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Properties-of-fluid

A lubricating oil of viscosity `mu` undergoes steady shear between a fixed lower plate and an upper plate moving at speed V. The clearance between plate is h. Show that linear velocity profile results if fluid doesn't slip at eir place.

SOLUTION:

For the given geometry and motion, the shear stress `tau` is constant throughout. 

Now, from Newton's law of viscosity, We have,

`tau=mu*(du)/(dy)`, where shear stress is constant.

or, `(du)/(dy)=tau/mu=Constant`

or, `u=a+by`

The constant a and b are evaluated from no slip conditions at the upper and the lower plates.

So, at y=0, u=0

Thus, a=0

Also,

At y=h, u=V,

`V=a+bh`

or,`V=0+bh`

or, `b=V/h`

A lubricating oil of viscosity `mu` undergoes steady shear between a fixed lower plate and an upper plate moving at speed V. The clearance between the plate is h. Show that the linear velocity profile results if the fluid doesn\'t slip at either place.

Thus, the velocity profile between the  plates is ....Show More

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A lubricating oil of viscosity `mu` undergoes steady shear between a fixed lower plate and an upper plate moving at speed V. The clearance between the plate is h. Show that the linear velocity profile results if the fluid doesn't slip at either place.

Properties of fluid

Fluid-Mechanics