521 ADV FLUID MECH II Winter 2003Hwk 2 (Due Tu Feb 11)1. Find the fundamental matrix gpq for a two dimensional homogeneous coordinate system qi where the new coordinate system has the horizontal axis rotated by angle a but the vertical axis is left alone.2. Find the fundamental metric of a polar coordinate surface.
3. Prove the corollary to the Reynolds transport theorem
4. Find the principle stresses and axes for simple shear flow, where the velocity in the x-direction u = ky, where k is a constant.
5. Show if dissipation is positive that m>0 and l+2/3 m>0. (Hint: use principle axes)