Dimensional Analysis and task letter

I was just wondering where the dimensional analysis comes into play in this lab. When do we have to use it? Also how do we assess the blowers as pumps to circulate water at 10 degrees celsius and a frequency of 1 Hz?

Dimensional analysis is actually the entirety of the lab. You will need it for the final deliverable, as you didn't test a compressor running at 1 Hz speed, flowing water. You are going to use the data collected in the lab to find a characteristic blower response so that you can upscale your results to the larger compressor in the AC systems that are flowing water. That characteristic response is found through all the non-dimensional quantities in your lab handout.

Specifically, you are interested in that efficiency, eta. Efficiency is a function of several non-dimensional groups (Reynolds number, Froude number, flow coefficient), but you need to prove that it can be boiled down to a function of only flow coefficient in this particular flow regime. Once you have that important plot of efficiency versus flow coefficient, you can pick off the most efficient point on your non-dimensional compressor map which will fix the values of those two quantities. Then, you use the density of water at 10 deg C, the speed of 1 Hz and the compressor inlet diameter and you'll be able to figure out the volumetric flow for the AC compressor using your lab data and all the dimensional analysis I just ran through.

You probably want to start by first calculating all your energy rise rates and volumetric flow rates for all your operating conditions. This will require a decent amount of sorting the data appropriately first. Also remember that you'll need to compare the measured velocity from the hot-wire anemometer against your calculated velocity.

It's a pretty complex lab, with a lot of moving parts (no pun intended). The lecture slides actually give a pretty decent way as to proceed with the analysis (pages 11-15).