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UP Jal Nigam E&M 2016 Official Paper

Option 2 : Ratio

__Explanation:__

The difference between the maximum and minimum speeds during a cycle is called the maximum fluctuation of speed. The ratio of the maximum fluctuation of speed to the mean speed is called the coefficient of fluctuation of speed. The reciprocal of the coefficient of fluctuation of speed is known as the coefficient of steadiness.

Let \({N_1}\) and \({N_2}\) = Maximum and minimum speeds in r.p.m. during the cycle

Range of speed = N1 - N2

\(N\) = Mean speed in r.p.m. \(= \frac{{{N_1} + {N_2}}}{2}\)

Coefficient of fluctuation of speed

\({C_s} = \;\frac{{{N_1} - {N_2}}}{N} = \;\frac{{2\left( {{N_1} - {N_2}} \right)}}{{{N_1} + \;{N_2}}}\)

and coefficient of steadiness

\(\begin{array}{l} m = \frac{1}{{Coeff.\;of\;fluctuation\;of\;speed}}\\ = \frac{{{N_{mean}}}}{{{N_{max}} - {N_{min}}}} = \frac{{{N_1} + {N_2}}}{{2\left( {{N_1} - {N_2}} \right)}} \end{array}\)