Measuring Pressure For Compressible Fluid Systems?

[iScience]

Is measuring pressure for a compressible fluid system angle dependent?For a compressible fluid, Bernoulli's Law gives us a relation between two points along a closed system. More specifically it gives us the relation between two cross sections belonging to two distinct points in the closed system.

But I'm curious about the cross section itself for any given point in a closed system.
Consider:

A closed system of compressible fluid moving about smoothly (laminar flow).
The system has four straight edges and four corners resembling a rectangle while maintaining a uniform cross sectional area throughout the system.

Along the edges I expect no difference in velocity and pressure within the cross section of any given point (along the edges). But for a corner cross section there should be a velocity and pressure gradient (right?).If this is correct, does this mean pressure measurements taken at curvature points are angle dependent?

 

[Bystander]

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.688 , like this?

 

[russ_watters]

A closed system of compressible fluid moving about smoothly (laminar flow).
The system has four straight edges and four corners resembling a rectangle while maintaining a uniform cross sectional area throughout the system.

I'm having trouble picturing that. Are the surfaces everywhere parallel to the flow? Can you draw a diagram?

In a well designed Venturi tube where the flow is always parallel to the surface, the orientation of the surface doesn't matter (self evident). It is only when measuring pressure with a sensor who's opening isn't parallel to the flow that velocity pressure comes into play.

 

[boneh3ad]

Is measuring pressure for a compressible fluid system angle dependent?

In short, yes. Any pressure measurement, whether in a compressible or incompressible flow, is angle-dependent because any real sensor has finite size and therefore has an effect on the flow. If you could make a true point measurement without changing the flow at all, then there is no angle dependence, but this is not reality.

For a compressible fluid, Bernoulli's Law gives us a relation between two points along a closed system. More specifically it gives us the relation between two cross sections belonging to two distinct points in the closed system.

For a compressible fluid, Bernoulli's equation does not apply. Incompressibility is a fundamental assumption required to derive the equation.

But I'm curious about the cross section itself for any given point in a closed system.
Consider:

A closed system of compressible fluid moving about smoothly (laminar flow).
The system has four straight edges and four corners resembling a rectangle while maintaining a uniform cross sectional area throughout the system.

Along the edges I expect no difference in velocity and pressure within the cross section of any given point (along the edges). But for a corner cross section there should be a velocity and pressure gradient (right?).If this is correct, does this mean pressure measurements taken at curvature points are angle dependent?

I agree with @russ_watters that a diagram would be incredibly useful here. I am having a really tough time imagining what you mean.

 

[Chestermiller]

Are you assuming that the fluid is inviscid, or does the fluid have viscosity? Either way, are you saying that you have steady flow along a channel of rectangular cross section?