Question

In: Civil Engineering

Question 1 The storage - outflow relationship for a small dam is given in Table 1....

Question 1 The storage - outflow relationship for a small dam is given in Table 1. The inflow hydrograph for the uncontrolled spillway of this dam is tabulated in Table 2. Determine:

  1. the outflow hydrograph from the spillway (fill the table and add more rows if necessary),
  2. attenuation, translation, and lengthening in the base time of the outflow hydrograph.
  3. Draw inflow and outflow hydrographs on the same figure and show the parameters asked in part b on this figure (draw in Excel and paste it here).
  4. Comment on the location of peak discharge of outflow hydrograph, i.e. why is it coincident with the inflow hydrograph?

Hint: Use Table 1 values to obtain S=f(Q).

Table 1

Q (m³/s)

50

100

150

200

250

2S/Δt (m³/s)

300

450

600

750

900

Table 2

t
(hr)

Inflow
(m
³/s)

0

45

2

175

4

370

6

540

8

390

10

280

12

215

14

175

16

135

18

100

20

70

22

45

Solutions

Expert Solution

TABLE 1

O (m3/s) 2S/dt (2S/dt)+O
50.0 300.00 350.00
100.0 450.00 550.00
150.0 600.00 750.00
200.0 750.00 950.00
250.0 900.00 1150.00

TABLE 2

assume initial outflow 50m3/s

Time (h) Inflow (m3/s) Ij+Ij+1(m3/s) (2Sj/dt)-Oj (2Sj+1/dt)+Oj+1 Outflow(m3/s)
0.0 45.0 250.00 50.00
2.0 175.0 220.00 310.00 470.00 80.00
4.0 370.0 545.00 502.50 855.00 176.25
6.0 540.0 910.00 781.26 1412.50 315.62
8.0 390.0 930.00 930.62 1711.26 390.32
10.0 280.0 670.00 875.30 1600.62 362.66
12.0 215.0 495.00 760.28 1370.30 305.01
14.0 175.0 390.00 650.14 1150.28 250.07
16.0 135.0 310.00 555.44 960.14 202.35
18.0 100.0 235.00 470.22 790.44 160.11
20.0 70.0 170.00 395.12 640.22 122.55
22.0 45.0 115.00 330.06 510.12 90.03

PEAK DISCHARGE = 390.32 m3/s

d. at this point inflow and outflow are equal.


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