A fluid with viscosity fills space between two long co -axial cylinders o radii R1 and R2 , with R1 < R2. The inner cylinder is stationary while the outer is rotated with angular velocity 2.The fluid flow is laminar.Taking into account that the friction friction force acting on a unit area of a cylindrical surface of radius r is defined by the formula =( /r ).Find angular velocity of the rotating fluid as a function of radius r.
I am not sure how you define your frictional force per unit area (Its not dimensionally correct) But still if i take it as such (which i should not) my solution will be following Consider a small cylendrical shell at of inner and outer radius r and r+dr. Inner Net force on this should be zero So L*2*pi[r( /r)(at r+dr)-r( /r)(at r)] therefore /r(r/r) = 0 So r/r=A (where A is a constant of integration) /r=A/r so = Aln(r) + B Use boundry condition that omega at R1 = 0 and at R2 = omega2 and you will get the answer.
Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi
Moderation Team
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fills space between two long co -axial cylinders o radii R1 and R2 , with R1 < R2. The inner cylinder is stationary while the outer is rotated with angular velocity 
2.The fluid flow is laminar.Taking into account that the friction friction force acting on a unit area of a cylindrical surface of radius r is defined by the formula 
=( 
1
/
