Circular Pipe Full Flow Calculator: Q = 0.312 D^(8/3) S^(1/2) / n

The flow a round culvert or drain carries when it runs full.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • Q = \frac{\pi}{4\cdot4^{2/3}}\frac{D^{8/3}S^{1/2}}{n}
  • D = \left(\frac{Qn}{0.3117\sqrt S}\right)^{3/8}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the full-pipe flow: full-pipe flow = (pi / (4 x 4^(2/3)) x inside diameter of the pipe^2.6667 x slope of the pipe (fall per length)^0.5) / (manning roughness n)
  2. Put the values in (every value in its SI unit): full-pipe flow = (pi / (4 x 4^(2/3)) x 0.6^2.6667 x 0.01^0.5) / (0.013)
  3. The answer: full-pipe flow: 0.614012 m3/s
  4. The same answer in other units: 614.012 litres per second; 2210.44 m3/h

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Inside diameter of the pipe; Full-pipe flow (leave it as it is if this is what you are finding) 0.61415 m3/s; Manning roughness n (leave it as it is if this is what you are finding) 0.013; Slope of the pipe (fall per length) (leave it as it is if this is what you are finding) 0.01 m/m.

  1. The formula, arranged to find the inside diameter of the pipe: inside diameter of the pipe = ((full-pipe flow x manning roughness n) / (pi / (4 x 4^(2/3)) x slope of the pipe (fall per length)^0.5))^0.375
  2. Put the values in (every value in its SI unit): inside diameter of the pipe = ((0.61415 x 0.013) / (pi / (4 x 4^(2/3)) x 0.01^0.5))^0.375
  3. The answer: inside diameter of the pipe: 0.600051 m
  4. The same answer in other units: 600.051 mm

Common questions

What is Manning's equation?

A formula for the flow in a channel or a gravity pipe from its size, its slope and the roughness of its walls.

How much flow does a 600 mm pipe carry?

About 0.6 m3/s when full at a fall of 1 in 100 for concrete.

Does this work for a culvert with a high water level at the inlet?

No. That is inlet control. Use this for pipes flowing under the pull of gravity along their length.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any hydraulics text (Manning's equation). Check against the Australian Rainfall and Runoff guide for design.

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