Fluid Velocity Calculator
GPM (US Gallons/min)
LPM (Liters/min)
m³/hr (Cubic meters/hour)
CFS (Cubic feet/sec)
Inches (in)
Millimeters (mm)
Feet (ft)
Meters (m)
Linear Velocity (Imperial):
0.00 ft/s
0.00 ft/s
Linear Velocity (Metric):
0.00 m/s
0.00 m/s
How to Calculate Linear Velocity from Flow Rate
Understanding the relationship between volumetric flow rate and linear velocity is fundamental in fluid dynamics, pipe sizing, and hydraulic engineering. While flow rate tells you how much fluid is moving, linear velocity tells you how fast it is traveling through the pipe.
The Formula
The calculation is based on the continuity equation. To find the linear velocity, you divide the volumetric flow rate by the cross-sectional area of the pipe.
v = Q / A
Where:
- v = Linear Velocity (e.g., ft/s, m/s)
- Q = Volumetric Flow Rate (e.g., GPM, m³/s)
- A = Cross-Sectional Area of the pipe (e.g., ft², m²)
Step-by-Step Calculation Logic
Since pipes are usually circular, calculating the Area ($A$) requires the pipe's diameter ($D$). The formula for the area of a circle is $A = \pi \times (D/2)^2$.
Here is how the calculation works in practice:
- Convert Units: Ensure flow rate and diameter are in compatible units. For example, convert GPM to cubic feet per second, and inches to feet.
- Calculate Area: Square the radius (Diameter / 2) and multiply by Pi ($\pi$).
- Divide: Divide the standardized Flow Rate by the calculated Area.
Example Calculation
Let's say you have water flowing at 100 GPM through a 3-inch diameter pipe.
- Convert Flow: 100 GPM ≈ 0.2228 cubic feet per second (CFS).
- Convert Diameter: 3 inches = 0.25 feet.
- Calculate Area: Radius = 0.125 ft. Area = $\pi \times 0.125^2 \approx 0.049$ sq ft.
- Calculate Velocity: $v = 0.2228 / 0.049 \approx 4.54$ ft/s.
Why Velocity Matters
Maintaining the correct linear velocity is crucial for system efficiency and longevity:
- Too Slow (< 2-3 ft/s): Solids suspended in the fluid may settle out, causing blockages (sedimentation).
- Too Fast (> 7-10 ft/s): High velocity can cause pipe erosion, water hammer issues, noise, and excessive friction head loss (requiring larger pumps).
Standard Velocity Guidelines
For general water systems, design guidelines often suggest:
- Suction Side: 2 to 5 ft/s
- Discharge Side: 5 to 8 ft/s
- Drain Lines: 2 to 4 ft/s