Parshall flumes are a particular form of venturi flume developed by the late Dr. Ralph Parshall . They are intended to be installed in open channels in order to determine the flow of water The narrow throat produces a differential head which under the proper conditions is proportional to flow rate. The relationship between depth and flow is exponential. For each throat width their exists a simple exponential equation of the form: Q = kH^n where Q is the flow in cubic feet per second, H is the depth in feet and k and n are constants that depend on the size of the flume. A detailed discussion of Parshall flumes is contained in the "WATER MEASUREMENT MANUAL" United States Department of the Interior, Bureau of Reclamation.
The table 2-1 below gives the values of "k" and "n" for various flume sizes. The flumes are sized by the width of the Throat. The throat is the narrow portion in the middle of the flume. With these values you will be able to calculate the flow using the exponential formula given above. If you prefer not to use the formula you can use the discharge table provided as an appendix In order to use either the formula or the discharge table you first need to measure the depth of the water The depth is measured above the flumes Crest. The crest is the flat floor in the entrance portion of the flume. The depth is measured along a particular cross section called Ha (read H sub a). To find Ha measure two thirds of the distance upstream from the entrance to the throat to the entrance to the flume (refer to drawing PS1001).
To use the formula you must know the depth in feet. If you measure the depth in other units like inches or centimeters you must first convert them to feet before attempting to use the formula. You must also remember that the formula gives the flow in cubic feet per second, if you want other units like gallons per minute you must make a conversion. Some common conversions are listed below.
Throat Width k n max. depth max. Flow 'W' in inches 'Ha' in feet 'Q' in cfs
1 .338 1.550 0.69 0.19 2 .676 1.550 0.79 0.47 3 .992 1.547 1.09 1.13 6 2.06 1.580 1.50 3.91 9 3.07 1.530 2.00 8.87 12-96 see below * 2.50
*For throat widths from 1 to 8 feet: k = 4 W ,that is four times the throat width in feet. n= 1.522 times the throat width in feet raised to the 0.026 power . k = 4W n = 1.522^.026 Conversions for common flow units: gpm = cfs x 448.8 MGD = cfs x .6463 Cu. Meters/sec. = cfs x .0283
Measuring the Depth -- Once you have determined the location of Ha you are ready to measure the depth of the water. A word of caution: because of the exponential nature of the discharge formula small errors in measuring the depth cause large errors in measuring the flow particularly at lower flows. If your flume is equipped with a molded in staff gage this will allow you to get a rough measurement very quickly by just reading the gage. Be aware that your eye will tend to be fooled into reading the tops of the small surface waves in the flume causing you to over estimate the depth For more accuracy or if you don't have a staff gage follow this procedure:
This is the procedure to use when verifying the depth in order to initialize an open channel flow meter. Never measure the depth by simply sticking a ruler into the flow The water will pile up on the leading edge and throw your measurement off considerably
Parshall flumes are said to be operating under free flow conditions if the water is not backing up from downstream by an excessive amount. For a given size flume there is a maximum allowable ratio between the head downstream and the head at Ha These ratios are called the submergence ratios and are usually given as a percentage, see table 3-1 for the maximum allowable submergence ratios for various throat widths. The head downstream is measured at a particular point in the throat of the flume called Hb The location of this point varies with flume size. To locate this point along the horizontal axis measure from the downstream end of the throat upstream by the specified distance "X" for your throat size ( table 3-1 ). The "zero" elevation is always referenced to the level of the crest not the floor of the throat.
Throat Width (in.) 1 2 3 6&9 12-96 Maximum Submergence 50% 50% 50% 60% 70%
If the above submergence ratios are exceeded the flume is not operating under free flow and the discharge equation no longer applies. While it is possible to determine the flow through a submerged flume, the procedure is cumbersome and should be avoided wherever possible Therefore it is important to set the crest of the flume high enough to raise the flume above the maximum downstream water depth such that the maximum submergence ration is not exceeded.