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Old 09-09-2020, 11:48 AM   #1 (permalink)
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Professor Hummel's Figure 2.4, considerations

This one has set off a lively exchange and I thought it deserving of its own thread, so as not to be lost in the noise of the thread where it first came up.
Professor, and Doctor of Engineering, Dietrich Hummel, contributed the chapter on fluid mechanics which appears, beginning on page 47 of Hucho's 2nd-Edition, the first English translation from German. It runs through page 82, 32-pages in total.
Figure 2.4 appears on page 51. The caption concerns a streamlined body in two-dimensional, 'inviscid' flow, with an accompanying pressure profile.
I'd shared the image, as it's one of very few which address streamlined forms and their pressure trends, owing to their streamlined nature. Mr. Julian Edgar took me to task, with respect to the pressure profile, especially for the aft-body. And that's okay with me, however I'd hoped to flesh out my thesis on streamlined bodies, in advance of comments.
Caveats / conditions / qualifications / context :
* 'Inviscid' does not appear until page 49. It appears again on page 50. Again on page 51. And page 52.
* 'Inviscid' is not listed in the book's index on page 560.
* 'Ideal inviscid' occurs for the first and only time on page 52, the page after page 51 where Figure 2.4 appears.
* 'Ideal inviscid' appears nowhere on page 560 of the book's index.
* If a student were particulary interested in one of the most important concepts in fluid mechanics, as 'inviscid' flow, they'd have to read the entire text, hoping to find it by accident.
1) Hummel sets the stage for Figure 2.4, as 'qualitative', in which mathematics may accurately predict the position of the streamlines.
2) As a 'qualitative' representation, any 'quantitative' pressure values derived from the streamlines with Bournoulli's theorem must be adjusted for viscous flow in the boundary layer.
3) On page 49, Hummel defines 'real fluid' as ' inviscid', when it lies outside the boundary layer ( a common convention in aerodynamics ),provided that no flow separation takes place ( a condition of a streamlined body form ).
4) On the next page, AFTER Figure 2.4 , Page-52, Hummel muddies the water with the use of ' ideal inviscid' flow ( a condition of zero-viscosity, zero-torque, irrotational, frictionless fluid ) not mentioned with specificity in the figure caption, which leads to D' Alembert's paradox, of which it's classical depiction does not occur until later, at page-58, providing a very awkward and contextual introduction to the reader.
Quantitative considerations of the Figure 2.4 pressure profile:
* A streamlined body satisfies the condition of zero separation.
* A streamlined body is devoid of pressure drag.
* A streamlined body is devoid of separation-induced vortex -train drag.
* A streamlined body has only surface friction drag.
* A streamlined body has minimum surface area.
* A streamlined body has minimum skin friction drag.
* Bernoulli's theorem, for a frictionless incompressible fluid can be applied to real incompressible fluids with good results in situations where frictional effects are very small ( Daugherty & Franzini, page 87 ).
1) Julian Edgar, in his book, gives a range of 10% to 20% skin friction as a fraction of the total drag for automobiles.
2) For the sake of argument, if we take the 10% value for a streamlined body ( not improbable ), then, if skin friction is all there is, then by default, the total available energy at the end of a streamlined vehicle is basically 90% of the original gross.
3) Given this, the actual pressure profile of a streamlined body would be within 10% of the pressure profile depicted in Hummel's Figure 2.4.
* Julian is perfectly correct with respect to 'quanta' depicted in Hummel's figure, if we take 'ideal' in the context of ' does not occur in reality '.
* If a reader presumed that all 'conditions ' for the Figure 2.4 were defined within the caption of Figure 2.4, and 'inviscid' was interpreted as 'real', as is the convention, it would ( is ) very confusing, especially to anyone just getting acquainted with aerodynamics.
* My thought is that we're experiencing a ' nomenclature malfunction.'
* I don't believe in an upper limit for anal retentiveness when it comes to precise wording specificity.

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