Flow Rate Measurement From A Vertical Pipe

100mm or 4in pipe is about right for this application.

It is a little unusual to want to use the overflow height for flow measurement in a vertical pipe, as variable area flowmeters that operate vertically are readily available, relatively cheap, and will give rather more accurate flow reading than any measurement based upon the discharge from a vertical circular weir! Of course, the selected fluid needs to be transparent to be able to see the bob in some types, though a magnetically-coupled bob with a scale read-out is available in the larger sizes.

Depending upon the nature of the fluid, electromagnetic flowmeters can also be used on conducting fluids economically at this sort of pipe size, and many manufacturers can supply.

If the principle of using a small pipe with a flowmeter is not suitable, the Gourley formula for water at ambient temperature was published in the Proceedings of the Institution of Civil Engineers, Part 2, 1910, p297:

q = 3.0 L H^1.4

where q is the flowrate in ft³/sec, L the length of the weir in ft, and H the height over the weir in ft. (Reference: Perry's Chemical Engineers' Handbook 1941, p864)

The length of the weir will drop out of that, and the required pipe diameter will follow. Beware of the units of that 3.0!

A back-of-the-envelope calculation would suggest a pipe diameter of 40.1ft. Use a flowmeter instrument instead!

Another formula given is

q = 2.0 (L H) ^1.3 for incoming flow, which gives a pipe diameter of 735mm, a non-standard size.

The smart money is still on the flowmeter.

Whoops! 4.48ft!

Ah! This formula is for outgoing flow.

It should be solved by Benouli eqation. I think

I just gave the formula for flow of water through a pipe.

Q = 3.142/4 x A2 x V x3600/1000000

Q = m3/hr

A = mm dia

V = Velocity water 1.5 - 3 m/s (1-10 bar)

air/gas 8-15m/s (1-2 bar) & 5-7 m/s (200-300 bar)

Since you have not mentioned media for velocity you should take as stated.