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Units in circular culvert freedischarge water 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
FreeFlowing Water Circular Culvert (Pipe) Drawings and Equations
Introduction to Circular Culvert FreeDischarge Calculation using End Depth Method
Discharge (flow rate) can be computed for water flowing out of a circular culvert that is
up to half full. The end depth method is based on the International Organization of
Standards publication 4371 dated 1984 (ISO, 1984). Knowing
the culvert diameter and the depth of flow where the water drops off (i.e. at the end of
the culvert), the discharge can be computed. If it is more easy or accurate to
measure the water top width at the dropoff (instead of water depth), the top width can be
used with diameter to compute the discharge. For the equation to be used properly,
there are several criteria that should be met:
• Clear water.
• Circular crosssection for a distance at least 20h upstream of the dropoff.
• Culvert should be horizontal although a slight downward slope (up to 1/2000) is okay.
• Culvert 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 ratio h/D should be between 0.095 and 0.5, and cannot exceed 0.5.
Variables for Circular Water Pipe FreeDischarge Equations
[L] indicates length units. [T] indicates time units.
d=Drop elevation [L]. Elevation difference between bottom of channel and tail
water. Must be at least h for the discharge equation to be reliable.
D=Culvert diameter [L]. Note that h/D must be between
0.095 and 0.5 for the discharge equation to be reliable. The calculation only
functions for h/D≤0.5.
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 discharge equation to be reliable. Note
that h/D must be between 0.095 and 0.5 for the discharge equation to be reliable.
The calculation only functions for h/D≤0.5.
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 flow rate.
T=Top width of water in the culvert [L]. Must be greater than 0.3 m (11.8
inch) for the discharge equation to be reliable.
Error Messages for Circular Culvert FreeFlow Water Calculation
Messages indicating input values are out of the acceptable ranges (the seemingly redundant
messages are checked at different phases of program execution):
"D must be > 0",
"h must be > 0",
"h/D must be ≤ 0.5",
"Must have 0< h/D ≤ 0.5",
"T must be > 0",
"T must be ≤ D",
"Enter 1e5 ≤ D ≤ 1000 m",
"Enter 1e7 ≤ h/D ≤ 0.5",
"Enter 1e5 ≤ h ≤ 1000 m".
The calculation finished, but per ISO (1984), equation accuracy is reduced when the following messages appear:
"Need h/D > 0.095 for accuracy",
"Need h > 0.05 m for accuracy",
"Need T > 0.3 m for accuracy".
References for Circular Culvert FreeDischarge Equations
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).
© 20002015 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
Please contact us for consulting or other questions.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone: (740) 5921890
LMNO@LMNOeng.com http://www.LMNOeng.com

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End Depth Method: Rectangular Triangular
Weirs: Rectangular Vnotch (triangular)
Cipoletti
Other related calculations:
Circular Culverts using Manning Equation
Culvert Design using Inlet and Outlet Control
Critical Depth in Circular Culvert
Unit Conversions
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