Consider steady, axisymmetric flow of an incompressible liquid in the gap between two horizontal disks of...

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Consider steady, axisymmetric flow of an incompressible liquid in the gap between two horizontal disks of radius R, as shown in Figure 1. The liquid is injected at a constant volumetric flow rate Q through small inlets at the center of each disk and flows radially outward. The liquid pressure (p) varies along the r- direction. It is assumed that the flow is only in the radial direction (i.e. Ue = 0 = uz). The inlet radius (R.) and disk spacing (2H) are such that R/H << 1 and H/R << 1. The liquid density is p. 1- Briefly explain why the average radial velocity (u,) changes in the r direction. 2- The viscosity (7) of the liquid can be described by a power-law model as follows. 7 = Kÿ"-1 %3D where K is the consistency index; n is the power-law index; Y is the magnitude of the strain-rate tensor. Write out the nine components of the strain-rate tensor (Y), and then use these components to write out the nine components of the viscous stress tensor (T) for this power-law fluid at a given point in the flow between the disks. Explain why each component of the strain-rate tensor and the viscous stress tensor is zero or non-zero. Consider steady, axisymmetric flow of an incompressible liquid in the gap between two horizontal disks of radius R, as shown in Figure 1. The liquid is injected at a constant volumetric flow rate Q through small inlets at the center of each disk and flows radially outward. The liquid pressure (p) varies along the r- direction. It is assumed that the flow is only in the radial direction (i.e. Ue = 0 = uz). The inlet radius (R.) and disk spacing (2H) are such that R/H << 1 and H/R << 1. The liquid density is p. 1- Briefly explain why the average radial velocity (u,) changes in the r direction. 2- The viscosity (7) of the liquid can be described by a power-law model as follows. 7 = Kÿ"-1 %3D where K is the consistency index; n is the power-law index; Y is the magnitude of the strain-rate tensor. Write out the nine components of the strain-rate tensor (Y), and then use these components to write out the nine components of the viscous stress tensor (T) for this power-law fluid at a given point in the flow between the disks. Explain why each component of the strain-rate tensor and the viscous stress tensor is zero or non-zero.

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