Lab 03: Flow under a sluice gate - 120921 - 120927
[RDA] Good morning
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[RDA] Today we are going to explain and demonstrate
the flow under a sluice gate using the energy principle.
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[RDA] The theoretical formula based on the conservation of specific energy is:
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[RDA] 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.
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[RDA] This theoretical formula can be expressed in terms of the gate opening y2
by defining a contraction ratio Cc
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[RDA] This leads to:
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[RDA] in which the discharge coefficient Cd is:
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[RDA] Now we turn on the pump on the demonstration flume.
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[RDA]We set the bed slope equal to zero...
and check the level...
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[Point to the width of the flume] [RDA] The width B of the flume is 6 inches, or 152.4 mm
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[RDA] [Point to the point gage] Note that the point gage is at zero.
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[RDA] Now we are going to measure the height to the bottom of the flume
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[RDA] The height is X mm
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[RDA] Now we are going to measure the height to the top of the gate opening
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[RDA] The height is Y mm
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[RDA] The gate opening y2 is equal to: ... X - Y
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[RDA] Now we are going to measure the height to the water surface upstream of the sluice gate
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[RDA] The height is Z mm
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[RDA] The upstream head or depth y1 is equal to: ... X - Z
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[RDA] Now we are going to measure the height to the water surface downstream of the sluice gate
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[RDA] The height is V mm
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[RDA] The downstream depth y3 is equal to: ... X - V
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[RDA] Now we apply the theoretical formula in terms of upstream head y1 and downstream depth y3:
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[RDA] The discharge is Q1 [actual number] liters per second.
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[RDA] Next we apply the practical formula in terms of upstream head y1 and gate opening y2:
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[RDA] The discharge is Q2 [actual number] liters per second.
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[RDA] Note that both equations give the same answer: Q = ... .
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[RDA] Thank you.
Q = B y1 y3 [ 2g / (y1 + y3) ]1/2
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Cc = y3 / y2
Q = B Cd y2 (2g y1)1/2
Cd = Cc / [ 1 + Cc (y2 / y1)]1/2
