Establishment of uniform flow

Today we are going to demonstrate the establishment of uniform flow in an open channel, under two Froude numbers:
1) supercritical, and 2) critical.
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We use the friction equation
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S_o = f F²
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in which S_o is the bottom slope, lower case f is the friction factor, and upper case F is the Froude number.
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The friction factor is equal to 1/8 of the Darcy-Weisbach friction factor. It is equal to:
f = g n² / (k² R^1/3)
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In SI units, g is equal to 9.81 m/s² and k = 1.
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The wall of the flume is made out of lucite, i.e. acrylic glass. We assume a Manning n equal to 0.008.
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We estimate a hydraulics radius equal to 3 centimeters, that is, 0.03 m.
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Therefore: f = 0.002
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We turn on the pump in the demonstration flume.
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We set the slope at 0.01, a steep slope, and check the level.
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The calculated Froude number is:
F = (S_o / f )^1/2 = (0.01 / 0.002)^1/2 = 2.24
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This Froude number corresponds to supercritical flow.
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Now we set the slope at 0.002, the critical slope, and check the level.
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The calculated Froude number is:
F = (S_o / f )^1/2 = (0.002 / 0.002)^1/2 = 1.
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We have shown the flow in this channel operating under supercritical and critical conditions.