# Engineering Hydrology Questions and Answers – Flood Empirical Formulas

This set of Engineering Hydrology Multiple Choice Questions & Answers (MCQs) focuses on “Flood Empirical Formulas”.

1. Which of the following equations for flood estimation is most suitable in the Western Ghats?
a) Rational formula
b) Dickens formula
c) Ryves formula
d) Inglis formula

Explanation: Inglis formula was developed in 1930 and was arrived at based on years of flood data of catchment area in the Western Ghat region of Maharashtra. With slight modifications, it can also be applied to other smaller catchments in Maharashtra.

2. Which of the following equations for flood estimation is most suitable in the state of Karnataka?
a) Rational formula
b) Dickens formula
c) Ryves formula
d) Inglis formula

Explanation: Ryves formula was developed in 1884 originally in the region of the Tamil Nadu state. However, it is also applicable to other southern regions of India like parts of Karnataka and Andhra Pradesh.

3. Which of the following represents Dickens formula for peak discharge (in m3/s)? CD = Dickens constant, A = catchment area in km2.
a) Q=CD. A1/3
b) Q=CD. A2/3
c) Q=CD. A1/4
d) Q=CD. A3/4

Explanation: Dickens formula in 1865, was one of the earliest empirical formula to be developed. It is most reliably used in the central and northern parts of India with differing values of constant. It is given as, Q=CD. A3/4.

4. As per Inglis formula, the peak discharge is a function of which of the following?
a) Catchment area only
b) Return period and rainfall intensity
c) Catchment area and return period
d) Catchment area, return period and rainfall intensity

Explanation: Inglis formula is a very basic regional empirical formula using only the catchment area as a parameter to estimate the peak flood flow. It neglects any other factor that may affect the peak flood that is used in rational formula. This is the similar case with most of the empirical equations.

5. What is the minimum value of Dickens constant?
a) 6
b) 11
c) 14
d) 22

Explanation: The Dickens constant varies widely between 6 and 30 as we move from the northern regions to the more central parts of India. It varies from 6-14 in the northern plain and hilly regions to 14-28 in central and coastal regions.

6. A Ryves constant of 8.5 is appliable for catchments in which of the following regions of India?
a) Areas within 80 km from the east coast
b) Areas that are 80-160 km from the east coast
c) Areas within 80 km from the west coast
d) Areas that are 80-160 km from the west coast

Explanation: Ryves formula was developed in Tamil Nadu and is applicable in the neighboring south-east regions of India. The Ryves constant varies based on the distance of the area from the east coast. For areas within 80 km it is 6.8, and for areas between 80-160 km from the east coast it is 8.5.

7. What of the following does not represent the correct equation for Inglis Formula to find peak flood (Qp in m3/s)? A represents area of the catchment is hectares.
a) $$Q_p=\frac{12.4A}{\sqrt{0.1A+104}}$$
b) $$Q_p=\frac{1.24A}{\sqrt{0.01A+10.4}}$$
c) $$Q_p=\frac{124A}{\sqrt{100A+104000}}$$
d) $$Q_p=\frac{12.4A}{\sqrt{A+1040}}$$

Explanation: The general form of the Inglis formula is given as,
$$Q_p=\frac{124A}{\sqrt{A+10.4}}$$, where Qp is in m3/s and A is in km2.
By converting the unit of input from km2 to hectare we get,
$$Q_p=\frac{124*\frac{A}{100}}{\sqrt{\frac{A}{100}+10.4}}=\frac{1.24A}{\sqrt{0.01A+10.4}}$$⋯⋯⋯(1)
$$=\frac{124A}{100\sqrt{0.01A+10.4}}=\frac{124A}{\sqrt{10000}.\sqrt{0.01A+10.4}}=\frac{124A}{\sqrt{100A+104000}}$$⋯⋯⋯(2)
$$=\frac{12.4A}{10\sqrt{0.01A+10.4}}=\frac{12.4A}{\sqrt{100}.\sqrt{0.01A+10.4}}=\frac{12.4A}{\sqrt{A+1040}}$$⋯⋯⋯(3)
Therefore, equations (1), (2) and (3) represent the correct forms of Inglis equation.

8. All empirical formulae concerning the peak flood estimation, relate the peak flood to the catchment area only.
a) True
b) False

Explanation: Most of the empirical formulae like Dickens, Ryves and Inglis, relate the peak flood only to the catchment area. However, some empirical equations, like Fuller’s formula also take into account the flood frequency along with the catchment area.

9. What is the range of the constant in Fuller’s formula for peak discharge estimation?
a) 0.18 to 1.18
b) 0.88 to 1.81
c) 0.18 to 1.88
d) 0.81 to 1.88

Explanation: Fuller’s formula was developed in USA and relates the maximum flood discharge to both the area of the catchment and flood frequency. It also involves a constant that varies regionally between 0.18 and 1.88.

10. The empirical equations derived from envelope curves are of which of the following types? Q is the peak flood discharge, f represents a function, A is catchment area, i is rainfall intensity, T is time period.
a) Q=f(T)
b) Q=f(A)
c) Q=f(A,T)
d) Q=f(A,T,i)

Explanation: Envelope curve is a quick method of obtaining rough estimates of peak discharge values of areas with limited flood data available. If an empirical equation is tried to fit to an envelope curve for a region, it will be of the form Q=f(A) , where A is the catchment area.

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