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

#### akin-iii

Summary
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.

Related Differential Equations News on Phys.org

#### 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.

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

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving