3. Consider the stratified fluid depicted below which is being sheared between two infinite parallel plates....

 

Transcribed Image Text:

3. Consider the stratified fluid depicted below which is being sheared between two infinite parallel plates. If the upper plate is constrained to move with velocity U, the lower plate is fixed, and the viscosities and thicknesses of the two layers are and and h and h, respectively, calculate the following: H U h h a. Write down the Navier Stokes equation for momentum in the direction of the flow in each region and show which terms are non-zero. b. What are the velocity and shear stress distributions? What is the force on the lower plate? Hint: Remember that both the velocity and shear stress much be continuous across the interface formed between the two liquids. This determines the conditions at the interface. 3. Consider the stratified fluid depicted below which is being sheared between two infinite parallel plates. If the upper plate is constrained to move with velocity U, the lower plate is fixed, and the viscosities and thicknesses of the two layers are and and h and h, respectively, calculate the following: H U h h a. Write down the Navier Stokes equation for momentum in the direction of the flow in each region and show which terms are non-zero. b. What are the velocity and shear stress distributions? What is the force on the lower plate? Hint: Remember that both the velocity and shear stress much be continuous across the interface formed between the two liquids. This determines the conditions at the interface.