Question

what is the formula for calculating uncertainty in dimensional analysis problems?

Answer 1

From my reading of the first lecture, dimensional analysis is a method whereby an equation is derived by looking at the quantities that we suspect have a relationship with the quantity for which an expression is sought. The result is an equation expressing one quantity with respect to others.
The 'uncertainty' in this regard is i suspect "have the correct quantities been selected?"

The result gives us a function that we can test experimentally (if we can think of an experiment to test it) I suppose this could be called a hypothesis.

Each measurement made in the experiment, ex length +/_ the error in the length reading, has an uncertainty in it. The uncertainty of each measurement depends on the device used to make the measurement. On my meter stick the smallest graduation are mm.

My 2 cents worth.