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I am currently reading up on fluid mechanics and was reading up on the drag force equation, and it come to my attention I am not sure how one can find the coefficient of drag of and object without knowing the drag force. But my understanding is so far that the drag force equation is a purely experimentally derived one, thus this is causing me confusion as I can find the necessary information on what experiment were carried out to to find this equation.

An example in one of my text book give a square plate oscillating up and down in what I assume to be water, and I was wondering how can one find the drag force on this square plate, if the coefficient is not known? Which I believe you cannot.

I have look on various book ect but with fluid mechanics I seem to feel like I am going around in circles, every-time I research drag coefficient I keep getting the rearrangement of the the drag equation.

I was just wondering if maybe could someone could expand on how, it possible to find the drag coefficient of a square plate, if the drag force is not known.

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  • $\begingroup$ Have you heard of the Naiver-Stokes equation? $\endgroup$
    – Chet Miller
    Commented Dec 11, 2018 at 17:58
  • $\begingroup$ I have come across it in my reading, but I by no means have a full understanding of it as such, very new to fluids mechanics. Alot of the naiver stoke I have come across dose really, help me link it all together intuitively. $\endgroup$
    – james2018
    Commented Dec 11, 2018 at 18:02

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The Naiver-Stokes equations describe the behavior of a viscous fluid in laminar flow (i.e., the pressure and velocity variations as functions of time and position). They can be used to solve your problem, but it would typically require numerical analysis. At very low fluid velocities and/or high fluid viscosities, the behavior reduces to Stokes creeping flow, in which the inertial terms in the equations can be neglected. As a first approximation, you would solve this problem using the Stokes flow approximation. Then you would add the inertial terms and the transient behavior. It would be a nasty problem at this level, but it can be done (using computational fluid dynamics).

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