The time t for a flywheel with moment of inertia 1 to reach

The time t, for a flywheel, with moment of inertia. 1, to reach an angular velocity, omega from res, depends on the applied torque. T, and the following flywheel bearing properties: The oil viscosity, it, clearance gag., diameter. D. and Length L. Use dimensional analysis to find out the n parameters that characterize this phenomenon. Choose omega, D. T as your repeating variables in the given order.

Solution

There are 3 independent parameters M,L,T

Given 4 physical parameters, Mu,T,omega,L ( delta and L have have units so count as one) we expect one group to fall out.

Units of viscosity   Kg/(ms)= (Pa.s)

T orque T = Nm= Kg m²/s²

omega = 1/t

L = length (m)

consider Mu L^a delta^b omega^c T^d

By inspection, get the grouping T/(mu .Omega.L)