Simplified Trapezoidal Flume Discharge Equations

One of the problems in applying Trapezoidal flumes has been that many of the flumes lack free-flow equations in the standard (and short) format:

short form discharge equation used for many flumes

found with other popular flumes (the Parshall / Montana in particular).

In their wide-ranging work on the subject, "Trapezoidal Flumes for Open-Channel Flow Measurement", Robinson and Chamberlain acknowledged the difficulty, noting:

…for the other flumes which have flat bottoms in the throat sections, the relationship is not as simple (as those for V-notch flumes)…

This in turn has lead to difficulties in using many popular flow meters which only accept either short form equations or flow-level points (from which the meter generates a strapping table). With no short form equation available for many of the Trapezoidal flumes covered by Robinson and Chamberlain, the default solution has been the use of strapping tables via manually entered flow-level points - a time consuming and potentially error prone process.

In his lectures notes for his BIE 5300/6300 (Fall Semester 2004) Irrigation Conveyance & Control: Flow Measurement & Structure Design, Dr. Gary Merkley of Utah State University presents a solution to this problem by offering standard (short) from constants and exponents (Imperial units) for a variety of Robinson and Chamberlain's Trapezoidal flumes to fit the standard form equation above.

Trapezoidal Flume	C_ft	n_ft
Trapezoidal Flume	C_ft	n_ft
Small 60ª V	1.55	2.58
Large 60ª V	1.55	2.58
2-Inch 60ª WSC	1.99	2.04
2-Inch 45ª WSC	3.32	2.18
2-Inch 30ª WSC	5.92	2.28
4-Inch 60ª WSC	2.63	1.83
2-Inch 30ª CSU	4.80	0.64

While the coefficients and exponents for the Small and Large 60ª V Trapezoidal flumes had previously been published by Robinson and Chamberlain, the those for the other flumes reprensent a welcome addtion.

Not that the equations are for Trapezoidal flumes operating under free-flow conditons only. Laboratory investigations would be requried to determine submeged flow adjustments.