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Tangencial force aplied by fluid friction

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Using the formula F = 0.5*Cd*p*A*v²*sin(theta) we can compute the 'normal' force the fluid with density p aplies on a flat surface with coefficient of drag friction Cd, surface area A and linear velocity v(theta is the angle between the surface normal and the velocity vector). How can I compute the force it applies tangencially to the surface?

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I really have no clue, but I think that the force applied is actually coming from the side of the object with the highest pressure and thusly must be a function of pressure diffrence.

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There actually isn't any helpful information at all in the formula. It merely converts from a unitless drag coefficient into a force, but says nothing about what contributes to the drag.

That is to say, the Cd in that formula potentially is the total drag coefficient, and so therefore might encompass skin friction drag (the tangential part), pressure drag (which is due to an inbalance in pressures as projected into the direction of the freestream flow---ultimately due to boundary layer separation), and induced drag (drag-due-to-lift, e.g., a component of lift that is tilted back into the free stream direction due to downwash, the turning/tilting of the freestream flow due to circulation). If you choose a value of Cd that actually does include all this, you will not be able to separate the two. Its all in the choice of Cd.

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I've developped a formula that computes the tangencial force applied by the fluid friction but the results gives extremelly high amounts of force because the pressure has a very high value (10000N/m² = 1atm) and the force is proportional to the pressure so the pressure enters as a multiplier in the formula. BUT, if I use a different Cd for this formula (a very low value) I can get interesting results... I just want to know if there's a physically accurate method to determine this force.

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