CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2006
HOMEWORK No. 3
- Using the specific energy principle, show that the discharge q through a sluice gate in a wide rectangular channel is:
q = y1y2 (g/ybar)1/2
where y1 = upstream flow depth, y2 = downstream flow depth, ybar = average of these two depths,
and g is the gravitational acceleration.
Calculate the discharge for a sluice gate with the following depths: y1 = 0.6 m; y2 = 0.08 m.
Verify your results with onlinechannel.sdsu.edu.
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Using the specific energy principle and critical flow properties [critical depth yc is equal to 2/3 of the specific energy E], show that the ratio σ = bc/b1, where b1 is the upstream channel width of a rectangular channel,
and bc is the channel width at a constriction that forces critical flow to occur, is
σ = [(27)1/2 F1] / (2 + F12)3/2
Assume negligible energy loss through the constriction.
Calculate bc and yc, given a rectangular
channel with discharge Q = 10 m3s-1, width b1 = 6 m, and depth y1 = 1.5 m.
Verify your results with onlinechannel.sdsu.edu.
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Using the specific force principle, show that the force f (in kN/m) exerted by a blunt obstruction at the bottom of a wide rectangular channel is:
f = γ y12 {(1/2)(1 - α2) + F12[1 - (1/α)]}
where γ = unit weight of water [9.81 kN/m3], F = Froude number, y1 = upstream
depth, y2 = downstream depth, and α = y2/ y1.
Calculate the force f given: q = 1.5 m2/s, v1 = 1 m/s, and α = 0.9.
In what direction is this force acting?
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