Triangular Open Channel Waterfall Discharge

Compute waterfall discharge, depth, top width, or angle for a triangular open channel with a sudden drop-off.  Uses ISO 4371 equation.

Triangular open channel waterfall end depth flow calculation is mobile-device-friendly as of September 29, 2014

 Compute Q (h,a known) Compute Q (T,a known) Compute Q (h,T known) Compute h (Q,a known) Compute h (Q,T known) Compute T (Q,h known) Compute T (Q,a known) Compute a (Q,h known) Compute a (Q,T known) Discharge, Q: m3/s (cms) ft3/s (cfs) U.S. gal/min (gpm) U.S. gal/day (gpd) Acre-ft/yr Water Depth, h: cm m inch ft Top Width, T: m Angle, a: radians degrees ©2014 LMNO Engineering, Research, and Software, Ltd. http://www.LMNOeng.com

Units in triangular waterfall 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

Triangular Open Channel Waterfall End Depth Method Drawings and Equations

Introduction to Triangular End Depth Method for Waterfalls
This web page describes using the end-depth method for analysis or design of a triangular channel that freely discharges. The equation shown above for determining discharge is from the International Organization of Standards publication 4371 dated 1984 (ISO, 1984). For the equation to be used properly, there are several criteria that should be met:
• Clear water.
• Triangular cross-section for a distance at least 20h upstream of the drop-off.
• 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 sub-critical upstream of the drop-off.
• 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 50o and 90o.

Variables for Triangular End Depth Waterfall 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/s2.
h=Measured water depth at end of channel (i.e. at the drop-off) [L]. Must be greater than 0.05 m (1.97 inch) for the equation to be reliable.
L=Straight length upstream of drop-off [L]. Must be at least 20h for the flow to be well-established.
Q=Discharge [L3/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.

Error Messages for Triangular Waterfall Discharge Calculation
Messages indicating input values are out of the acceptable ranges:
"h must be >0",  "a must be 0<a<180o",  "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 calculation finished, but equation accuracy is reduced when the following messages appear:
"Need 50o<a<90o",  "Need h>0.05m",  "Need T>0.3m".

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 non-rectangular channels with a free overfall (approximate method).  Reference number: ISO 4371-1984(E).

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August 25, 2015: Made text fields show 8 significant figures rather than 16. Calculation still uses double precision internally.

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