Determine if the following equation is dimensionally correct: v = P 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 left-hand side (velocity, v ) are: [v] = [L T⁻¹] The dimensions of the terms on the right-hand side are: Pressure, P = Force Area = [M L T⁻²] [L^2] = [M L⁻¹ T⁻²] Density, = Mass Volume = [M] [L^3] = [M L⁻³] Substituting these into the right-hand side expression: P = [M L⁻¹ T⁻²] [M L⁻³] = [L^2 T⁻²] = [L T⁻¹] Since the dimensions of the left-hand side are equal to the dimensions of the right-hand side, the equation is dimensionally correct.