Rework example 5.2.4 with discharges of 0, 25, 75, 125, and 200 cfs.
EXAMPLE 5.2.4
Compute the specific force curves for the channel and flow rates used in example 5.2.2.
SOLUTION
The specific force values are computed using equation (5.2.25) with the values presented in Table 5.2.2. The curves are plotted in Figure 5.2.8.
Table 5.2.2 Computed Specific Force Curve Values for Example 5.2.4
Depth, y (ft) | Specific force, F (ft3) | |||
Q = 0 | Q = 50 | Q = 100 | Q = 300 | |
0.1 | 0.10 | 38.92 | 155.38 | 1397.62 |
0.2 | 0.40 | 19.81 | 78.04 | 699.16 |
0.4 | 1.60 | 11.30 | 40.42 | 350.98 |
0.6 | 3.60 | 10.07 | 29.48 | 236.52 |
0.8 | 6.40 | 11.25 | 25.81 | 181.09 |
1.0 | 10.00 | 13.88 | 25.53 | 149.75 |
1.2 | 14.40 | 17.63 | 27.34 | 130.86 |
1.4 | 19.60 | 22.37 | 30.69 | 119.42 |
1.6 | 25.60 | 28.03 | 35.30 | 112.94 |
1.8 | 32.40 | 34.56 | 41.03 | 110.04 |
2.0 | 40.00 | 41.94 | 47.76 | 109.88 |
2.2 | 48.40 | 50.16 | 55.46 | 111.92 |
2.4 | 57.60 | 59.22 | 64.07 | 115.83 |
2.6 | 67.60 | 69.09 | 73.57 | 121.35 |
2.8 | 78.40 | 79.79 | 83.95 | 128.31 |
3.0 | 90.00 | 91.29 | 95.18 | 136.58 |
3.5 | 122.50 | 123.61 | 126.94 | 162.43 |
4.0 | 160.00 | 160.97 | 163.88 | 194.94 |
4.5 | 202.50 | 203.36 | 205.95 | 233.56 |
5.0 | 250.00 | 250.78 | 253.11 | 277.95 |
Figure 5.2.8 Specific force curves.
EXAMPLE 5.2.2
For a rectangular channel of 20 ft width, construct a family of specific energy curves for Q = 0 50, 100, and 300 cfs. Draw the locus of the critical depth points on these curves. For each flow rate, what is the minimum specific energy found from these curves?
The specific energy is computed using equation (5.2.1):
Computing critical depths for the flow rates using equation (5.2.14) with q = Q/B yields
Computed specific energies are listed in Table 5.2.1.
The specific energy curves are shown in Figure 5.2.3. The minimum specific energies are:
Table 5.2.1 Computed Specific Energy Values for Example 5.2.2
Depth, y (ft) | Specific energy, E (ft-lb/lb) | |||
Q = 0 | Q = 50 | Q = 100 | Q = 300 | |
0.5 | 0.50 | 0.89 | 2.05 | 14.86 |
0.6 | 0.60 | 0.87 | 1.68 | 10.57 |
0.8 | 0.80 | 0.95 | 1.41 | 6.41 |
1.0 | 1.00 | 1.10 | 1.39 | 4.59 |
1.2 | 1.20 | 1.27 | 1.47 | 3.69 |
1.4 | 1.40 | 1.45 | 1.60 | 3.23 |
1.6 | 1.60 | 1.64 | 1.75 | 3.00 |
1.8 | 1.80 | 1.83 | 1.92 | 2.91 |
2.0 | 2.00 | 2.02 | 2.10 | 2.90 |
2.2 | 2.20 | 2.22 | 2.28 | 2.94 |
2.4 | 2.40 | 2.42 | 2.47 | 3.02 |
2.6 | 2.60 | 2.61 | 2.66 | 3.13 |
2.8 | 2.80 | 2.81 | 2.85 | 3.26 |
3.0 | 3.00 | 3.01 | 3.04 | 3.40 |
3.5 | 3.50 | 3.51 | 3.53 | 3.79 |
4.0 | 4.00 | 4.50 | 4.2 | 4.22 |
4.5 | 4.50 | 5.00 | 4.52 | 4.68 |
| 5.00 |
| 5.02 | 5.14 |
Figure 5.2.3 Specific energy curves for example 5.2.2.
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