CIV E 445 - APPLIED HYDROLOGY
SPRING 2014
HOMEWORK No. 4 SOLUTION


  1. Elevation (%) 0 10 20 30 40 50 60 70 80 90 100
    Cumulative Area (%) 0 24 40 52 66 77 82 86 95 98 100
    Snow-water equivalent (mm) 3 3 3 4 4 5 5 7 7 8 8
    Incremental area (%) - 24 16 12 14 11 5 4 9 3 2
    Average water equivalent per
    elevation increment (mm)     		0 3.0 3.0 3.5 4.0 4.5 5.0 6.0 7.0 7.5 8.0

    The catchment's overall snow-water equivalent W is the average water equivalent weighted in terms of the incremental area:

    W = [(3.0 × 24) + (3.0 × 16) + (3.5 × 12) + (4.0 × 14) + (4.5 × 11) + (5.0 × 5) + (6.0 × 4) + (7.0 × 9) + (7.5 × 3) + (8.0 × 2)] / 100 = 4.18 mm.   ANSWER.


  2. Vertical No. 1 2 3 4 5 6 7 8 9 10 11
    Width (m) 5 5 5 5 5 5 5 5 5 5 5
    Depth (m) 0.0 0.6 0.9 1.3 1.6 2.6 3.1 2.1 1.3 0.7 0.0
    Average velocity (m/s) 0.0 0.40 0.60 0.80 1.05 1.25 1.55 1.20 0.85 0.60 0.00
    Unit discharge (m3/s)0.00 1.20 2.70 5.20 8.40 16.25 24.03 12.60 5.20 2.10 0.00

    The discharge is the sum of the unit discharges: 77.68 m3/s.   ANSWER.

  3. Cs = 12,000 ppm

    Ce = 15 ppm

    Qs = 100 L/s

    Using Eq. 3-6 shown below:

    Q = [(12,000 / 15) - 1] × 100 L/s = 79,900 L/s or 79.9 m3/s.   ANSWER.


  4. The upstream conveyance Ku (Eq. 3-7a) is 378,378; the downstream conveyance Kd (Eq. 3-7b) is 293,837; the reach conveyance K (Eq. 3-8 shown below) is 333,439. The first approximation to the energy slope (Eq. 3-9) is 0.0002816.

    The first approximation to the peak discharge (Eq. 3-10) is 5595 m3/s. The result of the iteration is summarized below.

    The flood discharge is: Q = 5275 m3/s   ANSWER.

    Running the SLOPE AREA calculator confirms the result: Q = 5275.1 m3/s   ANSWER.