Accurately measuring the flow of water through various parts of an irrigation system is vitally important for any medium- to large-scale agricultural project. Water is becoming a scarce resource in many parts of the world so using it sparingly is as important as giving your crops or livestock the water they need to grow. It's a delicate balancing act that requires proper measurement of water flow through both horizontal and vertical pipes of various diameters.
Calculate Flow From a Vertical Pipe
Measure the inside diameter of the vertical pipe in inches.
Measure the height of the water in inches from the top of the pipe. As the water flows from the top of the pipe, draw an imaginary line across the highest point of the water flow. Measure from this imaginary line to the top of the pipe in inches. This measurement is the height of the water.
Determine if the water is flowing in a jet or circular weir. A jet is the result of water under significant pressure while a circular weir is characterized by a crown of water flowing up and over the edges of the top of a vertical pipe. The pressure of a water jet will result in a significantly greater volume of water flow than that of a circular weir, so each require a different equation to accurately estimate flow.
If the height of the water over the top of the pipe is greater than 1.4 times the inside diameter of the pipe then it is a jet flow. If the height of the water is less than 0.37 times the inside diameter of the pipe then it is flowing like a circular weir.
Calculate the flow from the pipe.
For water flowing as a jet, calculate the flow with the following equation.
Gallons Per Minute = 5.01d^1.99 h^0.53
Where d = the inside diameter of the pipe and h = the height of the water.
For water flowing as a circular weir use the following equation.
Gallons Per Minute = 6.17d^1.25 h^1.35
These equations were formulated by Lawrence and Braunworth at Cornell University and were first published in the American Society of Civil Engineers, Transactions, Vol. 57, 1906.
New Mexico State university has already done the math for a series of commonly used pipe dimensions and flow rates. They offer a chart displaying the gallons per minute for each possibility at http://aces.nmsu.edu/pubs/_a/a-104.pdf.
Before you spend the time working through the equations yourself, you might take a look at this handy reference.