Question

In the solution to the 1st question in the Units and Dimensional Analysis Challenge problem set, the author states " We can assume the speed of the liquid leaving the container does not depend on the cross-sectional area of the hole" then introduces the flow rate as v*A_2 where A_2 is the cross sectional area of the hole. In which case, the flow rate does depend on the cross section of the hole. Furthermore, the time is shown to be dependent on the ratio of A_1/ A_2 - Is this a typo or am I missing something?

Answer 1

Flow rate in this case means volume/time rather than speed. In this approximation, speed depends only on pressure, which depends on depth and the density of the fluid. Volume/time = speed x cross-sectional area.