Why does the drag force increase with velocity and viscosity?

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SUMMARY

The drag force is directly proportional to the velocity raised to a power, n, which increases with both velocity and the viscosity of the medium. This increase in n is attributed to the rise in turbulence as velocity increases. The relationship between drag coefficient and Reynolds number is crucial, as it illustrates how drag varies with velocity. In many scenarios, the drag force can be approximated as F ~ v^2 or F ~ v, depending on the flow conditions.

PREREQUISITES
  • Understanding of drag force and its dependence on velocity
  • Familiarity with turbulence and its effects on fluid dynamics
  • Knowledge of Reynolds number and its significance in fluid mechanics
  • Basic mathematical skills for interpreting power laws and coefficients
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  • Research the relationship between drag coefficient and Reynolds number in fluid dynamics
  • Explore turbulence models and their impact on drag force calculations
  • Study the mathematical derivation of drag force equations in various flow regimes
  • Examine experimental data and plots related to drag force and velocity
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This discussion is beneficial for students and professionals in physics, engineering, and fluid dynamics, particularly those interested in understanding the principles of drag force and turbulence in various mediums.

TMM
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I know that the drag force is proportional to the velocity to some power, n, and that n increases with velocity and with the viscosity of the medium.

I want to know why n increases, and how (mathematically) it increases. Some general speed ranges for v and v^2 in STP would be appreciated as well.
 
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n increases because turbulence increases.
The drag is so shape dependent, that I don't if there are formulas for n.
The fact that n depends on v means that n is really meaningless,
and is just used to make problems tractable
 
This sort of thing is usually discussed by specifying how the drag coefficient varies with Reynolds number (which depends on velocity). You should find some nice plots if you search for those terms. Although these can be complicated, there are large regions where the drag coefficient remains approximately constant (F ~ v^2) or goes like 1/R (so F ~ v).
 
Alright, I looked up some things on Reynolds number as you suggested.

Thanks for the info.
 

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