What kind of pipe?

VelocityFull pipe, Q = V × AGravity sewerManning, partly fullForce mainHazen-Williams head loss

Your numbers

Pipe diameterin

FlowgpmMGDcfs

This assumes the pipe is flowing full, like a force main or a surcharged sewer. Use Gravity sewer for a pipe running partly full.

Velocity

3.97

ft/s

Pipe area

0.1963

ft²

Flow for 2 ft/s

176.3

gpm

Your numbers, step by step

1. Diameter in feet6 in ÷ 12 = 0.5 ft
2. Pipe area0.7854 × 0.5² = 0.1963 ft²
3. Flow in cubic feet per second350 gpm ÷ 448.83 = 0.7798 cfs
4. Velocity0.7798 cfs ÷ 0.1963 ft² = 3.97 ft/s
5. Flow needed to reach 2 ft/s2 ft/s × 0.1963 ft² = 0.3927 cfs × 448.83 = 176.3 gpm

Why it works

Full pipes follow the continuity rule on the formula sheet: flow equals area times velocity. Know any two and you have the third. Everything is done in feet and seconds, so inches become feet and gpm becomes cubic feet per second first. One cfs is 448.83 gpm.

Gravity sewers rarely run full, so the area is only the wetted slice of the circle. Manning's equation sets the speed from three things: how rough the pipe is (n), how steep it is (slope), and the hydraulic radius, which is the flow area divided by the length of pipe wall the water touches. A pipe running half full has the same hydraulic radius as a full one, so it moves at the same speed carrying half the flow.

Force mains are full and under pressure, so the question becomes how much head friction eats. Hazen-Williams answers that from flow, diameter, length and a smoothness factor (C). Higher C means a smoother pipe and less loss. Head loss climbs with flow to the 1.85 power, so a pump running 20% faster loses about 40% more head in the main.

Example: a slow night in an 8-inch sewer

An 8-inch sewer laid at 0.40% slope, the usual minimum for that size, is running 2 inches deep at 3 a.m. Using the design n of 0.013:

• d/D = 2 ÷ 8 = 0.25, so the wetted area is 0.0682 ft²
• Hydraulic radius = 0.0682 ÷ 0.698 = 0.0978 ft
• V = 1.486 ÷ 0.013 × 0.0978^2/3 × 0.004^1/2 = 1.53 ft/s
• Q = 1.53 × 0.0682 = 0.105 cfs, about 47 gpm

Full, the same pipe carries about 343 gpm at 2.2 ft/s. At night it is using about 14% of that and moving below 2 ft/s, so grit and grease can settle. That is normal on a low-flow night. Daily peaks should flush it, but a reach that stays shallow all day belongs on the cleaning schedule.

Put this example in the calculator

Example: checking a force main

A lift station pushes 350 gpm through 2,400 ft of 6-inch cement-lined ductile iron (C ≈ 120).

• (100 ÷ 120)^1.85 = 0.714
• 0.002083 × 2,400 × 0.714 × 350^1.85 ÷ 6^4.8655 = 29.7 ft of friction loss
• 29.7 ÷ 2.31 = 12.9 psi
• 350 gpm = 0.78 cfs ÷ 0.196 ft² = 3.97 ft/s

Add the static lift to the 29.7 ft to get the head the pump works against. If discharge pressure creeps up over the years at the same flow, the C value is dropping: buildup in the main, or a partly closed valve.

Put this example in the calculator

Do the numbers look reasonable?

Pipe	Typical velocity	Why it matters
Gravity sewer	2 ft/s or more at design flow	Below about 2 ft/s solids settle; above about 10 ft/s the pipe wears.
Force main	About 2–8 ft/s	Slow mains collect solids and go septic; fast ones waste energy and risk water hammer.
Manning's n	About 0.011–0.015	Most design standards use 0.013 for any material, allowing for slime and joints.
Hazen-Williams C	About 100–150	New plastic is near 140–150; old unlined iron can fall below 100.

Before you trust the answer

• Use the inside diameter. A nominal 8-inch pipe can be a little more or less inside. For rough checks nominal is fine.
• Manning assumes steady, uniform flow. Depth taken just upstream of a drop, a bend or a backed-up junction won't match the formula.
• Compare with a real number. A flow meter, a pump drawdown or a timed wet-well fill beats any formula. Use the math to spot a meter that's drifting.
• Friction is only part of the head. Pump total dynamic head also includes static lift and fitting losses.

This is a study and field-check aid, not a design tool. Your utility's standards and engineer take priority over any number on this page.