TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Pipe Flow Rate & Velocity Calculator

Flow rate from average velocity and pipe inside diameter, or velocity from flow rate.

Inputs

Calculate from
Side view of a pipe running full, inside diameter D, with flow arrows showing average velocity v, and the circular flow area A at the open end.AvDQ = v × A
Liquid fills a pipe of inside diameter D and moves at average velocity v. The volume passing each second is Q = v × A, where A = πD² ÷ 4 is the inside area. Diagram not to scale.

The bore (inside) diameter, not the nominal size or outside diameter. For example, a steel pipe of nominal size DN 50 schedule 40 has a bore of about 52.5 mm.

Mean velocity over the whole cross-section (flow rate ÷ area), not the peak velocity at the centre.

Leave empty if you do not need mass flow. Water is about 1000 kg/m³ (998 at 20 °C).

Result

Volumetric flow rate
14.1372
Flow area (inside cross-section)
1,963.5

Liquid moving at an average of 2 m/s through a bore of 50 mm (area 1,963.5 mm²) gives a flow of 14.1372 m³/h.

Educational estimate — check the assumptions below.

About this calculator

The volume of fluid passing through a pipe each second equals the average velocity multiplied by the inside cross-sectional area. Use it to check how fast water or another liquid moves in a pipe for a given flow, or how much flow a pipe carries at a known velocity. It is a quick first check when choosing a pipe bore — for example, many water systems are designed for average velocities of roughly 1 to 3 m/s.

Volumetric flow is a volume per unit time (m³/h, L/min). Mass flow is a mass per unit time (kg/h) and needs the fluid density.

Formula

Q = v × A    A = πD² ÷ 4

v = Q ÷ A    ṁ = ρ × Q

Q = volumetric flow rate (m³/s), v = average velocity (m/s), A = inside cross-sectional area (m²), D = inside diameter (m), ṁ = mass flow rate (kg/s), ρ = fluid density (kg/m³).

Worked example

Find flow: water at 2 m/s in a pipe with a 50 mm bore.

  • Area = π × 0.05² ÷ 4 = 0.0019635 m² (1963.5 mm²)
  • Flow = 2 × 0.0019635 = 0.003927 m³/s = 14.14 m³/h (3.93 L/s)
  • With ρ = 1000 kg/m³: mass flow = 3.93 kg/s = 14 137 kg/h

Find velocity: 100 US gal/min through a 4 in bore. Area = 12.566 in² = 0.0081073 m²; flow = 0.0063090 m³/s; velocity = 0.0063090 ÷ 0.0081073 = 0.778 m/s (2.55 ft/s).

Assumptions and limitations

  • The pipe runs full, with a circular bore of the diameter entered.
  • Velocity is the average across the section. The real velocity is higher at the centre and near zero at the wall.
  • This is a continuity (volume balance) calculation only. It does not calculate friction loss, pressure drop, pump head, turbulence or flow in a pipe network.
  • For gases, volume flow changes with pressure and temperature; enter the velocity and flow at the same conditions.

References

  • Continuity equation for incompressible flow, Q = v·A; mass flow ṁ = ρ·Q.