I have 2D PC MRI velocity data in a square matrix. I want to calculate the pressure differences at different points between the inlet and outlet of left atrium from this data. I have calculated using Bernoulli equation where I could calculate the pressure differences along a particular streamline only. I want to know how can I calculate pressure difference in the whole flow?
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Many years ago I worked on this topic, some of my papers on RG illustrate some details. However, if you have a matrix of the two velocity components on a plane, assuming the flow has a divergent-free velocity field, you could set the solution in terms of the 2D Poisson problem for computing the pressure gradient in the plane.
However, I immagine that you have a slice (say the x,y - plane) of 3D real flow and the condition for the 2D continuity du/dx+dv/dy=0 is not satisfied as you have the dw/dz component.
Using Bernoulli is a wrong approximation for a viscous fluid.
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