Aerodynamics: Optimization of an aircraft engine

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The discussion focuses on the derivation of the aerodynamic drag equation, specifically the formula F_d = 1/2 * ρ * u² * A * C_d. The drag coefficient (C_d) is defined through dimensional analysis and is influenced by the shape of the object and flow conditions, such as Reynolds and Mach numbers. Resources like the book "Aerodynamic Drag" by Hoerner provide extensive C_d values for various shapes. Participants encourage better search strategies to find relevant information on this topic. Understanding the variability of C_d with geometry is highlighted as a critical aspect of aircraft engine optimization.
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New user has been reminded to always show their work on schoolwork problems.
I am writing an essay about optimization of an aircraft engine. I have to show the derivation of aerodynamic drag eq. I need help about it because i couldn't find where it came from.
 
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Hi there, welcome to the forum! :welcome:

It is probably better to start a new topic on this next time instead of replying to an old thread (last post almost a year ago). We try to keep threads limited to the original topic.

But do you mean by 'the aerodynamic drag eq.' this one:
$$
F_d = \frac{1}{2}\rho u^2 A C_d
$$
If so then you ought to know that this is just the inverse of the definition of the drag coefficient (##C_d = \frac{2 F_d}{\rho u^2 A}##). The drag coefficient comes from dimensional analysis (The Buckingham ##\pi## Theorem). This drag coefficient is found to be similar for similarly shaped object. There are whole books written that give (a range of) ##C_d## values for differently shaped objects (most notably the historic 'Aerodynamic Drag' by Hoerner). But please note that ##C_d## is not always constant for even the same object in different flow conditions (like for different Reynolds numbers or different Mach numbers). Also, the million dollar question is how ##C_d## varies for small changes in the geometry.
 
dd5139 said:
I am writing an essay about optimization of an aircraft engine. I have to show the derivation of aerodynamic drag eq. I need help about it because i couldn't find where it came from.
Welcome to PF.

Please show us your Google search terms that you have been using so far. This seems like a pretty easy search, so we would like to help you learn how to do searches like this better in the future. :smile:
 
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