Find the centroid (centre of mass when the surface density is
constant) of the frustum of the circular cone
Find the total flux that passes through the hemisphere
the surface projection method and
What can you say about the relative orientation of the vector field D and the normal N to the hemisphere?
Find the total flux of the vector field
through that part of the
circular paraboloid
A thin sheet, in the shape of the paraboloid
Fluid is flowing along a cylindrical pipe. The circular
cross section inside the pipe has a constant radius of
a (m).
The Cartesian coordinate system is aligned with the x axis
along the line of symmetry (centre line) of the pipe. The other
two axes are in the plane of one of the circular cross sections.
The velocity of fluid at any point
Find the flux Q (in m3/s) (the
rate at which fluid is flowing through the pipe).
Complete the evaluation (in Example 2.6.3 of the lecture notes) of the line integral around the unit square in the x-z plane for , (without using Stokes’ theorem).
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