Flow under a sluice gate
Today we are going to demonstrate
the flow under a sluice gate using the energy principle.
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The theoretical formula based on the conservation of specific energy is:
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in which Q is the discharge, B is the width of the flume, y1 is the upstream flow depth, y3 is the downstream flow depth, and g is the acceleration of gravity.
For practical purposes, this theoretical formula can be expressed in terms of the gate opening y2
by defining a contraction ratio Cc:
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This leads to:
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in which the discharge coefficient Cd is:
[Point to the width of the flume] The width B of the flume is 6 inches, or 152.4 mm.
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We set the gate opening y2 = 15 mm
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We turn on the pump.
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We set the bed slope equal to zero...
and check the level...
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[Point to the point gage] Note that the point gage is at zero at the bottom of the flume.
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Now we are going to measure the upstream flow depth y1.
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The upstream flow depth is y1 = X mm
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We move the gage downstream of the sluice gate.
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[Point to the point gage] Note that the point gage is at zero at the bottom of the flume.
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Now we are going to measure the downstream flow depth y3.
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The downstream flow depth is y3 = X mm
Applying the theoretical equation based on the conservation of specific energy, the discharge is Q1 = X liters per second.
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Next we calculate Cc and Cd.
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With these coefficients we calculate Q2 = X liters per second.
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Note that both equations give the same answer:
Q1 = B y1 y3 [ 2g / (y1 + y3) ]1/2
Cc = y3 / y2
Q2 = B Cd y2 (2g y1)1/2
Cd = Cc / [ 1 + Cc (y2 / y1)]1/2
