What is the method for calculating the angle Θu in compressible flow?

[pipe08]

Hello good people!

I'm studying the compressible flow and the book refers to this example. I can't understand how does it calculate the angle Θ_u?
In the previous example, there is a method to calculate it but it requires all the properties once the fluid is deflected, therefore, that's not the way because they are asking for the pressures.

anything light is greatly appreciated.

 

[boneh3ad]

Much like $\theta_l$, $\theta_u$ is set by the surface inclination due to the no-penetration condition.

 

[NatSusan]

Hi there!

Firstly, I want to say that it's great that you're studying compressible flow. It can be a challenging topic, but it's also very interesting.

To answer your question, the angle Θu is typically calculated using the conservation of momentum equation in the direction of flow. This equation takes into account the change in momentum due to the deflection of the fluid, as well as the pressure forces acting on the fluid.

In some cases, the angle can also be approximated using the Mach angle, which is the angle at which a shock wave is formed in supersonic flow. However, this is only applicable in certain situations and may not always give an accurate result.

I understand that the previous example may have used a different method to calculate the angle, but it's important to remember that there are often multiple ways to solve a problem in fluid mechanics. It's always best to understand the underlying principles and equations, rather than just memorizing specific methods.

I hope this helps! Let me know if you have any other questions. Good luck with your studies!