Linear Velocity to Volumetric Flow Rate Calculator
Calculate fluid discharge based on pipe diameter and flow speed.
Calculation Results
Understanding Linear Velocity vs. Volumetric Flow Rate
In fluid dynamics, understanding how the speed of a liquid (linear velocity) relates to the total volume passing through a conduit (volumetric flow rate) is essential for plumbing, irrigation, and industrial process engineering.
The Fundamental Formula
The relationship between these two metrics is governed by the Continuity Equation. For a pipe with a constant cross-sectional area, the formula is:
Q = v × A
- Q: Volumetric Flow Rate (e.g., m³/s)
- v: Linear Velocity (e.g., m/s)
- A: Cross-sectional Area of the pipe (e.g., m²)
How to Calculate Pipe Area
Since most pipes are cylindrical, the cross-sectional area is a circle. The area is calculated using the internal diameter (d):
A = π × (d / 2)²
It is crucial to use the internal diameter, as the pipe wall thickness does not contribute to the flow area.
Practical Example
Imagine you have a pipe with an internal diameter of 100 mm and water is moving through it at a velocity of 2 meters per second.
- Convert diameter to meters: 100mm = 0.1m.
- Calculate Area: A = 3.14159 × (0.1 / 2)² = 0.007854 m².
- Calculate Flow Rate: Q = 2 m/s × 0.007854 m² = 0.015708 m³/s.
- Convert to Hourly: 0.015708 × 3600 = 56.55 m³/h.
Frequently Asked Questions
Why does velocity change if the pipe diameter gets smaller?
According to the principle of conservation of mass, if the flow rate (Q) remains constant, a decrease in the cross-sectional area (A) must result in an increase in linear velocity (v) to maintain the same volume of fluid movement.
What is a "safe" linear velocity for water pipes?
In general domestic plumbing, velocities are kept between 1.5 to 2.5 meters per second (5 to 8 feet per second). Velocities higher than this can lead to pipe erosion, noise, and "water hammer" effects.