A journal bearing has a shaft diameter of $$40$$ $$mm$$ and a length of $$40mm.$$ The shaft is rotating at $$20$$ $$rad/s$$ and the viscosity of the lubricant is $$20$$ $$mPa$$-$$s$$. The clearance is $$0.020$$ $$mm.$$ The loss of torque due to the viscosity of the lubricant is approximately:

A cubic block of side $$'L'$$ and mass $$'M'$$ is dragged over an oil film across table by a string connects to a hanging block of mass $$'m'$$ as shown is fig. The Newtonian oil film of thickness $$'h'$$ has dynamic viscosity $$'\mu '$$ and the flow condition is laminar. The acceleration due to gravity is $$'g'.$$ The steady state velocity $$'v'$$ of block is :

For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, $$\overrightarrow V $$ where is the velocity vector, which one of the folllowing is a necessary condition ?

The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate comes down at a uniform speed $$V$$ towards the stationary bottom surface, as shown in the figure. In the process, the fluid contained between the two plates flows out radially. The fluid is assumed to be incompressible and inviscid.

The radial component of the fluid acceleration at $$r=R$$ is