# Engineering Hydrology Questions and Answers – Floods – Rational Method

This set of Engineering Hydrology Multiple Choice Questions & Answers (MCQs) focuses on “Floods – Rational Method”.

1. What is the maximum area limit for the application of rational formula for peak flood estimation?
a) 5 km2
b) 50 ha
c) 50 km2
d) 5000 km2

Explanation: Rational formula is the method of flood estimation used in design of drainages, small culverts and bridges. Further, its application is restricted to give reliable results for only small size catchments of area less than 50 km2.

2. Which of the following is the correct equation for peak flood discharge (in m3/s) by rational formula? A = area in ha, C = runoff coefficient, R = rainfall intensity in cm/hr.
a) $$\frac{ACR}{3.6}$$
b) $$\frac{ACR}{36}$$
c) $$\frac{ACR}{360}$$
d) $$\frac{ACR}{3600}$$

Explanation: The discharge by rational formula is generally given as,
Q=$$\frac{ACR}{3.6}$$, where A is in km2 and R is in mm/hr.
By converting the units of terms,
$$Q=\frac{(\frac{A}{100} ha)*C*(10*R cm/hr)}{3.6}=\frac{ACR}{36}$$, where A is in ha and R is cm/hr.

3. Time of concentration is the largest duration of rainfall for which the rational formula can be used.
a) True
b) False

Explanation: Time of concentration is the minimum duration for which rational formula is applicable. If the duration exceeds time of concentration, the runoff will be constant and at peak value.

4. A drain is to be designed for peak discharge ‘Q’ by rational method. If a storm of same intensity but three times the design duration occurs, what will the peak discharge?
a) Q
b) 3Q
c) Q/3
d) Q3

Explanation: As per rational formula, the minimum duration is taken as the time of concentration. Even if the duration exceeds the time of concentration, runoff remains same, intensity remains same and hence, the peak flood remains the same.

5. Which of the following factors affect the runoff coefficient?
a) Land use and slope only
b) Slope and type of surface only
c) Land use, slope and rainfall intensity
d) Nature of surface, rainfall intensity and time of concentration

Explanation: Runoff coefficient is the ratio of runoff depth to rainfall depth and is an important factor to be considered in rational formula. It represents a combined effect of catchment losses and depends on the type of land use or cover, the slope of the area and the rainfall intensity.

6. Find the equivalent runoff coefficient for an area of which 24% has a runoff coefficient of 0.12, 28% has 0.36, 30% has 0.51 and the rest of the area has 0.75.
a) 0.37
b) 0.42
c) 0.53
d) 0.61

Explanation: The equivalent runoff coefficient is given as,
$$C_{eq}=\frac{(0.12*24)+(0.36*28)+(0.51*30)+(0.75*(100-24-28-30))}{100}$$=0.4176≅0.42

7. A plot of land has the following land use pattern and runoff coefficients.

Land Use Area (in Ha) Runoff Coefficient
Cultivation 120 0.40
Pasture 44 0.16
Forest 182 0.25
Housing 54 0.34

Estimate the equivalent runoff coefficient for the land.
a) 0.21
b) 0.25
c) 0.3
d) 0.37

Explanation: The equivalent runoff coefficient is,
$$C_eq=\frac{∑(sub area*coefficient)}{Total area}$$ $$=\frac{(120*0.4)+(44*0.16)+(182*0.25)+(54*0.34)}{120+44+182+54}$$ $$=\frac{48+7.04+45.5+18.36}{400}$$=0.29725≅0.3

8. The rainfall intensity to be used in the rational method depends on which of the following?
a) Time of concentration and return period
b) Return period and rainfall intensity
c) Rainfall intensity and time of concentration
d) Rainfall intensity, return period and time of concentration

Explanation: The rainfall intensity to be used in the rational formula is evaluated from specific rainfall-frequency-duration curves of the area for a flood of a given return period and duration (time of concentration).

9. A watershed of 7.5 km2 area has a runoff coefficient of 0.42. The time of concentration of the catchment is 1 hour. A 6-hour storm of intensity 4.2 cm/hr occurs over the catchment. Find the peak discharge by rational method.
a) 3.67 m3/s
b) 36.75 m3/s
c) 0.37 m3/s
d) 367.5 m3/s

Explanation: The peak discharge by rational method is,
$$Q=\frac{AIR}{360}=\frac{(750 ha)*0.42*(42 mm/hr)}{360}$$=36.75 m3/s.

10. A catchment of 225 ha area has a runoff coefficient of 0.33. A storm of duration more than the time of concentration and intensity 7.78 cm/hr occurs over the area. Find the peak discharge by rational method.
a) 16 m3/s
b) 1600 L/sec
c) 160 cm3/s
d) 16000 L/min

Explanation: The peak discharge by rational method is,
$$Q=\frac{AIR}{360}=\frac{(225 ha)*0.33*(77.8 mm/hr)}{360}$$≅16 m3/s.

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