# If the speed of an engine varies between 390 and 410 rpm in a cycle of operation, the coefficient of fluctuations of speed would be

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If the speed of an engine varies between 390 and 410 rpm in a cycle of operation, the coefficient of fluctuations of speed would be
1. 0.01
2. 0.02
3. 0.04
4. 0.05

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Correct Answer - Option 4 : 0.05

Concepts:

Fluctuation of speed:

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

Coefficients of fluctuations of speed when N (rpm) is given:

${C_s} = \frac{{{N_1}\;-\;{N_2}}}{{{N_{mean}}}}$

Coefficients of fluctuations of speed when angular velocity (ω) is given:

${C_s} = \frac{{{\omega _1}\;-\;{\omega _2}}}{{{\omega _{mean}}}}$

We know that,

${N_{mean}} = \frac{{{N_1}\;+\;{N_2}}}{2},\;and$

${\omega _{mean}} = \frac{{{\omega _1}\;+\;{\omega _2}}}{2}$

Calculation:

Given:

N1 = 410 rpmN2 = 390 rpm.

${C_s} = \frac{{{N_1}\; - \;{N_2}}}{{\frac{{{N_1}\; +\; {N_2}}}{2}}}$

$C_s= \frac{{410\; - \;390}}{{\frac{{410 \;+ \;390}}{2}}}= \frac{{20}}{{400}} = \;\;0.05$

The reciprocal of the coefficient of fluctuation of speed is known as the coefficient of steadiness. It is denoted by (m).

$m = \frac{1}{{{C_s}}}\; = \;\frac{{{N_{mean}}}}{{{N_1} - {N_2}}}$