Drag force on a sphere moving through a fluid

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SUMMARY

The drag force experienced by a sphere moving through a fluid is defined by the equation F = kp (R^2) (v^2), where F is the drag force, k is a constant, R is the radius of the sphere, p is the fluid density, and v is the velocity of the sphere. This relationship indicates that the drag force is directly proportional to the square of the velocity and the square of the radius. For accurate calculations of drag force in practical scenarios, simulations are often utilized due to the complexity of real-world fluid dynamics.

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A body moves through a fluid, a retarding force due to turbulence may be experienced. In case of a sphere of radius R moving with speed v through a stationary fluid of density p which it at rest, this force is given by
F = kp (R^2) (v^2)
k
is a constant.
Why F is proportional to kp (R^2) (v^2) ?
 
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Google for "drag force calculation" and you'll find many good derivations. In practice, with real objects moving through real fluids, the calculations are hairy enough that we often resort to simulations.
 

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