Answer to Tutorial (1)


T1=6 hrs T2=2 hrs D=2.0 (cm)            
Time (hr) Q(m^3/s) Qb(m^3/s) (Q-Qb) u(6,t) S(t)/T1 S(t) T2*u(2,t) u(2,t)
0 18 18 0 0.0 0.0 0 0 0.0
2 21 20 1 0.5 0.5 3 3 1.5
4 28 25 3 1.5 1.5 9 6 3.0
6 44 32 12 6.0 6.0 36 27 13.5
8 70 40 30 15.0 15.5 93 57 28.5
10 118 47 71 35.5 37.0 222 129 64.5
12 228 54 174 87.0 93.0 558 336 168.0
14 342 61 281 140.5 156.0 936 378 189.0
16 413 68 345 172.5 209.5 1257 321 160.5
18 393 75 318 159.0 252.0 1512 255 127.5
20 334 79 255 127.5 283.5 1701 189 94.5
22 270 77 193 96.5 306.0 1836 135 67.5
24 216 73 143 71.5 323.5 1941 105 52.5
26 171 69 102 51.0 334.5 2007 66 33.0
28 138 66 72 36.0 342.0 2052 45 22.5
30 113 63 50 25.0 348.5 2091 39 19.5
32 97 60 37 18.5 353.0 2118 27 13.5
34 84 57 27 13.5 355.5 2133 15 7.5
36 75 55 20 10.0 358.5 2151 18 9.0
38 66 52 14 7.0 360.0 2160 9 4.5
40 59 49 10 5.0 360.5 2163 3 1.5
42 54 47 7 3.5 362.0 2172 9 4.5
44 49 44 5 2.5 362.5 2175 3 1.5
46 46 42 4 2.0 362.5 2175 0 0.0
48 42 40 2 1.0 363.0 2178 3 1.5
50 40 38 2 1.0 363.5 2181 3 1.5
52 38 37 1 0.5 363.0 2178 -3 -1.5
54 36 35 1 0.5 363.5 2181 3 1.5
56 34 34 0 0.0 363.5 2181 0 0.0
58 33 33 0 0.0 363.0 2178 -3 -1.5
60 33 33 0 0.0 363.5 2181 3 1.5
Sum: 3703 1523 2180 1090.0   48759 2181 1090.5

Note:
  1. u(6,T)=(Q-Qb)/D, where D is the effective rainfall depth (cm).

  2. the unit step response function, or S-hydrograph, is defined as S(t)=T[u(T,t)+u(T,t-T)+u(T,t-2T)+…]

  3. the unit pulse response function u(T,t) is related to S(t) by u(T,t)=[S(t)-S(t-T)]/T

  4. The comparsion between U(6,t) and U(2,t)

    ChartObject Chart 4



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Last Updated on 11/12/98
By Xiong Lihua