CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2008
HOMEWORK No. 3

  1. 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 m and the gate opening is 0.1 m. How much would the gate have to be raised to pass a discharge of 600 L/s/m?

  2. 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 m, v1 = 1 m/s, and b1 = 3 m. What would be the required throat width if the upstream width is instead 2 m?

  3. 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 = 0.9, calculate the force fo. Assuming the flow is from left to right, in what direction is the force foacting?