Determine if the following equation is dimensionally correct: V = P r^4 t 8 l where h = height, S = surface tension, = density, P = pressure, V = volume, = coefficient of viscosity, = frequency and I = moment of inertia.

Step-by-step solution

The dimensions of the terms are evaluated as follows: [V] = [L^3] [P] = [M L⁻¹ T⁻²] [r] = [L] [t] = [T] [ ] = [M L⁻¹ T⁻¹] [l] = [L] Substituting these dimensions into the right hand side of the given equation: [M L⁻¹ T⁻²] [L^4] [T] [M L⁻¹ T⁻¹] [L] = [M L^3 T⁻¹] [M L^0 T⁻¹] = [L^3] Since the dimensions of the left hand side and right hand side are equal, the equation is dimensionally correct.