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 |
u(6,T)=(Q-Qb)/D, where D is the effective rainfall depth (cm).
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)+…]
the unit pulse response function u(T,t) is related to S(t) by u(T,t)=[S(t)-S(t-T)]/T