transport phenomena

1. Parallel disk viscometer : ( 100 points) A fluid, whose viscosity is to be measured, is placed in the gap of thickness B between the two disks of radius R. (a) What is the frame of reference for this problem. What coordinate system would you use. ( 5 point) (b) What velocity components are present. What variables do that velocity and pressure depend on. (c) Write out the equations of continuity and simplify for the problem (10 points) (d) Write out the three equations of motion for this system (10 points) (e) What is the velocity profile obtained from integrating ( 10 points) (f) What boundary conditions are pertinent for this system. How does the velocity profile look after applying boundary conditions (10 points) (g) Determine the pressure profile. ( 10 points) (h) Calculate the shear stress on the top surface ( 10 points) (i) If the total shear stress is resisted by the torque T, can you rewrite the expression to find the viscosity of the fluid between the two plates. Disk at z=B rotates Fluid with viscosit with angular and density is velocity held in place by surface tension Disk at z=0 is fixed Both disks have radius R and R>B Fig. 3B.5. Parallel-disk viscometer