(Solved): Water density =1000kg/m3, water viscosity =0.001kg/m.s, Oil density =830kg/m3, Oil vis ...

Water density $$?=1000\mathrm{kg}/{\mathrm{m}}^3$$, water viscosity $$?=0.001\mathrm{kg}/\mathrm{m}.\mathrm{s}$$, Oil density $$?=830\mathrm{kg}/{\mathrm{m}}^3$$, Oil viseosity $$?=0.1\mathrm{kg}/\mathrm{m}.\mathrm{s}$$, Gravitation acecleration $$g=9.8\mathrm{m}/{\mathrm{s}}^2$$, mercury density $$=13,600\mathrm{kg}/{\mathrm{m}}^3$$ Prob. 1 (40 points). There is an oil film in the clearance between a solid cone and base $$\mathrm{R}=0.04\mathrm{m}$$. The cone is rotating inside its seat with angular velocity $$0=3\mathrm{rad}/\mathrm{s}$$. Neglect air drag. Cone angle $$?=2=0.035\mathrm{rad}$$. Find: (1) Clearance h (gap under shear deformation) at $$=0.03\mathrm{m}$$ ( 10 points). (2) Shear rate ( $$/\mathrm{s}$$ ) in the clearance at $$\mathrm{r}=0.03\mathrm{m}$$ ( 10 points). (3) Shear stress ( $$\mathrm{Pa})$$ in the clearance at $$r=0.03\mathrm{m}$$ (10 points) (a) Toraue $$(\mathrm{N}.\mathrm{m})$$ applied in the cone due to shear stress $$(10\mathrm{px}$$.