Flow Rate Calculator
Find volumetric flow rate from area and velocity, or use continuity to see how speed changes in a narrowing pipe.
That is 15.708 L/s or 56.549 m³/h. Q = A · v with A = 0.007854 m².
Volumetric flow rate is area times average velocity, Q = A · v. For a circular pipe the area is A = π·d² ÷ 4. A 0.1 m pipe carrying water at 2 m/s has A ≈ 0.007854 m², so Q ≈ 0.007854 × 2 = 0.0157 m³/s, which is 15.7 L/s or about 56.5 m³/h.
Volumetric flow and conservation of mass
Volumetric flow rate (Q) is the volume of fluid passing a cross-section each second. It is the cross-sectional area the flow occupies multiplied by the fluid’s average velocity through that area, so a wider pipe or a faster flow both carry more. For a round pipe the area comes straight from the diameter, A = π·d² ÷ 4.
Because an incompressible fluid such as water cannot pile up or vanish, the same volume that enters a pipe each second must leave it — this is the continuity equation, A₁v₁ = A₂v₂. Where the pipe narrows, the area shrinks, so the velocity must rise to keep Q constant. That is why water speeds up through a nozzle and why the flow rate, not the velocity, is what stays fixed along a pipe of changing width.
Q = volumetric flow rate (m³/s), A = cross-sectional area (m²), v = average velocity (m/s); for a round pipe A = π·d² ÷ 4
Worked example
Water flows through a 0.1 m diameter pipe at an average velocity of 2 m/s. Find the volumetric flow rate.
- 1 Find the cross-sectional area. For a circular pipe, A = π·d² ÷ 4 = π × 0.1² ÷ 4 = 0.007854 m².
- 2 Multiply area by average velocity. Q = A · v = 0.007854 × 2 = 0.015708 m³/s. Keep d in metres and v in m/s so Q comes out in m³/s.
- 3 Convert to convenient units. Q = 0.015708 m³/s × 1000 = 15.708 L/s, and × 3600 = 56.549 m³/h.
- 4 For a change in width, use continuity. If the pipe narrows to d₂ = 0.05 m, then v₂ = v₁·(d₁ ÷ d₂)² = 2 × (0.1 ÷ 0.05)² = 8 m/s, and Q stays 0.015708 m³/s.
Flow-rate unit conversions
Volumetric flow rate is a volume per unit time; these factors move between the common engineering units.
| From | Equals | Notes |
|---|---|---|
| 1 m³/s | 1000 L/s | Multiply m³/s by 1000 to get litres per second |
| 1 m³/s | 3600 m³/h | Multiply m³/s by 3600 (seconds per hour) |
| 1 L/s | 3.6 m³/h | Handy for pumps and pipe sizing |
| 1 m³/h | 0.2778 L/s | Divide m³/h by 3.6 |
| A = π·d² ÷ 4 | d = 0.1 m → 0.007854 m² | Circular-pipe area from diameter |
Assumptions and common pitfalls
The velocity in Q = A · v is the average across the section. Real flow in a pipe is fastest at the centre and zero at the walls, so use the mean velocity, not the peak. The continuity form A₁v₁ = A₂v₂ assumes an incompressible fluid — excellent for liquids and for gases at low speed, but it breaks down for gases moving near the speed of sound, where density changes matter.
The most common mistake is mixing units: enter the diameter in metres, not millimetres, or the area will be off by a factor of a million. This calculator reports volumetric flow (volume per second); to get mass flow rate, multiply Q by the fluid density (ṁ = ρ·Q).