Find the smallest listed Schedule 40 steel pipe that carries 100 US gpm without exceeding an assumed maximum average velocity of 6 ft/s. The velocity limit is an example input, not a universal design recommendation.
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 | US gpm |
| Maximum average velocity | 6 | ft/s |
| Standard steel pipe series | Schedule 40 |
2. Step-by-step Math
Convert flow to cubic feet per second
Q = 100 × 231 / (1728 × 60) Q = 0.222800925926 ft³/s
Use US gallons and the actual inside diameter. Nominal pipe size is only the size designation.
Solve continuity for the minimum inside diameter
V = 4Q / (πD²) Dmin = √[4Q / (πVmax)] Dmin = √[4 × 0.222800925926 / (π × 6)] Dmin = 0.217439244193 ft ≈ 2.61 in
This is a continuous mathematical diameter. It does not mean a pipe with that exact bore is available.
Check the next available sizes
NPS 2½ Schedule 40: ID ≈ 2.47 in V = 4 × 0.222800925926 / [π × (2.469/12)²] V = 6.701120418 ft/s → exceeds 6 ft/s NPS 3 Schedule 40: ID ≈ 3.07 in V = 4 × 0.222800925926 / [π × (3.068/12)²] V = 4.339891695 ft/s → meets 6 ft/s
The calculator selects NPS 3 (DN 80), the first size in its table with an inside diameter at least as large as the calculated minimum.
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 |
|---|---|---|
| Minimum inside diameter | 2.61 in | __________ |
| Selected nominal size | NPS 3 / DN 80 | __________ |
| Selected inside diameter | 3.07 in / 77.9 mm | __________ |
| Selected average velocity | 4.34 ft/s / 1.32 m/s | __________ |
Second check
A 50 gpm cross-check at the same 6 ft/s limit gives a minimum diameter of 2.61 / √2 = 1.85 in. NPS 2 Schedule 40 has a 2.07-inch bore and carries that flow at 4.78 ft/s.
4. Assumptions and Method
This is velocity-only sizing using the calculator’s listed steel pipe IDs. Complete pressure-drop, mechanical, corrosion, erosion, noise and service checks before selecting a line. Consult the pipe schedule reference for dimensions.
Equation definitions and implementation: Pipe Sizing Calculator. See also calculation methodology and other worked examples.