# The maximum and minimum speeds of a flywheel are 630 rpm and 600 rpm. The coefficient of fluctuation of speed is

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CIL MT Mechanical: 2020 Official Paper
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1. 0.0500
2. 0.0487
3. 0.0300
4. 0.0476

Option 2 : 0.0487
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CT 1: Growth and Development - 1
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## Detailed Solution

Concept:

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

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

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

Calculation:

Given:

N1 =630 rpm and N2 = 600 rpm

then,

N  = Mean speed in r.p.m. $$= \frac{{{N_1} + {N_2}}}{2}=\frac{{{630} + {600}}}{2} =615\ rpm$$

and range of speed = 630 - 600 = 30 rpm

and $${C_s} = \;\frac{{{N_1} - \;{N_2}}}{N} = \;\frac{{2\left( {{N_1} - {N_2}} \right)}}{{{N_1} + {N_2}}}=\frac{30}{615}$$

thus, CS = 0.0487
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