Pipe Diameter Calculator
Calculation based on continuous flow.
How to Calculate Pipe Diameter from Flow Rate
Determining the correct pipe size for a specific application is a fundamental task in fluid dynamics and plumbing design. While the flow rate is often determined by the process requirements (e.g., how much water needs to be moved), the pipe diameter must be calculated to ensure the fluid moves efficiently without excessive pressure loss or noise.
To calculate the internal diameter of a pipe, you need two key variables:
- Volumetric Flow Rate (Q): The volume of fluid passing through a cross-section per unit of time.
- Flow Velocity (v): The speed at which the fluid travels through the pipe.
The Core Formula
The relationship between flow rate, velocity, and area is described by the continuity equation:
Q = A × v
Where:
- Q = Flow Rate
- A = Cross-sectional Area of the pipe
- v = Average Velocity of the fluid
Since pipes are circular, the Area (A) can be written in terms of Diameter (d): A = (π × d²) / 4. By substituting this into the continuity equation and rearranging for diameter, we get the formulas used in this calculator.
Imperial Formula (GPM & Inches)
When using Gallons Per Minute (GPM) and Velocity in Feet Per Second (ft/s), the derived formula for Diameter in inches is:
d (inches) = √ [ (0.4085 × GPM) / Velocity ]
Metric Formula (m³/h & mm)
When using Cubic Meters per Hour (m³/h) and Velocity in Meters Per Second (m/s), the derived formula for Diameter in millimeters is:
d (mm) = √ [ (353.68 × Flow) / Velocity ]
Selecting the Right Velocity
The hardest part of sizing a pipe is often deciding what "Velocity" to input. If the velocity is too high, you risk water hammer, erosion of pipe walls, and high friction loss (requiring larger pumps). If the velocity is too low, the pipe diameter becomes unnecessarily large and expensive, and suspended solids may settle out.
Here are standard industry guidelines for water applications:
| Application | Imperial Velocity (ft/s) | Metric Velocity (m/s) |
|---|---|---|
| General Water Service | 3 – 10 ft/s | 1 – 3 m/s |
| Pump Suction (Inlet) | 2 – 5 ft/s | 0.6 – 1.5 m/s |
| Pump Discharge (Outlet) | 5 – 12 ft/s | 1.5 – 3.5 m/s |
| Drain Lines | 2 – 4 ft/s | 0.6 – 1.2 m/s |
Example Calculation
Suppose you need to pump 150 GPM of water and you want to maintain a safe velocity of 8 ft/s.
1. Multiply Flow by Constant: 150 × 0.4085 = 61.275
2. Divide by Velocity: 61.275 / 8 = 7.66
3. Take the Square Root: √7.66 ≈ 2.77 inches
In this scenario, you would likely select a standard 3-inch pipe to accommodate the flow.