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 rpm, N2 = 390 rpm.
\({C_s} = \frac{{{N_1}\; - \;{N_2}}}{{\frac{{{N_1}\; +\; {N_2}}}{2}}}\)
\(C_s= \frac{{410\; - \;390}}{{\frac{{410 \;+ \;390}}{2}}}= \frac{{20}}{{400}} = \;\;0.05\)
Coefficient of steadiness:
The reciprocal of the coefficient of fluctuation of speed is known as the coefficient of steadiness. It is denoted by (m).
\(m = \frac{1}{{{C_s}}}\; = \;\frac{{{N_{mean}}}}{{{N_1} - {N_2}}}\)