CIV E 530 - OPEN-CHANNEL HYDRAULICS FALL 2008 HOMEWORK No. 3 The discharge per unit width under a sluice gate, assuming the conservation of specific energy, is: q = y1 y2 [2 g / (y1 + y2) ] 1/2 Derive this formula. Then use ONLINE CHANNEL 13 to calculate this discharge, when the upstream flow depth is 1.2 m and the gate opening is 0.15 m. How much would the gate have to be raised to pass a discharge of 900 L/s/m? (accuracy to 1 mm). The dimensionless throat width of a channel constriction that forces critical flow through it is: σ = bc / b1 = (27)1/2 F1 / (2 + F12) 3/2 Derive this formula. Then use ONLINE CHANNEL 17 to calculate the required throat width bc for the following upstream conditions:   y1 = 2.2 m, v1 = 1.2 m/s, and b1 = 3.2 m. What would be the required throat width if the upstream width is instead 2.5 m? Using the specific force principle, show that the force fo (in kN/m) exerted by a blunt obstruction at the bottom of a wide rectangular channel is: fo = - γ y12 [ (1 - α2) / 2   +   ( 1 -   1/α ) F12 ] where γ = unit weight of water, F1 = upstream Froude number, y1 = upstream flow depth, and α = y2/ y1, where y2 = downstream flow depth (after the obstruction). Given q = 1.5 m2/s, v1 = 1.0 m/s, and α = 0.91, calculate the force fo. Assuming the flow is from left to right, in what direction is the force foacting?