Calculate the drag force but I dont know the drag coefficient?

[skaboy607]

Hi

In a Drag problem, I'm trying to calculate the drag force but I don't know the drag coefficient? Is there any way to calculate it?

Thanks

 

[mgb_phys]

For simple shapes yes (although you can look them up in a table http://en.wikipedia.org/wiki/Drag_coefficient)
Generally for real shapes you have to measure it, either in a wind tunnel or a computer simulation (CFD)

 

[skaboy607]

Ok, I am trying to do a tutorial sheet on it, how do I calculate it say for sphere?

thanks

 

[minger]

If you click the link there is a table that lists the Drag Coefficient for a sphere as $$C_d = 0.47$$

 

[skaboy607]

Yea I have used that but it doesn't give me the required answer.

 

[mgb_phys]

Do you mean how do you calculate that it is 0.47 for a sphere, or how do you calculate the drag for a sphere in given conditions?

The drag equation ( propertional Area * velocity^2) is an approximation for high Reynolds number flow (eg air) it isn't necessarily correct for low speed or high viscosity cases.

 

[skaboy607]

Using the Drag force equation I am trying the force on a sphere as it moves through an oil. The only unknown that I have is the drag coefficient? And if I use 0.47, it doesn't give me the right answer.

Thanks

 

[minger]

The drag equation ( propertional Area * velocity^2) is an approximation for high Reynolds number flow (eg air) it isn't necessarily correct for low speed or high viscosity cases.

The drag coefficient is quite a function of Reynolds, and potentially other factors. Man, I must be in a good mood today. Let's see what I can find. For REALLY low Reynolds numbers, (Re < 1), we have

$$C_f = \frac{24}{R^*} \left( 1 + \frac{3}{16}R^* - \frac{7k}{48}R^* \right)\,\,R^*=2R$$
Not sure why it's written like that, but oh well. $$R\equiv$$ Reynolds number of course. $$k = V^* / U_\infty$$ where V* is the radial velocity of blowing through the surface...which I assume you can take to be zero in your case.

There is also a "famous" Oseen's (1910) drag coefficient forumula for a sphere in uniform stream:
$$C_D = \frac{24}{{Re}_D}\left(1+\frac{3}{16}{Re}_D\right)$$

Stokes gave an exact solution in the limit as Re->0, such as creeping flow, where:
$$C_D = \frac{24}{{Re}_D}$$
However, that's only valid where Reynolds is less than 0.2.

What type of Reynolds are you looking at?

 

[skaboy607]

Well I calculate my Reynolds number to be 9.9, the velocity of the sphere is 0.08m/s, the density is 850, diameter of the sphere is 14.7(10)^-3, and the viscosity is 0.1 which yields 9.996?

Also from the drag equation, where I use area, will it be the surface area of the sphere, i.e. d^2*pi.

Thanks

 

[Bob S]

Also from the drag equation, where I use area, will it be the surface area of the sphere, i.e. d^2*pi.

Thanks

The area you use is the frontal area, which is pi r^2 or (pi/4) d^2.