Not sure who could help me with this, but I have an 'exploratory' task to do for my Continuum Mechanics module. I need to answer the questions below. If anyone covers anything like this in their course, I would massively appreciate any input. The work is due tomorrow (Friday). I am very unmotivated to do it as I hate this kind of maths. x_{1} means x with a subscript of 1.

1. State the boundary condition for a inviscid fluid at an impermeable fixed boundary x_{3} - h( x_{1}, x_{2} ) = 0 where we do not permit normal velocity but permit non-zero tangential velocity.

2. State the boundary condition for an inviscid fluid at a prescribed moving boundary x_{3} - h( x_{1}, x_{2} , t ) = 0 where we do not permit normal velocity but permit non-zero tangential velocity.

3. State the normal stress boundary condition at an interface x_{3} - h( x_{1}, x_{2} , t ) = 0 between an inviscid incompressible fuid and a vacuum. You may assume that the interface has a constant surface tension.

4. State the normal stress boundary condition at an interface x_{3} - h( x_{1}, x_{2} , t ) = 0 between an viscous incompressible fuid and a vacuum. You may assume that the interface has a constant surface tension.

What are you doing doing applied maths?! After you've been doing so well at Advanced Topics In Combinatorics. *shakes his head in shame*

(I don't have the foggiest how to do that kind of stuff now, and Friday is too soon for me to study my notes I'm afraid.)

I'm doing it because I'm a numptie. Should have stuck with pure.