Units in discharge measurement calculator:
cm=centimeter, cfs=cubic foot per second, cms=cubic meter per second, ft=foot, gal=gallon (U.S.), m=meter, min=minute, s=second, yr=year
Discharge Measurement Drawings and Equations
Introduction to Discharge Measurement and Triangular End Depth Method for Waterfalls
Our discharge measurement page describes using the enddepth method for analysis or design of a triangular
channel that freely discharges. The discharge measurement equation shown above is from the International Organization of Standards publication 4371 dated 1984 (ISO, 1984). For the discharge measurement equation to be used properly, there are
several criteria that should be met:
• Clear water.
• Triangular crosssection for a distance at least 20h upstream of the dropoff.
• Channel should be horizontal although a slight downward slope (up to 1/2000) is okay.
• Channel walls should be smooth such as would be provided by a neat cement finish.
• Flow should be subcritical upstream of the dropoff.
• The drop, d, should be greater than h.
• The channel width, T, should be greater than 0.3 m (11.8 inch).
• The end depth, h, should be greater than 0.05 m (1.97 inch).
• The apex angle, a, should be between 50^{o} and 90^{o}.
Variables for Discharge Measurement Equations
[L] indicates length units. [T] indicates time units.
a=Apex angle; angle at bottom of triangle.
d=Drop elevation [L]. Elevation difference between bottom of channel and tail
water. Must be at least h for the equation to be reliable.
g=Acceleration due to gravity=9.8066 m/s^{2}.
h=Measured water depth at end of channel (i.e. at the dropoff) [L]. Must
be greater than 0.05 m (1.97 inch) for the equation to be reliable.
L=Straight length upstream of dropoff [L]. Must be at least 20h
for the flow to be wellestablished.
Q=Discharge [L^{3}/T]. Also known as flowrate.
T=Channel top width [L]. Must be greater than 0.3 m (11.8 inch) for the
equation to be reliable.
Discharge Measurement Error Messages
Messages indicating input values to the discharge measurement calculation are out of the acceptable ranges:
"h must be >0",
"a must be 0<a<180^{o}",
"T must be >0",
"h and T must be >0",
"Q must be >0",
"Q and T must be >0",
"Q and h must be >0".
The discharge measurement calculation finished, but equation accuracy is reduced when the following messages appear:
"Need 50^{o}<a<90^{o}",
"Need h>0.05m",
"Need T>0.3m".
Discharge Measurement References for Triangular Waterfall End Depth Flow Calculation
International Organization of Standards (ISO 4371). 1984. Measurement of
liquid flow in open channels by weirs and flumes  End depth method for estimation of flow
in nonrectangular channels with a free overfall (approximate method). Reference
number: ISO 43711984(E).
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Software, Ltd. All rights reserved.
Please contact us for consulting or questions about discharge measurement.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone: (740) 7072614
LMNO@LMNOeng.com https://www.LMNOeng.com

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