CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2008
HOMEWORK No. 7

  1. A perennial stream has the following properties:   discharge Q = 52 m3/s, bottom width b = 35 m, side slope z = 3, bottom slope So = 0.001, and Manning's n = 0.035. A 3-m high diversion dam is planned on the stream to raise the head for an irrigation canal. Use ONLINE WSPROFILES 21 to calculate: (a) the total length of the M1 water-surface profile. (b) the partial length of the profile, from the dam to a location upstream where the normal depth is exceeded by 2%.

  2. A mild stream flows into a steep channel. Assume critical depth near the change in slope. Use ONLINE WSPROFILES 22 to calculate the length of the M2 water-surface profile for the following conditions:   Q = 25 m3/s, bottom width b = 12 m, side slope z = 2, bottom slope So = 0.0007, and Manning's n = 0.03.

  3. An overflow spillway flows into a mild channel, producing a hydraulic jump. The channel is rectangular, with Q = 2 m3/s, bottom width b = 5 m, and Manning's n = 0.015. The flow depth at the toe of the spillway is 0.1 m and the approximate slope at the toe of the spillway is 0.1. The slope of the downstream mild channel, which functions as a stilling basin, is 0.0001. Use ONLINE WSPROFILES 23 to calculate:
    • the critical depth,

    • the length Ltc from the toe of the spillway to critical depth downstream,

    • the Froude number at the toe of the spillway,

    • the Froude number downstream of the jump,

    • the sequent depth y2 (flow depth downstream of the jump),

    • the length Ljump of the jump, assuming Ljump = 6.2 y2

    • the minimum length of the stilling basin Lsb.