CIV E 530 - OPEN-CHANNEL HYDRAULICS
FALL 2011
HOMEWORK No. 3

  1. 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?

  2. 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 fo acting?