Question

Module 1: Challenge Problem 1. Can someone explain how they knew where to start with this problem and what to do next.

Answer 1

It's a dimensional analysis. It's a little intuitive, but basically you consider everything that MIGHT be important to know the time the liquid would take to flow out.

So he thought, the time must be connected to the density of the fluid, to both areas (in and out), the distance(height) for the liquid to reach the container and gravity. If you think there's something else the time COULD depend on, you can add it, wont matter in the end.
"b" is a constant, because we need to assume that could be one.
Now you can start doing the analysis.
\[T = \rho ^{v} h ^{w} g ^{x} A _{1}^{y} A _{2}^{z}\]

Now you substitute each letter for the SI base unit. and you solve (v,w,x,y,z) knowing that the dimensions must satisfy that relation.
You only have time on one side. Time is in seconds and is elevated to 1.
1 = -2X (because gravity is \[m \sec ^{-2}\]. Nothing else is measured in seconds, so that equation is done and you get X = - 1/2. Hope you understand now what to do next.

Answer 2

Thanks