Contents preface (VII) introduction 1—37

(C) Computations for the derivation of 4-hr UH (Example 2.7)

Time	2-hr UH	2-hr UH	DRH of	4-hr UH
(hours)		lagged	2cm in
		by 2 hrs	4 hrs
(1)	(2)	(3)	(4)	(5)
0	0		0	0.0
2	20	0	20	10.0
4	47	20	67	33.5
6	62	47	109	54.5
8	35	62	97	48.5
10	15	35	50	25.0
12	5	15	20	10.0
14	0	5	5	2.5
16		0	0	0.0
				184.0

Discharge(cumecs)

60

50

40

4 - h UH

30

20

10

0

0 5 10 15 20
Time (hrs)

Fig. 2.27 (e) 4-hour Unit hydrograph (Example 2.7)

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Similarly, for 3T-hr UH i.e., 6-hr UH, one would require to superpose three 2-hr UH’s each separated from the previous one by 2 hrs. The ordinates of these three UH’s are in Cols. 2, 3 and 4 of Table D which, when added together, yield the ordinates of DRH (Col. 5 of Table D) of 3 cm rainfall in duration of 6 hrs. The values of Col. 5 of Table D are divided by 3 to obtain the ordinates of 6-hr UH (Col. 6 of Table D), Fig. 2.27 (f).

(D) Computation of 6-hr UH

Time		2-h Unit Hydrograph		DRH of	6-hr UH
(hours)	original		lagged		lagged	3 cm in
			by 2 hr		by 4 hr	6 hrs
(1)	(2)		(3)		(4)	(5)	(6)
0	0					0	0.00
2	20		0			20	6.67
4	47		20		0	67	22.33
6	62		47		20	129	43.00
8	35		62		47	144	48.00
10	15		35		62	112	37.33
12	5		15		35	55	18.33
14	0		5		15	20	6.67
16			0		5	5	1.67
18					0	0	0.00
							184.00

Discharge(cumecs)

60

50

40

30

6 - h UH

20

10

0 0 5 10 15 20
Time ( hrs )

Fig. 2.27 (f) 6-hour Unit hydrograph (Example 2.7)

84 IRRIGATION AND WATER RESOURCES ENGINEERING
In order to obtain 2-h UH from the derived 4-h UH, one has to use the S-hydrograph method. After having obtained 4-hr S-curve (Col. 3 of Table E), ordinates of another 4-hr S-curve (lagging the previous 4-hr S-curve by 2-h), Col. 4 of Table E, are subtracted from the previous 4-hr S-curve. The difference gives the ordinates of a hydrograph resulting from a rainfall excess of (2/4) cm i.e., 0.5 cm in a duration of 2 hours (Col. 5 of Table E). Therefore, the ordinates of the hydrograph (rainfall excess of 0.5 cm in a duration of 2 hours) are divided by 0.5 cm so as to have the hydrograph with rainfall excess of a 1 cm in a duration of 2 hours. (Col. 6 of Table E). The ordinates (Col. 6 of Table E), as expected, are the same as that of the ordinates of the original 2-hr, UH (Col. 6 of Table A). That is, this resulting hydrograph, Fig. 2.27 (b), is the 2-hr UH derived from the 4-h UH.

(E) Computation of 2-h UH from the derived 4-hr UH

Time	4-hr UH	4-hour S-Hydrograph	DRH of
				2-h UH
(hours)			Original	lagged by	0.5 cm in
			2 hours	2 hours
(1)	(2)	(3)	(4)	(5)		(6)
0	0.0	0		0.00	0
2	10.0	10	0	10.00	20
4	33.5	33.5	10	23.50	47
6	54.5	64.5	33.5	31.00	62
8	48.5	82	64.5	17.50	35
10	25.0	89.5	82	7.50	15
12	10.0	92	89.5	2.50	5
14	2.5	92	92	0.00	0
16	0.0	92	92	0.00

Sum of all the ordinates of any UH of this example is 184 m³/s which results in direct runoff depth of

184 × 2 × 3600	× 100	i.e., 0.995 cm ≈ 1.0 cm
133.1 × 10^6

Therefore, the computations are in order.
Also, the correctness of the computations of each S-curve can be examined by comparing the computed equilibrium discharge with the value obtained from Eq. (2.23). For example, for 3-hr S-curve,
Q_e = (2.78)(133.1/3) = 123.34 m³/s
which value compares well with the values of discharge around equilibrium conditions.
2.8. FLOODS
A flood represents an unusual high stage in a river such that the river overflows its banks and, thus, inundates the adjoining land. Floods cause huge loss of life and property besides disrupting all human activities resulting into large economic loss. India suffers greatly on account of floods or hydrologic droughts occurring recurrently in one or other part of the country. Hydrologic drought is a condition (or period) during which stream flows are inadequate to supply for the established uses (domestic, irrigation, hydropower etc.) of water under a given water-management system. Complete control over floods and droughts is impossible to achieve.

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For the purpose of designing any hydraulic structure, one needs to know the magnitude of the peak flood (or flow) that can be expected with an assigned frequency during the life of the structure.