Volumetric Flow Rate Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The volumetric flow rate is calculated with Q = velocity × cross-sectional area. For a fluid flowing at 2 m/s through a pipe with a 0.05 m² cross-section, the flow rate is 0.1 m³/s, i.e. 100 L/s.
Explanation
Volumetric flow rate measures the volume of fluid that crosses a given section per unit of time. This relationship follows directly from the continuity equation in fluid mechanics: in one second, the fluid travels a distance equal to its velocity, sweeping out a volume equal to that distance multiplied by the pipe's cross-section. This simple relationship assumes uniform flow across the whole section (the same velocity at every point), a reasonable approximation for so-called "plug flow" but one that departs from reality for viscous flow in a pipe, where velocity varies from the center toward the walls (a parabolic profile in laminar flow). An important consequence of this relationship, following from the conservation of flow rate in a closed pipe with no leaks: if the cross-section decreases (the pipe narrows), the velocity must increase to maintain the same flow rate, and vice versa — this is the principle that explains why water speeds up when leaving a garden hose partially blocked by a finger.
Example: flow at 2 m/s through a pipe with a 0.05 m² cross-section
Inputs
Velocity: 2 m/s. Cross-section: 0.05 m².
Calculation
Volumetric flow rate = 2 × 0.05 = 0.1 m³/s, i.e. 0.1 × 1,000 = 100 L/s.
Result
The flow rate in this pipe is 0.1 m³/s, i.e. 100 liters per second.
Frequently asked questions
How do I calculate the cross-section of a circular pipe?
For a circular pipe of radius r, the cross-section is calculated with π × r² (the area of a circle). Our circle area and circumference calculator lets you calculate it directly from the radius or diameter.
Why does velocity increase when a pipe narrows?
Because the volumetric flow rate is conserved in a closed pipe with no leaks or accumulation: if the cross-section decreases, the velocity must increase proportionally so that the product velocity × cross-section (and thus the flow rate) stays constant. This is the same physical principle that explains the Venturi effect.
Does this calculation hold for a gas as well as a liquid?
The relationship Q = v × A still holds for a gas, but with an important caveat: it assumes an incompressible fluid (constant volume regardless of pressure), an assumption that is almost always true for a liquid but becomes approximate for a gas at high speed or under strong compression, where density variations must be accounted for a rigorous calculation.