How do I derive a PDE for the volume flow rate of a tilting vessel?

[akin-iii]

TL;DR

How can the phenomenon of pouring liquid from a vessel (pouring beer from a can for example) be modelled as a partial differential equation?

So the other day, I was pouring beer from a can to a mug and I obviously know the flow rate depends on the height of the beer from the bottom of the can (fluid level in the vessel), angle of tilt and I think time as well.
I was wondering how to best model the PDE to describe such a phenomenon ( tried it myself but I’m not sure I know what I’m doing) with boundary conditions such as initial and final volume after a time t and probably the volume capacity of the vessel.
Also if I could get a solution to the PDE as well?
Thank you.

 

[Edwina Lee]

The 1st thing to bear in mind is what quantities do you want to know about and to input.
This way you get a set of variables relevant for your modelling.
You could try building something simple first, then add on more complexity.