CE522 Engineering Hydrology
Jorge A. Ramirez
Homework No. 2
1. Route the flood hydrograph given in the
following table through a reservoir having
a spillway crest elevation at 130 m. Assume that the reservoir pool level prior to the flood is also 130
m. Elevation discharge, and elevation-storage curves are also tabulated below. Use the following methods
a) trial and error, b) level pool (storage-indication), and c) Runge-Kutta of third order. Compute peak flow of
the outflow hydrograph and plot your results.
|
Elevation (m) |
Discharge (m3/s) |
Storage (106 m3) |
|
128 |
0 |
0 |
|
130 |
0 |
0 |
|
131 |
35 |
7 |
|
132 |
90 |
16 |
|
133 |
165 |
25 |
|
134 |
270 |
33 |
|
136 |
540 |
51 |
|
137 |
710 |
70 |
|
138 |
890 |
85 |
|
139 |
1080 |
100 |
|
140 |
1310 |
120 |
|
Inflow Time (h) |
Discharge (m3/s) |
Inflow Time (h) |
Discharge (m3/s) |
|
|
0 |
0 |
78 |
620 |
|
|
6 |
50 |
84 |
510 |
|
|
12 |
130 |
90 |
420 |
|
|
18 |
250 |
96 |
320 |
|
|
24 |
350 |
102 |
270 |
|
|
30 |
540 |
108 |
200 |
|
|
36 |
735 |
114 |
150 |
|
|
42 |
1215 |
120 |
100 |
|
|
48 |
1800 |
126 |
72 |
|
|
54 |
1400 |
132 |
45 |
|
|
60 |
1050 |
138 |
25 |
|
|
66 |
900 |
144 |
10 |
|
|
72 |
740 |
150 |
0 |
2. Estimate the Muskingum routing parameters, k and x, for a river reach using the inflow and outflow data tabulated below. Use the least squares and the graphical methods presented in class. The initial storage in the reach is 50 106 m3.
|
Time (days) |
Inflow (m3/s) |
Outflow (m3/s) |
Time (days) |
Inflow (m3/s) |
Outflow (m3/s) |
|
|
1 |
180 |
160 |
16 |
1160 |
1220 |
|
|
2 |
270 |
200 |
17 |
1100 |
1190 |
|
|
3 |
420 |
280 |
18 |
1000 |
1150 |
|
|
4 |
650 |
415 |
19 |
950 |
1100 |
|
|
5 |
890 |
590 |
20 |
900 |
1040 |
|
|
6 |
1100 |
770 |
21 |
790 |
980 |
|
|
7 |
1270 |
950 |
22 |
710 |
920 |
|
|
8 |
1360 |
1090 |
23 |
650 |
860 |
|
|
9 |
1380 |
1180 |
24 |
590 |
790 |
|
|
10 |
1390 |
1250 |
25 |
510 |
710 |
|
|
11 |
1370 |
1280 |
26 |
450 |
650 |
|
|
12 |
1350 |
1290 |
27 |
380 |
590 |
|
|
13 |
1310 |
1300 |
28 |
300 |
510 |
|
|
14 |
1260 |
1280 |
29 |
230 |
460 |
|
|
15 |
1210 |
1250 |
3. Use the values of k and x obtained in Problem 2 to route the inflow hydrograph of Problem
2 (That is, compare the predicted outflow hydrograph with the observed outflow
hydrograph).
The parameters of the Muskingum method should meet the following restriction, x < 0.5 Dt/k < 1-x, where Dt
refers to the time interval for routing. Use Dt
of 1 day. If the parameter estimation procedure has been carried out correctly, the suggested time interval of
1 day complies with the above restrictions.