CFD Online Discussion Forums - What EXACTLY are the "outflow" and "pressure outlet" BCs?

Hello,

I am just starting my MSc and we have been given an assignment in which we must model two dimensional, laminar, incompressible Poiseulle flow in a channel. We are supposed to use a VELOCITY INLET inlet boundary condition and two different outlet boundary conditions - the OUTFLOW boundary condition and the PRESSURE OUTLET boundary condition. The problem is I don't understand exactly what these boundary conditions are. I am dealing with a simple rectangular domain with four sides (Inlet, outlet, and top/bottom wall). The flow moves from left to right. I will make a list below showing which boundary conditions I know and which I do not know.

VELOCITY

Inlet : Dirichlet, $\boldsymbol u=\boldsymbol u_{\text{inlet}}$
Outlet : ???
Top and Bottom Wall : Dirichlet, $\boldsymbol u=0$

PRESSURE

Inlet : ???
Outlet : ???
Top and Bottom Wall : Neumann, $\boldsymbol n\cdot\nabla p=0$

As you can see, I am insure of the outlet conditions on $\boldsymbol u$ , and the inlet AND outlet conditions on

. I don't know what these are when Fluent is using the OUTFLOW and PRESSURE OUTLET conditions. I had a look at this thread, but it still isn't clear exactly what BCs Fluent is using. And the ANSYS official documentation is absolutely abysmal as well.

As I understand from the linked thread, the OUTFLOW condition assumes a Neumann condition on all flow variables except the pressure. So, what does it do with the pressure?!

And, it seems that the PRESSURE OUTLET boundary condition assumes a Dirichlet condition on the pressure. But what does it do with the velocity?!

Finally, in both of these cases, what boundary condition is the VELOCITY INLET choice assigning for the pressure at the inlet?

Would really appreciate some clarity here. As I said in my previous thread, I have an extensive background in mathematics, so please do not shy away from using any and all mathematical language you would deem as helpful. Thanks in advance.