Converging-Diverging Nozzle

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Discussion Overview

The discussion revolves around a homework problem involving the flow of air through a converging-diverging nozzle, specifically focusing on the conditions just upstream and downstream of a normal shock occurring in the diverging section. Participants are seeking to compute the Mach number, pressure, and temperature at these locations, while grappling with the relevant equations and concepts.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses uncertainty about the meaning of 'S' and 'S*' in the context of the equations provided in the lecture slides, questioning whether 'S' refers to an arbitrary cross-section along the nozzle.
  • Another participant indicates a lack of understanding regarding the reference to 'slide 9' and requests clarification on its content.
  • A participant mentions that the equations on slide 9 are being used but admits to not fully understanding their implications, particularly regarding the upstream and downstream conditions relative to the shock.
  • There is confusion about the definitions of T, P, and other variables in relation to the cross-sectional areas and whether they correspond to the reservoir conditions.
  • One participant references a table that supports their calculation of the Mach number being 1.80, suggesting that they may have found a source that aligns with their understanding.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the definitions of the variables or the specific calculations required for the problem. Multiple viewpoints and uncertainties remain regarding the interpretation of the equations and the conditions upstream and downstream of the shock.

Contextual Notes

Participants express uncertainty about the definitions and implications of various terms and equations, particularly regarding the upstream and downstream conditions of the shock. There is also a lack of clarity on the specific equations to apply for the calculations.

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Homework Statement


2. Air flows from a large supply tank in which the pressure is 147 psig and the temperature is 160 F through a converging - diverging nozzle. The velocity at the throat of the nozzle is sonic. A normal shock occurs at a point in the diverging section of the nozzle where the cross-sectional area is 1.44 times the cross-sectional area of the throat.

a) Compute the Mach number, pressure, and temperature just upstream of the shock.
b) Compute the Mach number, pressure, and temperature just downstream of the shock.


Homework Equations





The Attempt at a Solution


I thought the slide 9 would be the equation to use for this problem, but if S* is what they mean, that is just the cross sectional area of the throat, right? What is S supposed to be without the Asterisk?

I am not sure how I could determine the mach numbers up and downstream of the shock using any of the equations give in the lecture slides. is Po, To, etc just at the ''back pressure'' (back pressure is the tank pressure, right?)
 
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We have no idea what 'slide 9' refers to.
 
My apologies, I intended to post the slides
 

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I am just using the equation on the 9th slide. Honestly, I can't really say I understand what the equation means. I know S* is the cross sectional area where the velocity is sonic (the throat), but my best guess is that S is an arbitrary cross section anywhere along the pipe. However, I wonder if it is only for the divergent part of the nozzle?

slide 10 summarizes all the equations, and of course T, P, ρ, etc are probably corresponding with S? It explicitly states T0, P0, etc. are at the reservoir, but doesn't mention what T, P, etc are.

I am uncertain of what it meant by ''just upstream of the shock'' or ''just downsteam'' and how I am supposed to calculate these. Just upstream can be anything upsteam, what are they asking for more precisely?

This table seems to agree with my calculation of the mach number being 1.80
http://www.cchem.berkeley.edu/cbe150a/isentropic_flow.pdf
 

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