I'm working on this question:
Part a) was not a problem for me. For part b) I just want to check that I'm approaching this the correct way (or a way that will eventually land me at an answer)
I'm looking at my handbook which says this:
So, given this, I'm thinking that if I take $\frac{\partial u}{\partial t}$ of the given velocity field, and multiply through by $-\rho $, I'll end up with an expression that equals $\nabla$$p$, since body force is given to be $0$.
From there, I can use partial integration $dx$ to find an integral with $+f(y)$ on the end. I can then take $\frac{\partial p}{\partial y}$ to find what $f(y)$ is equal to. I then can take $\nabla$$p$ and integrate $dy$ with a $+f(x)$ on the end and solve for it like with $f(y)$.
I then should have an expression for $p$ as required by the question.
Is this a sound approach or is there another way that someone would suggest?
Thanks!
The Euler equation is only applicable for inviscid fluids ($\mu = 0$)—as a result, it doesn’t apply to your system.
The general idea is to utilize the full Navier-Stokes equations in two dimensions, and substitute/calculate every term (except for the pressure gradient term) for the flow you have. The equation itself will then furnish an equality for the components of the pressure gradient, which you can integrate and solve simultaneously for.