CIV E 445 - APPLIED HYDROLOGY
SPRING 2014
HOMEWORK No. 10 SOLUTION

  1. With K = 2 h, and Δt = 1 h, the routing coefficients (Eqs. 8-16 to 8-18) are: C0 = 1/5; C1 = 1/5; and C2 = 3/5.

    The routing computations are shown in the following table.

    The calculated peak outflow is 195.26 m3/s, and it occurs at 8 h.  The same answer is obtained with ONLINEROUTING01. ANSWER.

  2. With K = 2 h: S = 2 (O).

    With Δt = 1 h, the storage-indication-outflow relation O = [(2 • S / Δt) + O]

    is:

    O = (1 / 5) [(2 • S / Δt) + O].

    The calculations are shown in the following table.

    The calculated peak outflow is 195.26 m3/s, and it occurs at 8 h. The same answer is obtained with ONLINEROUTING02. ANSWER.

  3. First develop the spillway rating, using Q = CL H3/2 = 1.7 • 20 • H3/2.

    Elevation (m) 120 121 122 123 124 125
    Storage (hm3) 3.00 3.15 3.35 3.70 4.35 4.95
    Outflow (m3/s) 0.000 34.000 96.166 176.669 272.000 380.130

    Then, using ONLINEROUTING03, the peak outflow is: Qp = 167.051 m3/s.

    The maximum water surface elevation corresponding to this peak outflow is: 122.881 m.

    Since the dam crest elevation is at 125 m, the actual freeboard is: FB = 125.0 - 122.881 = 2.119 m.   ANSWER.

  4. With the given reservoir and design flood conditions, the objective is to determine the emergency spillway length (width) (rectangular cross section) that produces a maximum water surface elevation of 481.0 m, i.e., the difference between dam crest elevation (483.0 m) and design freeboard (2.0 m). The calculation proceeds by trial and error, using ONLINEROUTING03. The final spillway length (width) is 9.0 m.

    Outflow= 1.7 • 9.0 • Head1.5

    Elevation (m) 475 477 479 481 483
    Head (m) 0 2 4 6 8
    Storage (hm3) 5.0 5.3 6.0 7.0 8.5
    Outflow (m3/s) 0.0 43.275 122.400 224.863 346.199

    Using ONLINEROUTING03 with the given reservoir data and design flood conditions, the peak outflow is: Qp = 225.287 m3/s.

    The maximum water surface elevation corresponding to this peak outflow is: 481.007 m. Since the dam crest elevation is at 483 m, the actual freeboard is: FB = 483.0 - 481.007 = 1.993 m.   ANSWER.