Applying NS Equations to Interface b/w Two Media

[mcfc]

I need to answer this problem:
The interface between two media is positioned along the plane $x_3=0$. Medium 1 is a Newtonian incompressible fluid which occupies the region $x_3 \le 0$.
i)assuming the velocity and pressure fields in the fluid are given, determine the traction(?) that medium 2 exerts onto the fluid along the interface.
ii)now assume that only the velocity field in the fluid is known and that medium 2 is an inviscid fluid under pressure $p^{(2)}=P$. What is the fluid pressure at the interface?

Is this an application of the NS equations...I'm sorry for the vague question but I'm a little lost on how to approach the question...

 

[lippyka]

i) Yes, this is an application of the Navier-Stokes equations. The traction that medium 2 exerts onto the fluid at the interface is determined by the normal and tangential components of the stress tensor. The normal component is given by the pressure of fluid 1, while the tangential component can be calculated using the velocity field in fluid 1.ii) To determine the fluid pressure at the interface, you need to solve the NS equations for the pressure at the interface. This requires knowledge of both the velocity field and the pressure field in medium 1. The pressure of medium 2 (p^{(2)}=P) can then be used to calculate the pressure at the interface.