Question

what is stokes law? Derive the relation by the method of dimensiosns​

Answer 1

Answer:

Law define

Stokes' Law. ... He found what has become known as Stokes' Law: the drag force F on a sphere of radius a moving through a fluid of viscosity η at speed v is given by: F=6πaηv. Note that this drag force is directly proportional to the radius.....

derivation

Dimensional analysis proof of Stokes' Law

Suppose that the sphere has radius r and falls through a fluid of viscosity η. Let the terminal velocity be v (Figure 1).

We can calculate the viscous drag F on the sphere by dimensional analysis.

If

F = krxηyvz

We have MLT-2 = Lx(ML-1T-1)y(LT- 1)z

Solving this gives x = 1, y = 1 and z = 1.

By other methods k can be shown to be 6π.

Thus giving:

F = 6πηrv

Answer 2

Answer:

Stokes law defines the force required to move a sphere through a given viscous fluid at a low uniform velocity is directly proportional to the velocity and radius of the sphere.

Now, assume that the sphere has radius r which falls through a fluid of viscosity η.

Let, the terminal velocity be v. We can calculate the viscous F on the sphere by dimensional analysis.

Solving this ,

we obtain,

x = 1, y = 1 and z = 1.

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