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Introduction
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 50^o and 90^o.

Variables
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
"h must be >0."  Check your input.  h was entered as 0.0 or negative.
"a must be 0<a<180^o."  Check your input.   The angle must be in this range.
"T must be >0."  Check your input.  T was entered as 0.0 or negative.
"h and T must be >0."  Check your input.  h or T was entered as 0.0 or negative.
"Q must be >0."  Check your input.  Q was entered as 0.0 or negative.
"Q and T must be >0."  Check your input.  Q or T was entered as 0.0 or negative.
"Q and h must be >0."  Check your input.  Q or h was entered as 0.0 or negative.
"Need 50^o<a<90^o for accuracy."   The apex angle, a, was entered or computed as outside this range.  The calculation finished, but the equation is not accurate for this angle.
"Need h>0.05m for accuracy."  h (water depth) was entered or computed as <=0.05m.  The calculation finished, but the equation is not accurate for such a small depth.
"Need T>0.3m for accuracy."  T (channel top width) was entered or computed as <=0.3m.  The calculation finished, but the equation is not accurate for such a narrow channel.

References
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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