The flood runoff volume from the hydrograph ordinates (hourly) is found by:

Average of ordinates x basin area

Sum of ordinates divided by 3600

Asked 2/27
2069 Chaitra · 14 marks
2067 Shrawan (old course) · 16 marks

Effect of urbanization on UH and storm runoff

Short answer

Effective rainfall computed with φ indices, DRH by superposition of 1-h UH triangles. Peak increases from 17.19 to 30.00 m³/s (74.5%). Flood runoff volume after urbanization: 2.68×10⁵ m³, an increase of about 5.0×10⁴ m³ (23% over pre-urban 2.18×10⁵ m³).

A 1 hour unit hydrograph of a small catchment is triangular with peak value of 3.6 m $^3$ /s occurring at 2 hours from the start and a base time of 6 hours. Following urbanization over a period of two decades, the infiltration index $\phi$ has decreased from 0.7 cm/h to 0.4 cm/h. Also one hour unit hydrograph has now peak of 6.0 m $^3$ /s at 1 hour from start and time of base is 4 hours. If a design storm has intensities of 4 cm/hour and 3 cm/h for two consecutive one hour intervals,

a) Estimate the percentage increase in the peak storm runoff due to urbanization. b) The volume of flood runoff due to urbanization.

Method: effective rainfall (ER) is rainfall minus $\phi$ loss for each hour; the DRH is found by superposition of the 1-h unit hydrographs.

Unit hydrographs (hourly ordinates, triangles)

t (h)	0	1	2	3	4	5	6
Before: peak 3.6 at 2 h, base 6 h (m $^3$ /s)	0	1.8	3.6	2.7	1.8	0.9	0
After: peak 6.0 at 1 h, base 4 h (m $^3$ /s)	0	6.0	4.0	2.0	0	0	0

(Before: rising limb 0 to 3.6 in 2 h; falling limb 3.6 to 0 in 4 h. After: rising 0 to 6.0 in 1 h; falling 6.0 to 0 in 3 h.)

Effective rainfall

Storm intensities: 4 cm/h in hour 1 and 3 cm/h in hour 2.

	Before ( $\phi=0.7$ )	After ( $\phi=0.4$ )
Hour 1 ER	4 - 0.7 = 3.3 cm	4 - 0.4 = 3.6 cm
Hour 2 ER	3 - 0.7 = 2.3 cm	3 - 0.4 = 2.6 cm

Storm hydrograph $Q(t) = P_1\,u(t) + P_2\,u(t-1)$

t (h)	Before (m $^3$ /s)	After (m $^3$ /s)
1	3.3(1.8) = 5.94	3.6(6.0) = 21.60
2	3.3(3.6)+2.3(1.8) = 16.02	3.6(4.0)+2.6(6.0) = 30.00
3	3.3(2.7)+2.3(3.6) = 17.19	3.6(2.0)+2.6(4.0) = 17.60
4	3.3(1.8)+2.3(2.7) = 12.15	0+2.6(2.0) = 5.20
5	3.3(0.9)+2.3(1.8) = 7.11	0
6	2.3(0.9) = 2.07	0
Peak	17.19 at 3 h	30.00 at 2 h

(a) Increase in peak

\text{Increase}=\frac{30.00-17.19}{17.19}\times100 = 74.5\ \%

(b) Volume of flood runoff

V = \Delta t\sum Q = 3600\times\sum Q

Before: $\sum Q = 60.48$ m $^3$ /s, $V = 217\,728$ m $^3$ (this equals 5.6 cm over the 3.888 km $^2$ catchment area implied by its unit hydrograph).
After urbanization: $\sum Q = 74.40$ m $^3$ /s, $V = 267\,840$ m $^3$ (6.2 cm over 4.32 km $^2$ implied by its unit hydrograph).

Answer: (a) Peak increases by about 74.5 % (17.19 to 30.00 m $^3$ /s). (b) The flood runoff volume after urbanization is about 2.68 x 10 $^5$ m $^3$ , an increase of about 50 100 m $^3$ (23 %) over the pre-urban 2.18 x 10 $^5$ m $^3$ .

✓ Answer checked by Claude Sonnet 5.5

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