A catchment has 5 rain gauge stations, for a 6% error in estimation of mean rainfall and coefficient of variation of rainfall values of existing stations is 20. Determine additional no. of stations needed

Question

Question

This question was previously asked in

JKSSB JE CE 2021 Official Paper Shift 1 (Held on 29 Oct 2021)

Answer 1

Concept

The optimum number of rain gauges is given by

\(N = {\left( {\frac{{{C_v}}}{\epsilon}} \right)^2} \)

Where,

Cv is the coefficient of variation

ϵ is error percentage

The coefficient of variation is given by

\({C_v} = \frac{{{\sigma _{n - 1}}}}{{\bar P}}\)

Where,

\(\bar P\) is average rainfall

σ is the standard deviation

Calculation:

Given,

Number of Rain gauge = 5, error = 6 %, C_v = 20

The optimum number of rain gauge → n = (20/6)² = 11.11 we take it as 12

∴ The number of Optimum Gauges = 12.

As asked about the additional number of Stations i.e. 12 - 5 = 7.

∴ Number of Additional Stations = 7

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