How Do You Calculate Linear Drag Coefficient for Spherical Objects in Flight?

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SUMMARY

This discussion focuses on calculating the linear drag coefficient (b) for spherical objects, specifically at velocities around 5 m/s. The user highlights the distinction between linear drag coefficients and traditional drag coefficients (C_d), emphasizing that they possess different units. Bernard suggests using the formula b=6πμR, where μ is the dynamic viscosity of air, and provides links to tables of linear drag coefficients relevant for Stokes flow conditions. The conversation clarifies that at 5 m/s, linear drag is not applicable, but offers resources for those interested in the topic.

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  • Understanding of fluid dynamics principles
  • Familiarity with drag force equations
  • Knowledge of Stokes flow conditions
  • Basic physics of spherical objects in motion
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  • Research the formula for calculating linear drag coefficients in fluid dynamics
  • Explore the relationship between dynamic viscosity and drag force
  • Study the implications of Reynolds number on drag coefficients
  • Examine experimental methods for measuring drag coefficients of small spheres
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I'm trying to model the flight of a small spherical object (such as a ping-pong ball) through air at smallish velocities (\approx 5{_{m/s}}) with linear drag so that F_{d}=-bv. The problem is, I can't find a table of linear drag coefficients (b) anywhere; it's always just the normal drag coefficient C_{d} which is for when the drag force is proportional to v^2. I don't think you can just use C_{d}=b since they have different units.

However, I came across this, which I think is saying that b=6\pi \mu R, which would be good since I could look up \mu from say, here. Does that seem like a good idea?
 
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Well, 5m/s is not a speed at which a linear drag occurs.
To be sure of it, see that general curve :
https://commons.wikimedia.org/wiki/File:CX_SPHERE.png

But if you really wanted (I'm afraid it's too late) to calculate the flight of a sphere with a linear drag, I published recently these two tables of linear drag coefficients :
https://commons.wikimedia.org/wiki/...e_quelques_particules_en_Régime_de_Stokes.png
https://commons.wikimedia.org/wiki/File:Tableau_cx_lineaires_deuxieme.png

Friendly, Bernard of Go Mars
 

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