Drag Coefficient Of a Sphere In Hypersonic Flow

[K@meleon]

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!

[insane_alien]

can you post what you've done so far? this would help us quite a bit.

[K@meleon]

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