# Reynolds number and drag coefficient of a cylinder

Lately, I have conducted an experiment where I dragged various circular cylinders through water in order to find the resistance, and hopefully also the drag coefficient. It seems to me that this coefficient is dependent on what is called the Reynolds number. Using some sources, I can easily find the drag coefficient as a function of this number for cylinders. The problem, however, is that these are only for where the flow of the water is perpendicular to the height of the cylinder. In other words, the water meets the curved part of the cylinder. My question is if anybody knows where I can find a graph of the drag coefficient of a circular cylinder as a function of the Reynolds number, where the water flow meets the top (the flat part) of the cylinder?

Secondly, I understand that the Reynolds number is calculated accordingly;
R=V*L/μ
where V is velocity, L is a lenght scale, and μ is dynamic viscosity divided by the density.
Would L euqal the radius in my scenario?

Furthermore, from what I can gather, the relationship between the Reynolds number and the drag coefficient can only be confirmed experimentally, and therefore, I have no way of finding a solution analytically.

Thank you for considering this problem

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CWatters
Homework Helper
Gold Member
This isn't my field but I noticed Wikipedia suggests that Cd isn't always dependant on the Reynolds number...

http://en.wikipedia.org/wiki/Drag_equation

For sharp-cornered bluff bodies, like square cylinders and plates held transverse to the flow direction, this equation is applicable with the drag coefficient as a constant value when the Reynolds number is greater than 1000.

For smooth bodies, like a circular cylinder, the drag coefficient may vary significantly until Reynolds numbers up to 107 (ten million).
In the orientation you describe (flat face to the flow) it might be Cd is independent of the Reynolds number. Perhaps Plot the drag force vs velocity squared and if you get a straight line then that would appear to confirm it is independent, at least over the velocity range you are interested in.

In my experiment, however, I varied the velocity, so when I plotted the drag force vs velocity squared time surface area, I obtained a more or less straight line. However, the gradient was very different for each velocity. In addition, the Reynolds number for my data is far below 1000. Any ideas?

CWatters
Homework Helper
Gold Member
Humm. Really isn't my field but I'll have another go..

However, the gradient was very different for each velocity
Ok so that suggest the Cd is some function of the Reynolds number.

The gradient at each velocity gives you a value for Cd at those various velocities. So perhaps calculate the Re at those velocities using..

Re=V*L/μ

and plot Cd vs the calculated Re.

If that's a straight line then it's easy to work out what the relationship is between Cd and Reynolds number. If not a straight line then the function is more complex but with luck you can find a curve that fits the data.

Other than that I'm out of ideas.

Chestermiller
Mentor
Lately, I have conducted an experiment where I dragged various circular cylinders through water in order to find the resistance, and hopefully also the drag coefficient. It seems to me that this coefficient is dependent on what is called the Reynolds number. Using some sources, I can easily find the drag coefficient as a function of this number for cylinders. The problem, however, is that these are only for where the flow of the water is perpendicular to the height of the cylinder. In other words, the water meets the curved part of the cylinder. My question is if anybody knows where I can find a graph of the drag coefficient of a circular cylinder as a function of the Reynolds number, where the water flow meets the top (the flat part) of the cylinder?

Secondly, I understand that the Reynolds number is calculated accordingly;
R=V*L/μ
where V is velocity, L is a lenght scale, and μ is dynamic viscosity divided by the density.
Would L euqal the radius in my scenario?

Furthermore, from what I can gather, the relationship between the Reynolds number and the drag coefficient can only be confirmed experimentally, and therefore, I have no way of finding a solution analytically.

Thank you for considering this problem
The fluid mechanics equations can be solved numerically if the flow is laminar (i.e., low Reynolds number).
If the cylinder is very long, and the relative flow is parallel to the cylinder axis, then the drag caused by the leading edge will be negligible. There is probably a boundary layer solution for the laminar flow in this situation. Look up the drag on torpedoes. Certainly, this has been measured and also analyzed in great detail by researchers in the navy.

Chet