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derive stokes law by densional analysis

Answer»

Suppose a spherical body of radius r moves at speed v through a fluid of viscosityƞ,viscous force F acting on the body depends on r,v andƞ.According to the dimensional analysis we can write,

Let F =kravbƞ​c

Where k is the dimensional less constant.

MLT-2=kLa(LT-1)b(ML-1T-1)c

On equating the coefficients of M,L,T on both sides we get :a,b,c each = 1hence F =krvƞ,value of k =6π,hence stokes law becomes,

F =6πƞrv

This is the required stokes law



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