Assignment (4)

Quantitative Hydrology (Hydrograph) Solution : Question (1)

A storm lasting 6 hr has 1.55 in of rain and produces the following flows:

Time, hr flow, cfs Time, hr flow, cfs

0 20 28 110

4 110 32 80

8 180 36 60

12 250 40 40

16 200 44 30

20 160 48 20

24 130

Note: cfs = ft3/s & ft = 12 in and mil = 1760 * 3 ft

The basin has an area 12.5 mil2. Find the peak of the unit hydrograph. What fraction of

the precipitation appeared as runoff? Assume negligible base flow. Solution

Rain, P = 1.55 in , A = 12.5 mil 2

Time 0 4 8 12 16 20 24 28 32 36 40 44 48

Flow 20 110 180 250 200 160 130 110 80 60 40 30 20

Unit

Hyd

20/0.689

= 29

110/0.689

= 160 261 362 290 232 188.7 159.7 116 87 58 43.5 29

∑ flow = ( 20+110+180+ 250+----------) = 1390 cfs

Direct run off = 12*)3*1760)(3*1760(*5.12

3600*4*1390 = 0.689 inch

mile = 1760*3 ft

Peak of unit hydrograph = 362 cfs

Fraction runoff = 55.1

689.0 = 0.444

Solution : Question (2)

The 2-hr Unit hydrograph for a catchment is given in the following tabulated form.

Assuming zero base flow, you are asked to do the following:

(a) How large is the catchment area?

(b) If 2.5 cm of direct runoff is produced uniformly over a 2-hr period, find the

resulting hydrograph.

Time, hour Q, m3/sec Time, hour Q, m3/sec

0 0 8 116.0

1 11.3 9 90.6

2 70.8 10 67.9

3 124.5 11 45.3

4 169.8 12 25.5

5 121.3 13 11.3

6 172.6 14 5.7

7 141.5 15 0

Solution

Time 0 1 2 3 4 5 6 7 8

U H 0 11.3 70.8 124.5 169.8 121.3 172.6 141.5 116

Q, H 0 11.3*2.5 = 28.8 177 311..25 424.5 303.25 431.5 353.75 290

Continue

Time 9 10 11 12 13 14 15

U H 90.6 67.9 45.3 25.5 11.3 5.7 0

Q, H 226.5 169.75 113.25 63.75 28.25 14.25 0

∑ Q (unit hydrograph) = 1174.1 m3/s

Volume = 1174.1 *1.0 * 60 * 60 = 4226760 m3

Aarea

volume 4226760 = 1.0 cm = 0.01 m

A = 01.0

422670 = 422676000 m

2

A = = 422.67 km2