C. Fluids, rolling down on an inclined plane ( 30 points) The velocity profile of a fluid flowing down an inclined plane is described by equation 1: Eq.1. is the density of the fluid (you can assume: 1000kg/m3 ) g is the gravitational acceleration (you can assume earth: 10 m/s2) is the dynamic viscosity of the fluid (you can assume: 9104 Pa.s) h is the height of the fluid (you can assume 1mm ) is the angle of the inclination of the plane (you can assume 45 degrees) Hint-1: Sketch a diagram of the system and clearly label the key parameters (h,g,)and the frame of reference x and y. C.1. Develop an equation describing the shear stress inside the fluid as a function of the coordinate y and the parameters. (Hint-2: think about the definition of shear stress) C.2. Check the units of the shear stress given your equation. (If it is not the correct unit, you may have made a mistake) C.3. What is the value of the shear stress given the above numbers. C.4. What happens to u(y) if is changed from 45 degrees to 0 degrees? C.5. What happens to the shear stress (assume =45 ), if water is replaced by KRAFT Smooth Peanut Butter (=1.2105 Pa.s ) no need to calculate, just explain