Question

Derive Stokes' law by dimensional analysis.

Answer 1

The validity of Stokes law can be checked using dimensional analysis.  

Suppose a spherical body falling through a stationary fluid.

As one can predict the drag force on the body depends on the viscosity of the fluid , radius of the object  r and velocity of the object V

Hence it can be written that  

F=f(μ,r,v)

F = kμ^x,r^y ,V^z

Writing down the dimensions of all the physical quantities,

We have MLT^−2 =L^x (ML^−1 T^−1 )^y (LT^−1 )^z

 

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

K can be found experimentally as 6

Hence F=6πμrV

Answer 2

Answer:

Stokes' law by dimensional analysis

Explanation:

Consider a spherical body that falls through a stationary fluid.

As one can predict the drag force on the body depends on the viscosity of the fluid, the radius of the object r, and the velocity of the object V.

Hence it can be written that

F = f(μ, r, v)

F = μ $k^{x}$, $r^{y}$, $V^{z}$

Let, the dimensions of all the physical quantities,

We have

$MLT^{-2} =L^x (ML^{-1} T^{-1} )^y (LT^{-1} )^z$

Solving the above equation, we get

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

Hence, $k$ can be found experimentally as $6$.

Therefore, the value F = 6πμrV.

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