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

  1. A perennial stream has the following properties:   discharge Q = 54 m3/s, bottom width b = 36 m, side slope z = 2, bottom slope So = 0.0012, and Manning's n = 0.035. A 2.8-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%. Use n = 400 and m = 400.

  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 = 28 m3/s, bottom width b = 13 m, side slope z = 2.5, bottom slope So = 0.0008, and Manning's n = 0.04. Use n = 100 and m = 100.

  3. An overflow spillway flows into a mild channel, producing a hydraulic jump. The channel is rectangular, with Q = 2.2 m3/s, bottom width b = 6 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 0.00015. 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.
    Use n = 100 and m = 100.