Let S be the portion of the paraboloid z = 1 x - y in x...

 

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Let S be the portion of the paraboloid z = 1 x - y in x + y < 1 oriented by upwards unit normals with a fluid flow F (x, y, z) = xi+yj+zk. (a). By using surface integral, determine the fluid flowing through surface S. (12 marks) (b). By using Divergence Theorem, find the net volume of fluid that crosses the surface S in the direction of orientation in one unit of time. (c). Compare your answers in (a) and (b). Justify your comparison. (9 marks) (2 marks) (d). If there is a change in the direction of unit normals, how would it effects the flow rate of the fluid through surface S? (2 marks) Let S be the portion of the paraboloid z = 1 x - y in x + y < 1 oriented by upwards unit normals with a fluid flow F (x, y, z) = xi+yj+zk. (a). By using surface integral, determine the fluid flowing through surface S. (12 marks) (b). By using Divergence Theorem, find the net volume of fluid that crosses the surface S in the direction of orientation in one unit of time. (c). Compare your answers in (a) and (b). Justify your comparison. (9 marks) (2 marks) (d). If there is a change in the direction of unit normals, how would it effects the flow rate of the fluid through surface S? (2 marks)

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a To determine the fluid flowing through surface S we need to calculate the surface integral ffs F n... View the full answer