Flow Rate Formula
Calculate fluid flow rate Q = A × v (area × velocity).
Returns volume per time in L/s, m³/s, and GPM for pipes, channels, and orifice applications.
The Formula
Q = A × v
Flow rate is the volume of fluid that passes through a cross-section per unit time. It equals the cross-sectional area of the flow multiplied by the fluid velocity.
Variables
| Symbol | Meaning |
|---|---|
| Q | Volumetric flow rate (m³/s or liters/min) |
| A | Cross-sectional area of the pipe or channel (m²) |
| v | Average fluid velocity (m/s) |
Example 1
Water flows through a 5 cm diameter pipe at 2 m/s. Find the flow rate.
r = 0.025 m
A = π × (0.025)² = π × 0.000625 = 0.001963 m²
Q = 0.001963 × 2
Q = 0.00393 m³/s ≈ 3.93 liters/s ≈ 236 liters/min
Example 2
A rectangular channel (0.3 m × 0.2 m) carries water at 1.5 m/s
A = 0.3 × 0.2 = 0.06 m²
Q = 0.06 × 1.5
Q = 0.09 m³/s = 90 liters/s
When to Use It
Use the flow rate formula when:
- Sizing pipes for water supply or drainage systems
- Calculating how long it takes to fill a tank
- Designing irrigation and cooling systems
- Measuring river or stream discharge
Key Notes
- Flow rate scales with r² — doubling pipe diameter quadruples the flow at the same velocity; this is why slightly larger pipes give disproportionately large capacity gains
- The velocity v is the cross-sectional average — real pipe flow follows a parabolic Poiseuille profile (fastest at center, zero at wall); the formula uses mean velocity, not peak velocity
- Continuity equation: for incompressible flow, Q is constant along a pipe — if the cross-section narrows, velocity must increase (A₁v₁ = A₂v₂), which is why nozzles accelerate flow
- Mass flow rate (kg/s) = Q × ρ, where ρ is fluid density; for water at 20°C, ρ ≈ 998 kg/m³, so 1 L/s carries about 1 kg/s of mass
Key Notes
- Volumetric flow rate: Q = A × v (m³/s): Cross-sectional area A times average flow velocity v. For a pipe: Q = πr²v. Mass flow rate: ṁ = ρQ (kg/s). The distinction matters when density changes — for gases, use mass flow rate; for liquids, either works.
- Continuity equation: A₁v₁ = A₂v₂ (incompressible flow): Flow rate is conserved along a streamtube. Where the pipe narrows, velocity must increase proportionally. This is why blood accelerates through stenosed (narrowed) arteries — the same Q must pass through a smaller A.
- Measuring flow rate in practice: Venturi meter: pressure drop across a constriction gives Q. Orifice plate: simpler than Venturi, higher pressure loss. Ultrasonic flowmeter: non-intrusive, measures transit time of acoustic pulses. Coriolis flowmeter: measures mass flow directly via the Coriolis effect — most accurate for high-value or custody-transfer applications.
- Velocity profile — laminar vs turbulent: In laminar flow (Re < 2,300), the velocity profile is parabolic — zero at the wall, maximum at the center (v_max = 2v_avg). In turbulent flow, the profile is much flatter (v_max ≈ 1.2v_avg) due to turbulent mixing. Flowmeters must account for which profile exists.
- Applications: Flow rate calculations are used in pipe and pump system design, HVAC airflow balancing, irrigation scheduling, medical IV drip rate calculation (drops/min = flow rate / drop volume), wastewater treatment plant capacity, hydroelectric turbine power (P = ρQgh), and industrial process control.