Governing Formula
Pipe sizing for a target flow selects the internal diameter that produces an acceptable mean velocity. The continuity relation links the three quantities: flow rate, cross-sectional area, and velocity.
D = √(4·Q / (π·v)) Where:
-
Q= Volumetric flow rate (entered in m³/h, converted to m³/s for sizing) [m³/h] -
v= Target mean flow velocity at the design diameter [m/s] -
A= Required cross-sectional flow area = Q / v [m²] -
D= Required internal pipe diameter [mm]
Derived Equations:
A = Q / v D = √(4·A / π) D = √(4·Q / (π·v)) How the Calculation Works
The flow rate is converted from m³/h to m³/s, then divided by the target velocity to obtain the required flow area. Because the pipe is assumed circular, the internal diameter follows directly from the area of a circle:
A = Q / v · D = √(4·A / π)
The result is compared with the recommended design range of 0.5–2.5 m/s for potable and process water. The upper bound can be adjusted; at velocities above about 2.5 m/s erosion, noise, and surge concerns increase, while below about 0.5 m/s sedimentation and air-release issues become more likely in distribution piping. A suggested nominal (DN) size is selected as the next standard size above the computed internal diameter — the final bore still needs to be confirmed against the selected pipe schedule.
Worked Engineering Example
Design Scenario: Distribution Header, 36 m³/h at a Target Velocity of 1.5 m/s
- Convert flow to m³/s:
Q = 36 / 3600 = 0.010 m³/s - Required flow area:
A = Q / v = 0.010 / 1.5 = 0.00667 m² - Required internal diameter:
D = √(4 × 0.00667 / π) = 0.0921 m = 92.1 mm - Suggested nominal size:
92.1 mm → DN100 (next standard nominal size above the required diameter) - Velocity check at the selected bore:
v = 0.010 / ((π/4) × 0.1²) = 1.27 m/s → within the 0.5–2.5 m/s design range
Engineering Notes & Design Benchmarks
| Application | Common Design Velocity | Note |
|---|---|---|
| Potable water distribution | 0.5 – 2.0 m/s | Higher velocities can cause surge and noise |
| Process / chilled water piping | 1.0 – 2.5 m/s | Balanced against pumping energy and erosion |
| Pump suction lines | ≤ 1.5 m/s | Lower velocities reduce NPSH and air entrainment risk |
| Dosing / small-bore lines | 0.3 – 1.0 m/s | Very small bores can still be turbulent (see Reynolds number) |
These bands are common engineering practice, not code limits. The selected diameter must always be re-checked for head loss and pressure drop (see the Darcy–Weisbach calculator) because a smaller bore raises both velocity and friction losses.
Assumptions & Limitations
- Sizing is based on internal diameter, not the nominal DN; the actual bore depends on the pipe schedule or wall thickness selected.
- The recommended range of 0.5–2.5 m/s is an engineering convention for water, not a safety or code limit.
- Friction and pressure drop are not computed here; pump duty must include the friction losses from the final pipe route.
- Single-phase liquid flow in a uniform circular pipe is assumed; slurries, gases, or gravity flow need different sizing rules.
Frequently Asked Questions
Should I use the computed diameter or the suggested nominal size?
Select a standard pipe whose actual internal bore is at least the required diameter, then recheck the resulting velocity. The suggested nominal size is the next standard DN above the required diameter, but schedule-dependent bore thickness means the true velocity should be confirmed for the final pipe chosen.
Why does a smaller diameter need a recheck for head loss?
Sizing fixes the velocity, not the pressure drop. At the same flow, a smaller bore raises velocity and friction losses grow steeply (about the 1.85–2 power of velocity), so a diameter that appears acceptable on velocity alone can still produce an excessive pump head. Confirm with the Darcy–Weisbach calculator.
What happens if my target velocity is outside 0.5–2.5 m/s?
The calculator reports whether the result sits inside the recommended range. Above the range you risk erosion, noise, surge, and high friction losses; below it you risk sedimentation and air pockets in horizontal runs. Adjust the target velocity or accept the flagged trade-off deliberately.
Engineering Disclaimer
Engineering Note: This calculator provides preliminary pipe sizing from flow and a target velocity within the recommended range. It does not replace friction-loss, pressure rating, or code-based design; the final pipe size must be verified for head loss, pressure class, and applicable codes before purchase.
Technical References
- Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe (TP 410), 2009.
- White, F. M., Fluid Mechanics, 8th ed., McGraw-Hill, 2016.
- Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, Wiley.