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

In summary, Stokes' Law states that the viscous force acting on a spherical body in motion in a fluid is equal to 6πηav, where a is the radius of the body and v is its velocity. This is because the larger the surface area of the body, the more fluid it comes into contact with, resulting in a stronger reaction force from the fluid. This can be seen in the Dutch expression "big trees catch a lot of wind", meaning that larger objects experience more resistance. Additionally, the work done on the fluid by the moving sphere is also dependent on its surface area.
  • #1
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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  • #2
The more area, the more grip !
 
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  • #3
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?
 
  • #4
Yep !
Dutch expression: "big trees catch a lot of wind" :smile:
 
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  • #5
WORK DONE on the fluid the sphere is moving through depends on area.
 

1. What is Stokes' Law?

Stokes' Law is a mathematical equation that describes the relationship between the viscous drag force on a spherical object and its radius, velocity, and viscosity of the fluid it is moving through.

2. Why does viscous drag depend on the radius of the spherical body?

The larger the radius of the spherical body, the larger the surface area that is in contact with the fluid. This results in a larger surface for the fluid to exert a drag force on, leading to a higher viscous drag.

3. How does the velocity of the spherical body affect the viscous drag?

The faster the spherical body moves through the fluid, the greater the viscous drag will be. This is because a higher velocity results in a larger disturbance of the fluid molecules, leading to a higher resistance and thus a higher drag force.

4. What role does the viscosity of the fluid play in Stokes' Law?

The viscosity of the fluid determines how easily the fluid molecules can flow past each other. A higher viscosity means the fluid is more resistant to flow, resulting in a higher viscous drag force on the spherical body.

5. How is Stokes' Law used in real-world applications?

Stokes' Law is commonly used in industries such as chemical engineering, environmental engineering, and fluid mechanics to calculate the drag force on particles in a fluid. It is also used in the study of sedimentation, where it helps predict the settling velocity of particles in a fluid.

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