You want to determine the thickness of the film when a Newtonian fluid flows uniformly down an inclined plane at an angle $\theta$ with the horizontal at a specified flow rate. To do this, you design a laboratory experiment from which you can scale up measured values to any other Newtonian fluid under corresponding conditions.(a) List all the independent variables that are important in this problem, with their dimensions. If there are any variables that are not independent but act only in conjunction with one another, list only the net combination that is important.

(b) Determine an appropriate set of dimensionless groups for this system, in such a way that the fluid viscosity and the plate inclination each appear in only one group.

(c) Decide what variables you would choose for convenience, what variables would be specified by the analysis, and what you would measure in the lab.