In considering something like a jet engine, the thermodynamic analysis can be very mathematical and quite simple (e.g. one-dimensional flow). It's quite general and takes exactly the same mathematical form for many different engines. In contrast, there's the level of analysis at which a compressor map is made, which is kind of empirical. It comes from experiments or numerical simulations, and the resulting map is specific to a particular piece of equipment. We could also mention stress analysis of components, carried out mathematically and/or with finite element models.

My question is, how do engineers think of these "levels of analysis" fitting together? It's not obviously a case of a hierarchy of detail. Different analyses cover different aspects/dimensions of the machine. There's no single analysis which incorporates all the aspects (although I guess there could be). What's the intellectual framework for this, or the mental model of how the analyses fit together? (I'm wondering whether this is actually more of a philosophy of science question.)

  • $\begingroup$ states and energy for me... $\endgroup$
    – Abel
    Oct 16 '21 at 0:20
  • $\begingroup$ Some consider boundaries to include or exclude things. Or make other assumptions like assuming gravitational acceleration as 10 when the efficiency covers that small error. Hydro power is an example: P = Q * g * h * effy. Effy is about 50% so taking 10 instead of 9.81 makes little difference. $\endgroup$
    – Solar Mike
    Oct 16 '21 at 2:57
  • $\begingroup$ While, I thought I understood what you meant in the title (thermodynamic, fluid dynamical, mechanical), I got confused about what exactly different levels of analysis you perceive at "stress analysis of components, carried out mathematically and/or with finite element models.". Do you consider stress analysis carried out mathematically and with FEM as two different levels of analysis? $\endgroup$
    – NMech
    Oct 16 '21 at 5:58
  • $\begingroup$ Well, closed-form solutions (say for a cross-sectional moment of inertia) are a bit different from FEM. My knowledge of this is pretty basic, but I guess I count FEM as being able, in some cases, to model in detail the development of fractures, for example. A purely mathematical approach might just be limited to linear phenomena. That's what I was getting at. $\endgroup$
    – Theo H
    Oct 16 '21 at 15:37

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