Flow Rate Calculator

How to use the flow rate calculator

The volumetric flow rate (also called the discharge rate) is the volume of fluid that crosses a section of pipe per unit of time. The calculator offers two routes to it, chosen with the Solve via buttons.

• Pressure difference. For a round pipe, enter the pressures at the two ends, the inner diameter, the length of pipe between the gauges and the dynamic viscosity of the fluid. The flow is then found from the Hagen-Poiseuille law.
• Flow velocity. Enter how fast the fluid moves and describe the cross-section, either a round pipe (diameter) or a rectangular duct (width and height). The flow is the velocity times the area.

The unit system buttons decide which units the answers are printed in: cubic metres and litres for metric, or cubic feet, cubic yards and US gallons for US units. They do not change your inputs, because every field has its own unit menu and you can mix them freely, for instance psi for pressure and millimetres for diameter.

Each answer is given per hour together with a second figure per minute or per second, whichever reads more naturally for the size of the flow. If you enter the density of a liquid, a mass flow rate row is added; leave the density empty for gases.

Flow rate formulas

Flow rate Q is volume divided by time. There are two practical ways to obtain it, depending on what you can measure.

Worked examples

Round pipe, velocity known. Water moves at 2 m/s through a pipe with a 50 mm inner diameter. A = π × 0.025² ≈ 0.0019635 m², so Q = 2 × 0.0019635 ≈ 0.003927 m³/s. That is 3.927 litres per second or about 14.14 m³/h. With a water density of 1,000 kg/m³ the mass flow is 3.927 kg/s, or about 14.14 tonnes per hour.

Rectangular duct. Air travels at 4 m/s through a duct 0.3 m wide and 0.2 m high. A = 0.06 m², so Q = 0.24 m³/s, which equals 240 l/s or 864 m³/h.

US units. A 2 inch pipe carries a stream at 5 ft/s. The radius is 1 inch, or 1/12 ft, so A = π × (1/12)² ≈ 0.021817 ft². Then Q = 5 × 0.021817 ≈ 0.10908 ft³/s, which is about 392.7 ft³/h or 49.0 US gallons per minute.

Pressure drop. A lubricating oil with μ = 0.2 Pa·s is pushed through a 2 m pipe of 10 mm inner diameter by a pressure difference of 100 kPa. Q = π × (0.01)⁴ × 100,000 ÷ (128 × 0.2 × 2) ≈ 6.136 × 10⁻⁵ m³/s, about 0.0614 l/s or 221 l/h. The mean velocity is Q ÷ A = 0.78 m/s.

When the formulas apply

The velocity route is general: the flow is always the area times the average speed, whatever the fluid. The pressure route is much more restricted, because the Hagen-Poiseuille law assumes:

• Laminar flow. The fluid moves in smooth layers. In a pipe this holds when the Reynolds number is below roughly 2,000. Water at ordinary speeds in a 50 mm pipe has a Reynolds number near 100,000, far into the turbulent range, so the pressure mode suits thick, slow liquids such as oils, or very narrow tubes. Check yours with the Reynolds number calculator.
• An incompressible fluid. Liquids are fine; gases that expand noticeably along the pipe are not.
• A long, straight, full pipe. The flow must be fully developed, so short stubs, bends and valves break the assumption.
• A constant viscosity. Viscosity changes strongly with temperature, so use the value at the working temperature.

For turbulent flow the pressure loss follows the Darcy-Weisbach equation, which is not part of this tool. If you need the liquid density first, the density calculator can supply it from a mass and a volume. For the volume of a pipe section see the volume of a cylinder calculator.

Common mistakes

• Entering the radius as the diameter. The field wants the full inner diameter. Because the diameter is raised to the fourth power in the pressure formula, this mistake changes the answer by a factor of sixteen.
• Using absolute and gauge pressures together. Only the difference matters, but both readings must be on the same basis.
• Confusing the viscosity units. Water at room temperature is about 0.001 Pa·s, which is the same as 1 centipoise (cP). Oils range from tens to hundreds of cP.
• Reversing the pressures. Flow runs from high pressure to low. If the pressure at the start is lower than at the end, the result is negative, meaning the fluid moves the other way.
• Using outside dimensions. Pipe sizes are often quoted by nominal or outer diameter. Use the inside diameter of the bore.