Motion of a Newtonian liquid between two coaxial cylinders

4 Motion of a Newtonian liquid between two coaxial cylinders 

These are, very closely, the values for the light particles placed in the liquid. In a short time 8t ihe particle on streamline p moves from P to S and that on streamline q moves from Q to R, where  

The shear of the liquid that occurs in the small time interval St is 

Consider now a cylindrical shell of liquid lying between radii r and r + dr and extending the length L of the coaxial cylinders. The condition for the steady state is that the accelerating moment or torque on the outer surface of each such elementary shell of liquid is equal and opposite to that on the inner surface. Then the moment or torque T must be constant for all values of r. 

Using the defining equation for Newtonian viscosity, equation [4.6], gives for the viscous force F acting over the surface of radius r  

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