Flow Rate Calculator (Velocity Method)
Calculated Flow Rate
How to Calculate Flow Rate from Velocity
Calculating the volumetric flow rate of a fluid moving through a pipe is a fundamental task in engineering, plumbing, HVAC, and irrigation. By knowing the velocity of the fluid and the dimensions of the pipe, you can determine exactly how much volume is passing through a specific point over time.
The Fundamental Formula
The relationship between flow rate, velocity, and area is described by the continuity equation for incompressible fluids. The basic formula is:
Where:
- Q = Volumetric Flow Rate (e.g., m³/s, GPM)
- A = Cross-sectional Area of the pipe (e.g., m², ft²)
- v = Average Velocity of the fluid (e.g., m/s, ft/s)
Step-by-Step Calculation Guide
1. Determine the Pipe Area
Most pipes are cylindrical. To find the cross-sectional area (A), you first need the internal diameter (d). The formula for the area of a circle is:
or
A = (π × d²) / 4
Important: Ensure you convert your diameter to the same unit system as your velocity before calculating. If velocity is in meters per second, diameter should be in meters.
2. Measure the Velocity
The velocity (v) is usually determined by flow meters, pitot tubes, or calculated based on pressure drops. For this calculation, we assume the average velocity across the pipe section.
3. Multiply Area by Velocity
Multiply the Area (A) by the Velocity (v) to get the Flow Rate (Q). The resulting unit will be [Length Unit]³ / [Time Unit].
Real-World Example
Scenario: You have a water pipe with an internal diameter of 4 inches. The water is flowing at a velocity of 5 feet per second. What is the flow rate in Gallons Per Minute (GPM)?
Step 1: Convert units to feet
Diameter = 4 inches = 4/12 feet ≈ 0.333 ft.
Step 2: Calculate Area (ft²)
Radius = 0.333 ft / 2 = 0.1665 ft
Area = π × (0.1665)² ≈ 0.0873 ft²
Step 3: Calculate Flow Rate (Cubic Feet per Second)
Q = 0.0873 ft² × 5 ft/s = 0.4365 ft³/s
Step 4: Convert to GPM
1 ft³/s ≈ 448.8 GPM
Q = 0.4365 × 448.8 ≈ 195.9 GPM
Factors Affecting Accuracy
While the formula Q = Av is mathematically exact, real-world conditions can introduce variables:
- Viscosity: Highly viscous fluids may have a different velocity profile (laminar vs. turbulent flow).
- Pipe Roughness: Friction against the pipe walls reduces velocity near the edges.
- Obstructions: Valves and fittings create turbulence that alters local velocity.
For most general purposes in plumbing and process engineering, using the average velocity and internal diameter provides a sufficiently accurate estimate.