Simscape Local Restriction (G) Delta P Equation Documentation

I've been working on a custom The local restriction (G) component and I'm having a hard time deriving this equation.

Based on the bernoulli equation I get

Using the conservation of mass

This is as far as I am able to reduce the equation and I'm not sure where the disconnect is. Is there any documentation or references about how the location equation was derived?

Answer 1

[Suman]

Hi @Luke,

You can refer to the following documentation for more information on Local Restriction.

[Luke]

Hello @Suman

Thank you for taking the time to reply. I am familiar with that page on the local restriction but it does not point to how these equations were derived. I have not been able to match the equations up with the traditional approach of dealing with location restrictions, i.e. isentropic assumptions and the energy equation. As an example as r -> 0 the flow equation becomes

This equation is the same as the incompressible flow equations for a restriction but are not applicable for gases. This is why I would like to understand how the equations were derived to see if they are using the same assumptions that I would.