Pipe Flow Calculator

Gravity flow (Manning)

Q = (1.486/n) A R^2/3 S^1/2 for a circular section with n constant over the depth. The pipe carries its largest open-channel discharge near y/D = 0.938, about 7.6% more than flowing full. Between those two discharges two depths carry the same flow: the lower one is reported with a warning. Above the maximum the pipe would flow under pressure.

Hazen-Williams

V = 1.318 C R^0.63 S^0.54 in US customary units, for full pipes carrying water at ordinary temperatures.

Darcy-Weisbach

h_f = (f L/D + ΣK) V²/2g, water at 60 °F. The friction factor is 64/Re in laminar flow; in turbulent flow Swamee-Jain (explicit) or Colebrook (iterated). Reynolds numbers between 2,000 and 4,000 are flagged as transitional.

Units and numbers

Diameters are entered in inches (millimetres in SI). All calculations run in US customary units in your browser; SI values are converted for display.

The calculator is tested against the cases below every time its code changes.

Tolerances: depths ±0.01 ft or ±0.5%; discharge and velocity ±1% or half a unit of the last printed digit. HEC-22 uses 1.49 in Manning’s equation (this calculator 1.486). Pressure flow is checked against six EPANET 2.2 runs (head loss and velocity ±1%) and for internal consistency (round trips; Swamee-Jain against Colebrook).

• Darcy-Weisbach uses g = 32.174 ft/s²; programs that use 32.2 (EPANET, for example) give head losses about 0.08% lower.
• Steady flow in one pipe. Surcharged storm sewers, the hydraulic grade line through manholes and junctions, and water hammer are not computed.
• Non-circular conduits (boxes, arches, elliptical pipe) are not included; use the Channel Flow Calculator for open-channel flow in other shapes.
• Your city, county or TxDOT may set the n, minimum velocity, depth ratio and design flow to use. Those criteria decide the design.

Why can a partly full pipe carry more than a full one?

Near the crown the wetted perimeter grows faster than the flow area, so the hydraulic radius falls. With a constant n, the largest open-channel discharge occurs near y/D = 0.938 and is about 7.6% above the full-pipe value; between the two discharges, two depths carry the same flow; the calculator reports the lower one with a warning.

Hazen-Williams or Darcy-Weisbach?

Hazen-Williams is an empirical formula for water at ordinary temperatures in pressure pipes of moderate size and velocity. Darcy-Weisbach applies to any fluid and flow regime, with the friction factor from the Swamee-Jain or Colebrook equation (your choice). Many water utilities set which one to use.

Does n change with depth?

Not here: the calculator uses one n at every depth, the usual design assumption behind the hydraulic-elements curves. Some references let n vary with depth, which lowers the computed capacity of a partly full pipe.

Can I attach the calculation sheet to a design report?

You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.