How To Calculate Drag Coefficient?

In summary: The section on vortex motion is a special case of viscous flow.The section on viscous flow is a general explanation of all the above, and it is a real gem.The section on aerodynamics is about how the general approach is applied to aerodynamics, and the basic considerations that go into understanding the equations and what can be done with them.In the section on viscous flow there are two main equations, their solutions and their applications. The first equation is the one that gives the pressure distribution around a body in a flowing fluid (the Navier-Stokes equation).The second equation is the one that gives the drag coefficient.You guys are so helpful. I am very happy with the help I am receiving. Thank
  • #1
FredericChopin
101
0
We know that the drag force on an object is defined as:

FD = ρ*v2*CD*A/2

, where ρ is the density of the fluid the object is traveling in, v is the velocity of the object, CD is the drag coefficient of the object and A is the surface area of the object.

Rearranging the formula to find drag coefficient, we have:

CD = (2*FD)/(ρ*v2*A)

But suppose we needed to find the drag coefficient of an object in order to find the drag force on the object; in other words, let's say we didn't have any data on both drag coefficient and drag force. How would one find drag coefficient without using the above formula?

I heard that another way to find it was:

CD ≈ 0.01*θ

, where θ is the angle of attack of the object in radians.

What I don't like about this formula is the "≈" sign, and so I avoid using it completely.

Is there another formula to find the drag coefficient of an object?

Thank you.
 
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  • #2
Figure out a nice, easy way to do that, and you'll have basically solved aerodynamics.

Good luck.
 
  • #3
FredericChopin said:
Is there another formula to find the drag coefficient of an object?

There are hundreds of different formulas. The hard question is deciding which one applies to your situation.

In practice, that usually involves doing experiments, not theory.
 
  • #4
The drag coefficient on an object is regarded as a function of the Reynolds number, based on the relative velocity between the object and the free stream. There are graphs and tables of drag coefficient as a function of Reynolds number for many typical shapes like a sphere or an air foil (the latter also involves dimensionless geometric ratios such as angle of attack). You can find information of this type in handbooks or online. The graphs and tables were developed from experimental data on objects of these shapes taken, for example, in wind tunnels. The graphs apply to all objects having geometrically similar shapes. So you can apply the graphs to your object, as long as it one of the shapes that has been studied.

It is also possible to predict the drag coefficient as a function of Reynolds number theoretically if the flow is laminar. This can be done by solving the differential fluid mechanics equations. Reasonably good theoretical estimates for high Reynolds numbers can also be made using computational fluid dynamics packages that include turbulent flow approximations.
 
  • #5
Chestermiller said:
The drag coefficient on an object is regarded as a function of the Reynolds number.

Would you be able to show me the formula to calculate Reynold's number and then the formula showing the relationship between the drag coefficient and the Reynold's number of an object?
 
  • #6
FredericChopin said:
Would you be able to show me the formula to calculate Reynold's number and then the formula showing the relationship between the drag coefficient and the Reynold's number of an object?

Google Drag of a Sphere, and choose the NASA site.
 
  • #8
@Chestermiller:

Chestermiller said:
Google Drag of a Sphere, and choose the NASA site.

The drag formula is the formula I'm trying to avoid using to find drag coefficient; what I'm looking for is another formula that can find drag coefficient which doesn't use drag in its calculation.

You said that there's a relationship between Reynold's number and drag coefficient, which, when put in a formula, can find drag coefficient; that I'm interesting in and am looking for, but unfortunately, the NASA website only says that drag coefficient is mostly constant amongst a number of Reynold's values and doesn't mention a formula.

@bigfooted:

bigfooted said:
or have a look at one of these quite well written course notes (check out the section 'viscous flows'):
http://web2.clarkson.edu/projects/crcd/me537/downloads.html

I looked at the "Viscous Flows" section but there was nothing about drag coefficient I could find. I will, however, keep the weblink handy.

@All:

After some researching, I found a Physics Forum post about the relationship between drag coefficient and Reynold's number:

https://www.physicsforums.com/showthread.php?t=139377

What Astronuc is saying in his equations looks exacty like what I'm looking for - a different approaching to calculating drag coefficient. I'm having trouble understanding what he is saying in his calculations, however. Would anybody be able to help me with this?

Thank you to all who have posted so far.
 
  • #9
Maybe I should be a little more clear with my question.

What I'm looking for is a formula that calculates drag coefficient without using drag force in its calculation. This is why I avoid using the drag formula to calculate drag coefficient.

Chestermiller introduced the relationship between drag coefficient and Reynold's number, and I was happy to look into that since Reynold's number doesn't require drag force in its calculation.

I'm sorry if I confused anyone.
 
  • #10
The NASA website, and many other web sites (and books) as well, presents a graph of drag coefficient vs Re for a sphere. If you need this relation in the form of an equation, then you have to fit an equation to the graph. At low Reynolds numbers, the drag coefficient is equal to 24/Re, which is the Stokes solution for creeping flow. You can start off with this. How you fit an equation to a graph is a matter of your personal choice. I suggest piecewise linear in the logs.
 
  • #11
What you are asking is basically impossible without an aerospace engineering degree and/or CFD software. Figuring out the drag coefficient of an object is difficult because it depends on geometry and surface roughness.
 
  • #12
FredericChopin said:
What I'm looking for is a formula that calculates drag coefficient without using drag force in its calculation. This is why I avoid using the drag formula to calculate drag coefficient.

Take a more thorough look at the course note I referred to.
The section on Navier-Stokes equations gives you the general fluid dynamics equations.
However, they are too complicated to solve analytically, and even numerically they are challenging.
The section on exact solutions talks about how to simplify the equations, using appropriate assumptions, to something that can be solved analytically.
The section on stream functions explains a well known method to analyze incompressible fluid flow.
The section on drag on spherical particles explains how to get the exact solution for the drag coefficient of a sphere in creeping flow, as a function of the Reynolds number.

As you see, even for a sphere in the limit of very low Reynolds numbers, it takes some effort to get the drag coefficient. The analysis get more complicated when you move to slightly more complicated flows like Stokes flow. And that's not even turbulent. And it's still a sphere we're talking about.

For general drag coefficients of objects in high Reynolds (high velocity) flows, there are no analytical expressions. Only measurements, detailed simulations and curve fits to these results. And these results are valid only for very specific shapes.
 

1. How do you calculate drag coefficient?

To calculate drag coefficient, you need to know the drag force, the fluid density, the flow speed, and the object's characteristic length. The formula for calculating drag coefficient is CD = Fd / (0.5 x ρ x V^2 x A), where CD is the drag coefficient, Fd is the drag force, ρ is the fluid density, V is the flow speed, and A is the object's characteristic length.

2. What is the significance of drag coefficient?

Drag coefficient is a dimensionless quantity that represents the aerodynamic efficiency of an object in a fluid flow. It is a crucial parameter in designing vehicles, aircrafts, and other objects that move through a fluid medium. A lower drag coefficient means the object experiences less resistance and can move more efficiently through the fluid.

3. How does the shape of an object affect its drag coefficient?

The shape of an object has a significant impact on its drag coefficient. Generally, streamlined objects with a smooth surface and a pointed end have a lower drag coefficient compared to objects with a rough surface and a blunt end. This is because streamlined objects have a more aerodynamic shape that allows for a smoother flow of the fluid around it, resulting in less drag.

4. What are some factors that can affect the accuracy of drag coefficient calculations?

There are several factors that can affect the accuracy of drag coefficient calculations, such as experimental errors, assumptions made in the calculations, and variations in the fluid flow conditions. Other factors include the surface roughness of the object, the presence of turbulence, and the compressibility of the fluid. It is essential to carefully consider these factors when calculating the drag coefficient.

5. Can the drag coefficient of an object change?

Yes, the drag coefficient of an object can change depending on various factors such as the velocity of the fluid, the angle of attack, and the object's orientation. For example, the drag coefficient of a car can vary depending on its speed and wind direction. Additionally, any modifications made to the object's shape or surface can also affect its drag coefficient.

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