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In a Nut
Shell: Manning's Equations governs
Uniform Flow. It is a semi-empirical
equation relating discharge, Q,
X-sectional area, hydraulic radius, and channel slope.
Q = (k/n) A RH2/3 So1/2
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where Q is the discharge (flow rate) in ft3/sec or in m3/sec
k is a experimentally determined
constant
k = 1.0 for metric units
and 1.482 for English units
n is a roughness
coefficient obtained from a table for various channel materials
A is the X-sectional area
of the liquid (usually water) in the channel in ft2 or in m2
RH is the hydraulic radius of the X-section
in ft or in m
So is the slope of the channel
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For
a rectangular channel the area, A, equals the width, w, of the channel
times the
depth,
yN, of the channel. The
hydraulic radius, RH, equals the area of the channel
divided
by its wetted perimeter.
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Because
of the exponent for hydraulic radius, solution for channel depth, yN,
may require
an
iterative scheme given the flow rate, Q, channel slope, So,
channel shape, and channel material.
An
exception is when the channel is "wide" meaning the width of the
channel is substantially
much
larger than the depth of the channel.
In this case, the hydraulic radius, RH, reduces to
simply
the equilibrium depth, yN, of the channel thus simplifying the
calculations.
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