1. Consider a liquid placed between two infinite planar plates. The plates are oriented perpendicular to...

Transcribed Image Text:

1. Consider a liquid placed between two infinite planar plates. The plates are oriented perpendicular to the gravitational acceleration g and the liquid is at rest. At t = 0, one plate at z = 0 is suddenly moved in the x direction with the constant speed U, while the top plate at z = d is kept fixed in the laboratory. a) Simplify Navier-Stokes equation for this system and obtain boundary and initial conditions. (10)+ b) What are characteristic velocity and length? Non-dimensionalize the governing equation and obtain characteristic time. What is new boundary and initial conditions? Are the conditions are homogeneous? (10) c) Obtain steady-state solution for velocity profile. (10)+ d) Define transient solution as difference of unsteady velocity profile from steady-state velocity profile and obtain new equation and conditions. Are the conditions are homogeneous? (10) e) Solve the equation with conditions and obtain the equation for unsteady velocity profile. (15) f) For water in two plates with separation of 1 cm and pulling velocity U= 1 cm/s, plot the profiles at five different times (select the times which show different profiles from each other). (15) 1. Consider a liquid placed between two infinite planar plates. The plates are oriented perpendicular to the gravitational acceleration g and the liquid is at rest. At t = 0, one plate at z = 0 is suddenly moved in the x direction with the constant speed U, while the top plate at z = d is kept fixed in the laboratory. a) Simplify Navier-Stokes equation for this system and obtain boundary and initial conditions. (10)+ b) What are characteristic velocity and length? Non-dimensionalize the governing equation and obtain characteristic time. What is new boundary and initial conditions? Are the conditions are homogeneous? (10) c) Obtain steady-state solution for velocity profile. (10)+ d) Define transient solution as difference of unsteady velocity profile from steady-state velocity profile and obtain new equation and conditions. Are the conditions are homogeneous? (10) e) Solve the equation with conditions and obtain the equation for unsteady velocity profile. (15) f) For water in two plates with separation of 1 cm and pulling velocity U= 1 cm/s, plot the profiles at five different times (select the times which show different profiles from each other). (15)

Answer rating: 100% (QA)

a The NavierStokes equation for this 2D system is ut uux vuz 1 Px 2ux2 2uz2 vt uvx vvz 1 Pz 2vx2 2v... View the full answer