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Hi I need to calculat the Cd of three shapes with a sphere a rectangular and triangular bisect ion and that are upright prisms their height is 30cm
thecoolboyso

Posts: 5
Joined: Wed Dec 12, 2012 6:26 pm
Project Question: I am designing an experiment using a wind tunnel that my school owns. I've made four small towers out of wood that have the same height and base width - a cylinder, a rectangular prism, a triangular prism, and a pyramid. I want to figure out which shape is the most aerodynamic. I will put the towers into the wind tunnel, perpendicular to the ground, and put same amount of horizontal wind force on each of them. I need to know how I can calculate which shape is the most aerodynamic.
Project Due Date: 16 january 2013
Project Status: I am conducting my experiment

Hi

Interesting experiment! After reading your project question, I am assuming that your school's wind tunnel allows you to have at least some control and/or measurement of the velocity produced by the fan.

Under those assumptions all you will need to find the drag coefficient is the drag force and the reference area of your upright prisms. If your wind tunnel has something that measures the drag force on the object in question then great, but if not you could use a force probe that may be available at your school or some other force measurement method. (I suggest force probe and a computer because you do need fairly accurate measurements of the drag force to get a reasonably good measurements of the drag coefficients. Also taking multiple runs and then averaging them out would also be a good idea).

Now the reference area is a bit more tricky. This is the object of study of a lot of current research in fluid dynamics.

The drag coefficient has a pressure drag (also called form drag) component and a viscous drag component. Depending on the geometry of the object either the viscous component or the pressure component dominates the total behavior of the drag coefficient. If we think of drag force as being caused by friction between the air and the body, the correct choice for the reference area would be the total surface area of the body. If we think of the drag force as being the resistance to the flow, the correct choice would be the frontal area of the body.

In practice, drag coefficients are reported based on a wide variety of object areas and orientations. In the report, the person must specify the area used; when using the data, then we may have to convert the drag coefficient using the ratio of the areas.

Without complicating it for you, let me tell you that for "aerodynamic" or streamlined bodies we can usually get away with the assumption that viscous friction is dominant (so reference area = total surface area) and for blunt bodies pressure friction is dominant (so reference area = frontal area). In truth both of them contribute to the total friction.

For the cylindrical body and the rectangular prism use the frontal area of the body and for the triangular prism (assuming the "pointy" side is facing the wind and the base is not too thick) use the total surface area.

You can find the area formulas for all of them online.

Once you have those you can use the equation
Cd = (2*Fd)/(p*v^2*A)
where
Cd=drag coefficient
Fd=drag force
p= density of fluid at measured temperature
v= velocity of fluid
A= reference area

Let me know if you have any questions.
Dharman Kothari
Volunteer Expert
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DharmanKothari
Expert

Posts: 12
Joined: Tue Oct 09, 2012 8:00 pm
Occupation: Expert
Project Question: Expert
Project Due Date: N/A
Project Status: Not applicable

Thanks
thecoolboyso

Posts: 5
Joined: Wed Dec 12, 2012 6:26 pm