Hi every one, im having a few problems with some research im doing. I put this in the PDE section as it seams related, but it is for a specific application and im not sure that it wouldn't be better suited to the mechanical engineering section.(adsbygoogle = window.adsbygoogle || []).push({});

I am wanting to find the pressure distribution in a 2d flow that moves around a corner (ie bend in a pipe)

I have been using flexPDE to solve naiver stokes with FEM. however, i am unsure how to incorporate pressure.

the software examples do one thing my supervisor suggests another.

First my supervisor is saying to use Bernoulli dynamic pressure. But i feel he is confusing something as that is more related to potential pressure rather than actual

pressure. also due to "no slip" the pressure on the wall would always be 0.

also not to mention using this alone mean the software can close on a solution.

I suspect we need to solve for the static pressure in the system but I dont know how.

secondly the software examples assume slight compressibility of the fluid.

they give:

defining a hypothetical equation of state

1) p(dens) = p0 + L*(dens-dens0)

" where p0 and dens0 represent a reference density and pressure, and L is a large

number representing a strong response of pressure to changes of density. L is

chosen large enough to enforce the near-incompressibility of the fluid, yet not

so large as to erase the other terms of the equation in the finite precision

of the computer arithmetic."

The compressible form of the continuity equation

2) dt(dens) + div(dens*U) = 0

(U is a velocty vector field it seams, and dt(dens)= ddens/dt, i am unsure what they mean by p(dens))

they then do some magic and come out with

dt(p) = -L*dens0*div(U)

=

3) div(grad(p)) = M*div(U)

what I understand is vaguely how they formed the first and second equation, and how they got from dt(p)= div(grad(p))

I dont understand how to get from 1 and 2 to 3, or how to get usable real world value predictions from this as L / M is assumed

I suspect that this is only used to find a vague distribution and to enforce continuity in the equation.

any help in unraveling this for me would be much appreciated thank you in advance

Phill

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# Navier stokes and pressure on objects

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