The observed 6-h hydrograph gives effective rainfall of 5.02 cm; this is computed from:

Sum DRH x 6 x 3600 / basin area

A 12-h effective storm of 3.3 and 5.5 cm is treated as:

Two 6-h pulses, 3.3 cm first then 5.5 cm

2075 Chaitra · 10 marks

Flood hydrograph from 6-hr UH, two storms

Short answer

Separate constant baseflow40 m³/s, derive6-h UH from DRH (effective rainfall5.02 cm). For12-h storm with3.3 cm then5.5 cm effective rain, superposition gives flood hydrograph peaking at638 m³/s at30 h.

Following are the ordinates of hydrograph from a catchment area of 770 km $^2$ due to 6-hr rainfall. Derive the ordinates of flood hydrograph due to 3.3 cm and 5.5 cm effective rainfall of duration 12-hr.

t (hr)	0	6	12	18	24	30	36	42	48	54	60	66	72
Discharge (m $^3$ /s)	40	65	215	360	400	350	270	205	145	100	70	50	40

Assumptions: the 6-h hydrograph is the response to one 6-h effective-rainfall pulse. A 12-h effective storm is two successive 6-h pulses, the first giving 3.3 cm and the second 5.5 cm. The base flow of 40 m $^3$ /s (the initial and final flow) is constant.

Step 1: Direct runoff and 6-h UH

DRH = Q - 40. Sum of DRH ordinates $= 1790$ m $^3$ /s.

V=1790\times6\times3600 = 38.66\times10^6\ \text{m}^3,\qquad d=\frac{V}{A}=\frac{38.66\times10^6}{770\times10^6}=5.02\ \text{cm}

So the observed storm gave about 5.02 cm of effective rainfall, and the 6-h UH is $U = DRH/5.02$ .

Step 2: Superposition

Q(t)=40+3.3\,U(t)+5.5\,U(t-6)

t (h)	Observed Q	DRH	UH (m $^3$ /s per cm)	3.3 U(t)	5.5 U(t-6)	Flood Q (m $^3$ /s)
0	40	0	0.00	0.0	0.0	40.0
6	65	25	4.98	16.4	0.0	56.4
12	215	175	34.85	115.0	27.4	182.4
18	360	320	63.73	210.3	191.7	442.0
24	400	360	71.69	236.6	350.5	627.1
30	350	310	61.74	203.7	394.3	638.1
36	270	230	45.80	151.2	339.6	530.7
42	205	165	32.86	108.4	251.9	400.4
48	145	105	20.91	69.0	180.7	289.7
54	100	60	11.95	39.4	115.0	194.4
60	70	30	5.97	19.7	65.7	125.4
66	50	10	1.99	6.6	32.9	79.4
72	40	0	0.00	0.0	11.0	51.0
78	-	-	0.00	0.0	0.0	40.0

Answer: The flood hydrograph peaks at about 638 m $^3$ /s at 30 h; ordinates are in the last column.

✓ Answer checked by Claude Sonnet 5.5

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Flood hydrograph from 6-hr UH, two storms

Step 1: Direct runoff and 6-h UH

Step 2: Superposition

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