(a) Find the rate of flow upwards through the paraboloid z = 9- -1(x + y)...

  

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(a) Find the rate of flow upwards through the paraboloid z = 9- -1(x + y) where x + y <36 if a fluid with density, p = 3200 flows with velocity field given as v(x, y, z) = yi+j+zk. (Hints: Rate of flow=ff F.nds where F = pv). (12 marks) (b) Use Stokes' Theorem to evaluate ff, curlF n dS, where F(x, y, z) = xyzi + yzj+zek and S is the part of the sphere x + y + 2 = 5 in the first octant that lies above the plane z = 1 and S is oriented upward. (a) Find the rate of flow upwards through the paraboloid z = 9- -1(x + y) where x + y <36 if a fluid with density, p = 3200 flows with velocity field given as v(x, y, z) = yi+j+zk. (Hints: Rate of flow=ff F.nds where F = pv). (12 marks) (b) Use Stokes' Theorem to evaluate ff, curlF n dS, where F(x, y, z) = xyzi + yzj+zek and S is the part of the sphere x + y + 2 = 5 in the first octant that lies above the plane z = 1 and S is oriented upward.