Flow Rate Calculator (Physics)

Volumetric flow rate is defined by the continuity equation for incompressible flow:

$$Q = A \cdot v$$

where:

• Q — volumetric flow rate (m³/s)
• A — cross-sectional area of the flow channel (m²)
• v — average flow velocity (m/s)

This relationship arises from the principle of mass conservation. For an incompressible fluid (constant density), the volume of fluid passing through any cross-section per unit time must equal the product of that cross-section's area and the average velocity perpendicular to it.

For a circular pipe with diameter D, the cross-sectional area is:

$$A = \frac{\pi D^2}{4}$$

Unit conversions applied:

• 1 m³/s = 60,000 L/min
• 1 m³/s = 15,850.32 US gallons per minute (GPM)

The continuity equation also implies that for steady incompressible flow, if the cross-sectional area decreases, the velocity must increase proportionally — the basis for devices like Venturi meters and nozzles.

In practice, the velocity profile across a pipe cross-section is not uniform. For laminar flow, the profile is parabolic (Poiseuille flow), while for turbulent flow it is flatter. The value used in Q = Av is the mean velocity, which accounts for the integrated effect of the velocity distribution.

Flow rate measurement is critical in chemical processing, water distribution, oil and gas transport, and medical applications such as IV drip rate calculations. Instruments like flow meters, pitot tubes, and ultrasonic sensors measure velocity or flow rate directly.

The calculated flow rate tells you the volume of fluid passing through the specified area per unit time. Higher flow rates indicate more fluid transport capacity. Ensure that the pipe material and joints can handle the flow velocity — excessive velocities cause erosion, noise, and pressure drops. Typical design velocities in water systems are 1–3 m/s for distribution pipes and up to 6 m/s for short runs.