.
The continuity equation is a fundamental principle of fluid mechanics and fluid dynamics stating that for an incompressible fluid flowing through a closed pipe or channel system, the volumetric flow rate (Q) remains constant throughout — expressed mathematically as A₁V₁ = A₂V₂ = Q — where A is the cross-sectional area (m²) and V is the fluid velocity (m/s). This means that when a pipe narrows and cross-sectional area decreases, the fluid velocity must increase proportionally to maintain constant mass flow rate — the physical principle behind venturi meters, nozzles, and flow constrictions. Knowing any two of the three flow parameters — volumetric flow rate (Q) in m³/s or L/s, cross-sectional area (A) in m² or cm², or flow velocity (V) in m/s — allows the third to be precisely calculated using this flow rate calculator, making it essential for pipe flow analysis, hydraulic system design, HVAC duct sizing, irrigation system planning, and open channel flow calculations in both civil and mechanical engineering.
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Fluid Mechanics Calculator — Flow Rate, Pressure, Reynolds Number, and Bernoulli
Fluid mechanics governs everything from water distribution networks to aircraft aerodynamics. The continuity equation (A₁v₁ = A₂v₂) states that what flows into a pipe section must flow out — if the cross-section halves, velocity doubles. Bernoulli's equation adds pressure: increased velocity means decreased pressure, which explains lift on airplane wings, the Venturi effect in carburetors, and why shower curtains blow inward. The fluid mechanics calculator applies the continuity equation and Bernoulli's principle to pipe and nozzle problems with user-specified geometry and flow conditions.
Reynolds number Re = ρvD/μ predicts whether flow is laminar (smooth, Re < 2300) or turbulent (chaotic, Re > 4000), which determines friction losses in pipes. Water at 1 m/s in a 25mm pipe has Re ≈ 25,000 — fully turbulent. Oil at the same velocity in the same pipe has Re ≈ 2,500 due to much higher viscosity — near the transition zone. Turbulent flow creates significantly higher pressure losses than laminar flow, which is why pump sizing cannot ignore the flow regime. The calculator computes Re and identifies the flow regime for the given inputs.
Pressure drop in pipe systems — from Darcy-Weisbach or Hazen-Williams equations — determines the pump head required to maintain flow against system resistance. A 100m run of 50mm diameter pipe carrying 5 L/s of water loses roughly 4.5 m of head to friction. Adding fittings, valves, and elevation changes gives the total system head curve, which intersects the pump curve to determine operating flow. The calculator covers the pressure drop calculation for straight pipe sections as the foundation of pump selection.