Dimensionless analysis in engine cooling
Hi, I have a problem with measuring cooling performance of a car on a chassis dynamometer. But maybe I should start with the theoretical part of my problem, namely with the dimensional analysis.
If I have a physical system and I am interested in finding one variable as a function of all other variables on which this one depends, I can use the Buckingham pi theorem and reduce the number of parameters involved. I think I understand how to do that. But what if most of these parameters are kept constant all the time and I am not interested in how their changes influence my output variable, can I still use this theory?
In my particular case I measure temperatures in several places of an engine and of the cooling circuit as a function of mass flow of the coolant, blowing air velocity and temperature, braking power and rpm of the dynamometer and gas pedal position (not sure about this one though), some of which are themselves functions of time. The temperatures will be definitely dependant on changes of other parameters as well (thermal capacities, viscosities, densities etc.) but I am not changing these. Can I still use the dimensional analysis on my (probably) seven variables? And how many dimensionless parameters would that give me?
Thank you for any reactions.