K@meleon Posted December 31, 2006 Share Posted December 31, 2006 Well, I'm supposed to compute the drag coefficient of a sphere in a hypersonic newtonian flow. In a newtonian flow the pressure coefficient is given by: [math]C_p = sin(\alpha)[/math], with alpha the angle of attack. The pressure coefficient on the lee side is 0. Now. My problem is that I have to compute the total drag coefficient, integrating a surface integral over half a sphere. The final drag coefficient is supposed to be 1, but I just can't get it right , and my calculus book is a good 1000km away... Could someone help me out? Thanx a lot! Link to comment Share on other sites More sharing options...

insane_alien Posted December 31, 2006 Share Posted December 31, 2006 can you post what you've done so far? this would help us quite a bit. Link to comment Share on other sites More sharing options...

K@meleon Posted December 31, 2006 Author Share Posted December 31, 2006 Well, I tried for a cylinder in a flow so far, and got the right answer. It's supposed to be a cylinder of length 1, and radius R. I had: [math] C_p = 2 sin^2(\alpha) [/math] [math] C_n=\frac{1}{c} \cdot \int_0^c C_p \: dr [/math] with c = 2R (the frontal surface of the cylinder, seen by the airflow) [math] C_d = C_n \cdot sin(\alpha) [/math] [math] \Rightarrow C_d=\frac{1}{2R} \cdot \int_0^{\pi} 2sin^2(\alpha)\cdot sin(\alpha)\cdot R \cdot d\alpha [/math] Which, after integration by parts etc etc yields: [math] C_d = \frac{4}{3} [/math] The point is: I'm not sure I did it the right way, I just got the right answer.. For the sphere I started the same way, but with [math] c = \pi R^2 [/math]. I put the theory in attachement for clarity, the example they use is for a flat plate.. Hope it will help.. Thanx again. Newton.zip Newton2.zip Link to comment Share on other sites More sharing options...

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