How Do I Determine Velocity at Each Pressure Point in a Nozzle?

[Johnsy18]

Hey everyone.

So I just experimented on compressible flow through a converging diverging nozzle. The nozzle had 8 pressure points from where which pressure was measured, as well as inlet and outlet pressures. The inlet pressure and mass flow rate were adjusted to form subsonic flow and adjusted again to form super sonic flow.

I was able to read off pressure values from each pressure point and the mass flow rate too, as well as the inlet and outlet temperatures.

My questions are:

How do I determine the velocity at each pressure point for the subsonic and super sonic flow parts? I know that subsonic flow obeys Bernoulli's theorem, P1 + pV1^2/2 + pgh1 = P2 + pV2^2/2 + pgh2, so if I was to use that equation to find the velocity at a pressure point then how would I know V1 and V2? Do I just assume V1 is 0 and then calculate V2?

As for supersonic flow, how would I find the velocity at each pressure point? I know the density is not constant.

 

[boneh3ad]

The subsonic flow would not obey Bernoulli's equation, which does not apply to compressible flows without modification.

How familiar are you with compressible flows? Do you know about the isentropic relations?

 

[Johnsy18]

I have only just began learning about compressible flow. So, you say that with modification, subsonic flow does obey Bernoulli's theorem. What is this modification?

I've herd of Isentropic flows. Not fully aware of how and what it applies to.

 

[boneh3ad]

No, with modification you can use Bernoulli's equation for subsonic compressible flows. Are you familiar with the limitations of Bernoulli's equation? That should be a good starting place rather than just jumping straight into compressible flows.

That said, Bernoulli's equation, even when modified to allow for compressible flow, is not usually very useful. You are better off assuming the system is isentropic and using those aforementioned relationships, which are much simpler, easier to use, and very accurate in most situations.

 

[SteamKing]

Bernoulli's equation (without modification) is only valid for incompressible flow. For gas flows, compressibility effects can be neglected for gas velocities below about 0.3 Mach.

To study flows above this velocity, there are several different types of flow which can be considered: adiabatic (no heat transfer to/from the surroundings) or isothermal (constant temperature), both with and without friction. This topic is generally studied as an introduction to gas dynamics.

http://en.wikipedia.org/wiki/Compressible_flow

Ascher Shapiro wrote one of the first text on gas dynamics back in the 1950s (and is still in print), and his book was used to develop the formulas in the Crane Technical Paper 410. A more recent version of similar text is Gas Dynamics by Zucrow & Hoffman.

http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/shapiro-ascher.pdf

https://www.amazon.com/dp/0471066915/?tag=pfamazon01-20

https://www.amazon.com/dp/047198440X/?tag=pfamazon01-20

This website is based on Shapiro's work:

http://www.potto.org/gasDynamics/node61.php