GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 60 of 65

Marks: +1, -0

The ordinates,

{u}

of a 2 -hour unit hydrograph (i.e. for

1 {cm}

of effective rain), for a catchment are shown in the table.

T(hour)	0	1	2	3	4	5	6	7	8	9	10	11	12
${U}( {m}^{3} {/} {s})$	0	2	8	18	32	45	30	19	12	7	3	1	0

A 6-hour storm occurs over the catchment such that the effective rainfall intensity is 1

{cm} \/

hour for the first two hours, zero for the next two hours, and

0.5 {cm}{/}

hour for the last two hours. If the base flow is constant at

5 {m}^{3} {/} {s}

, the peak flow due to this storm (in

{m}^{3} {/} {s}

, round off to 1 decimal place) will be

Solution:

0-2 {hr}

- total rainfall

=1 × 2=2 {cm}

2-4 {hr}-

total rainfall

=0 {cm}

4-6 {hr}-

total rainfall

=2 × 0.5=1 {cm}

Time hour	${u}{m}^{3} {/} {sec}$	${u} × 2$ cm	${A} × {U}$ lagged by $2 {hr}$	$1 × {u}$ lagged by 1 hr.	Sum $=1+2+3$
0	0	0			0
1	2	4			4
2	8	16	0		16
3	18	36	0		36
4	32	64	0	0	64
5	45	90	0	2	92
6	30	60	0	8	68
7	19	38	0	18	56
8	12	24	0	32	56
9	7	14	0	45	59
10	3	6	0	30	36
11	1	2	0	19	21
12	0	0	0	12	12

Maximum ordinate is

92 {m}^{3} {/}{sec}

.
Maximum flood discharge

=92+5

=97 {m}^{3} {/} {sec}

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Time hour	${u}{m}^{3} {/} {sec}$	${u} × 2$ cm	${A} × {U}$ lagged by $2 {hr}$	$1 × {u}$ lagged by 1 hr.	Sum $=1+2+3$
0	0	0			0
1	2	4			4
2	8	16	0		16
3	18	36	0		36
4	32	64	0	0	64
5	45	90	0	2	92
6	30	60	0	8	68
7	19	38	0	18	56
8	12	24	0	32	56
9	7	14	0	45	59
10	3	6	0	30	36
11	1	2	0	19	21
12	0	0	0	12	12

Time hour	${u}{m}^{3} {/} {sec}$	${u} × 2$ cm	${A} × {U}$ lagged by $2 {hr}$	$1 × {u}$ lagged by 1 hr.	Sum $=1+2+3$
0	0	0			0
1	2	4			4
2	8	16	0		16
3	18	36	0		36
4	32	64	0	0	64
5	45	90	0	2	92
6	30	60	0	8	68
7	19	38	0	18	56
8	12	24	0	32	56
9	7	14	0	45	59
10	3	6	0	30	36
11	1	2	0	19	21
12	0	0	0	12	12

Time hour	${u}{m}^{3} {/} {sec}$	${u} × 2$ cm	${A} × {U}$ lagged by $2 {hr}$	$1 × {u}$ lagged by 1 hr.	Sum $=1+2+3$
0	0	0			0
1	2	4			4
2	8	16	0		16
3	18	36	0		36
4	32	64	0	0	64
5	45	90	0	2	92
6	30	60	0	8	68
7	19	38	0	18	56
8	12	24	0	32	56
9	7	14	0	45	59
10	3	6	0	30	36
11	1	2	0	19	21
12	0	0	0	12	12