Stokes' Law: Why does viscous drag depend upon the radius of the spherical body?

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SUMMARY

Stokes' Law quantitatively describes the viscous force acting on a spherical body moving through a fluid, expressed as Fviscous = 6πηav, where 'a' represents the radius of the sphere and 'v' is its velocity. The discussion emphasizes that the viscous drag increases with the radius due to the larger surface area in contact with the fluid, which results in a greater reaction force from the fluid. This principle is illustrated through the analogy of "big trees catch a lot of wind," highlighting the relationship between surface area and fluid dynamics.

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  • Basic knowledge of viscosity and its effects on motion
  • Concept of drag force in physics
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Kaushik
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Stokes' Law gives us the value fo viscous force when a spherical body is under motion inside a fluid.
##F_{viscous} = 6\pi\eta av## (where ##a## is the radius of the spherical body and ##v## is the velocity with which it is moving)
What is the reason for the Viscous drag to depend upon the radius of the spherical body?
 
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The more area, the more grip !
 
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BvU said:
The more area, the more grip !
Is it like, more the area, more fluid in contact. Hence, it pulls more fluid with it, consequently the reaction force by the fluid on the body is more?
 
Yep !
Dutch expression: "big trees catch a lot of wind" :smile:
 
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WORK DONE on the fluid the sphere is moving through depends on area.
 

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