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In many sources related to jet engine thrust calculations such as https://www.jet-x.org/a8.html , pressure thrust of a module such as combustion chamber, nozzle or compressor, is calculated by front and rear cross sectional area of them (including holes at their center) and flow pressure at front and rear of them.

If they were a complete solid disc without any hole, I could understand this calculation.

However, for turbine in an example, it has a hole at rear and front, so either pressure at rear can't act on the hole at rear or pressure at front can't on the hole at front. In my opinion, these holes should be taken out of cross sectional area term.

Why do we think as if fluid pressure is able to act on the whole cross sectional area including holes at the center whereas they can't physically?

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    $\begingroup$ Can you be more specific? The linked source is very long. Which portion do you think is wrong? And what do you think the correct answer should be? E.g. In section x they use use area Y m^2 but you think it should be area Z $\endgroup$
    – Daniel K
    Commented Jun 7, 2023 at 16:46
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    $\begingroup$ A diagram might help understand your question. $\endgroup$
    – Raffles
    Commented Jun 7, 2023 at 20:59
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    $\begingroup$ Specifically, where do you see the page state the cross-sectional area includes the “holes” (which are in fact opposite of holes, because it's the body with the shaft)? I only see them say “nozzle cross-sectional area” and that is just the area of the nozzle itself (which has annular shape). $\endgroup$
    – Jan Hudec
    Commented Jun 7, 2023 at 21:34

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This answer assumes that by "hole" you are talking about a non-physical boundary like the exit plane. If so, it's explained here: https://www.grc.nasa.gov/WWW/k-12/airplane/thrsteq.html

There is an additional effect which we must account for if the exit pressure p is different from the free stream pressure. The fluid pressure is related to the momentum of the gas molecules and acts perpendicular to any boundary which we impose. If there is a net change of pressure in the flow there is an additional change in momentum. Across the exit area we may encounter an additional force term equal to the exit area Ae times the exit pressure minus the free stream pressure. The general thrust equation is then given by:

F = (m dot * V)e - (m dot * V)0 + (pe - p0) * Ae

Normally, the magnitude of the pressure-area term is small relative to the m dot-V terms.

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