CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2012
HOMEWORK No. 7
Note: To save paper, summarize results of onlinewsprofilesxx. Do not include tabular output as part of your work.

  1. A perennial stream has the following properties:   discharge Q = 50 m3/s, bottom width b = 25 m, side slope z = 2, bottom slope So = 0.001, and Manning's n = 0.035. A 2.5-m high diversion dam is planned on the stream to raise the head for an irrigation canal.

    • Calculate the normal depth.

    • Calculate the total length of the M1 water-surface profile. Use n = 400 and m = 400.

    • Calculate the partial length of the M1 profile, from the dam to a location upstream where the normal depth is exceeded by 1%.

    Use ONLINE CHANNEL 01 and ONLINE WSPROFILES 21.

  2. A mild stream flows into a steep channel, producing an M2 upstream of the brink. The hydraulic conditions in the channel are:   Q = 26 m3/s, bottom width b = 13 m, side slope z = 2.5, bottom slope So = 0.0008, and Manning's n = 0.04. Assume critical depth near the change in slope.

    • Calculate critical and normal depth.

    • Calculate the length of the M2 water-surface profile using n = 100 and m = 100.

    • Calculate the length of the M2 water-surface profile using n = 200 and m = 200.

    • Calculate the length of the M2 water-surface profile using n = 400 and m = 400.

    • Comment on the results of b, c, and d.

    • Determine the design channel length at 99% of the normal depth. Use n = 400.

      Use ONLINE CHANNEL 05 and ONLINE WSPROFILES 22.

  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 = 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 [mild] downstream channel, which functions as a stilling basin, is 0.00015. 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 hydraulic jump,

    • the sequent depth y2 (the normal depth downstream of the hydraulic jump),

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

    • the minimum length of the stilling basin Lsb = Ltc + Lj

    Use ONLINE CHANNEL 02 and ONLINE WSPROFILES 23. In the latter, use n = 100 and m = 100.