An Otto cycle engine develops $50$ kW at $150$ rpm with $75$ explosions per minute. The change of speed

from the commencement to the end of power stroke must not exceed $0\mathrm{.}5\%$ of mean on either side. Find

the mean diameter of the flywheel and a suitable rim cross section having width four times the depth so

that the hoop stress does not exceed $4$ MPa. Assume that the flywheel stores $16/15$ times the energy

stored by the rim and the work done during power stroke is $1\mathrm{.}40$ times the work done during the cycle.

Density of rim material is $7200$ kg$/$m$3$