Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to
, where c (0 < c < 1) is a empirical constant. Determine a differential equation for the height h of water at time t for the cubical tank shown. The radius of the hole is 2 in., and g = 32ft/s2
The Attempt at a Solution
I am always confused in setting up a DE. Over here, the answer says that V= Aw(area of water). h . The next step written was that dh/dt = 1/Aw * dV/dt ... How does this make sense.. I am confused here. I understand that the "c.Ah.(2gh)^.5" given back in the question is dv/dt . But when you multiply it with 1/Aw, how do you get dh/dt ??? Thanks for any help!