Dimensional Analysis

In preparation for your physical model study on the flow within a stilling basin, and particularly the hydraulic jump formed within the stilling basin, you have decided to undertake a dimensional analysis of the problem. 

You have determined that the water depth downstream of the hydraulic jump, $h_2$, is a function of the water depth upstream of the hydraulic jump, $h_1$, the width of the channel, $b$, the flowrate per unit channel width $q$ (where $[q]=L^2T^{-1}$), gravitational acceleration, $g$, the fluid density, $\rho$, and the fluid (dynamic) viscosity, $\mu$.

Determine the relationship between the dimensionless product $h_2/h_1$ and the other dimensionless products resulting from this dimensional analysis. You should show full working and justify any assumptions or simplifications made. Your dimensional analysis should be presented as neat, hand-written calculations (either on paper or using a tablet).