Find the average velocity of a liquid flowing at 100 US gpm through a full circular pipe with a 2.067-inch inside diameter. Enter the actual bore, not the nominal 2-inch size.
1. Calculator Inputs
Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.
| Calculator field | Value | Unit / setting |
|---|---|---|
| Volumetric flow rate | 100 | gpm |
| Inside diameter | 2.067 | in |
2. Step-by-step Math
Convert the flow and diameter
Q = 100 × 231 / (1728 × 60) = 0.222800926 ft³/s D = 2.067 / 12 ≈ 0.172 ft
One US gallon contains 231 cubic inches. There are 1,728 cubic inches in a cubic foot and 60 seconds in a minute.
Calculate the internal flow area
A = πD² / 4 A = π × 0.17225² / 4 ≈ 0.0233 ft² A ≈ 0.00216 m²
Area depends on the square of the inside diameter. Keep the unrounded area for the next step.
Divide flow by area
V = Q / A V = 0.222800925926 / 0.0233028125954 V = 9.561117355 ft/s = 2.914228570 m/s
This is the cross-sectional average velocity, not the velocity at the pipe centerline.
3. Compare Your Answers
Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Flow area | 0.00216 m² | __________ |
| Velocity | 2.91 m/s | __________ |
| Velocity | 9.56 ft/s | __________ |
Second check
As a second check, reduce the flow to 50 gpm without changing the diameter. Velocity must halve to 4.78 ft/s. Doubling the diameter at the original flow would reduce velocity to one quarter.
4. Assumptions and Method
The pipe is full, circular, and carries a single phase. For gas, use actual volumetric flow at pipe conditions. This example does not establish an acceptable design velocity or include friction losses.
Equation definitions and implementation: Pipe Velocity Calculator. See also calculation methodology and other worked examples.