What base flow is assumed?

Constant 40 m3/s, the flow at start and end

How is the runoff depth of the 6-h UH found?

Sum of DRH x 6 x 3600 / area = 5.02 cm

Sum of observed Q x 3600 / area

2080 Bhadra · 8 marks

Flood hydrograph from 6-hr hydrograph, 3.3 and 5.5 cm

Short answer

Separate constant base flow of40 m³/s and derive the6-h UH by dividing DRH by the effective depth 5.021 cm. Convolve the UH with3.3 cm and5.5 cm lagged by6 h, then add base flow. The peak flood is 638 m³/s at 30 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 6-hr. Make suitable assumptions regarding the base flow.

Time (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

Assumption for base flow: the discharge at the start and end of the storm hydrograph is 40 m³/s, so a constant base flow of 40 m³/s is assumed.

Step 1: 6-h UH

Direct runoff ordinates = observed − 40. Volume = (sum of ordinates) × 6 × 3600.

\begin{aligned} \sum DRH &= 1790 \text{ m}^3/\text{s} \\ V &= 1790\times 21600 = 38,664,000 \text{ m}^3 \\ \text{depth} &= \frac{V}{A} = \frac{38,664,000}{770\times 10^6}\times 100 = 5.021 \text{ cm} \end{aligned}

UH ordinate = DRH / 5.021:

t (h)	0	6	12	18	24	30	36	42	48	54	60	66	72
Observed Q	40	65	215	360	400	350	270	205	145	100	70	50	40
DRH	0	25	175	320	360	310	230	165	105	60	30	10	0
UH (m³/s per cm)	0.0	5.0	34.9	63.7	71.7	61.7	45.8	32.9	20.9	11.9	6.0	2.0	0.0

Step 2: Flood hydrograph

Two successive 6-h effective rains of 3.3 cm and 5.5 cm:

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

t (h)	UH (m³/s)	3.3 cm × UH	5.5 cm × UH	Base	Q (m³/s)
0	0.00	0.0	0.0	40.0	40.0
6	4.98	16.4	0.0	40.0	56.4
12	34.85	115.0	27.4	40.0	182.4
18	63.73	210.3	191.7	40.0	442.0
24	71.69	236.6	350.5	40.0	627.1
30	61.74	203.7	394.3	40.0	638.1
36	45.80	151.2	339.6	40.0	530.7
42	32.86	108.4	251.9	40.0	400.4
48	20.91	69.0	180.7	40.0	289.7
54	11.95	39.4	115.0	40.0	194.4
60	5.97	19.7	65.7	40.0	125.4
66	1.99	6.6	32.9	40.0	79.4
72	0.00	0.0	11.0	40.0	51.0
78	0.00	0.0	0.0	40.0	40.0

Answer: peak flood ≈ 638 m³/s at t = 30 h.

✓ Answer checked by Claude Sonnet 5.5

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Flood hydrograph from 6-hr hydrograph, 3.3 and 5.5 cm

Step 1: 6-h UH

Step 2: Flood hydrograph

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