Module 17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications
Lecture 50 : Application of surface integrals [Section 50.2]
50.2 Applications of surface integrals :
50.2.1 Mass and center of mass of a surface.
 

Consider a surface of density (mass per unit area) . Then the mass of can be defined to be

The moments of about the three axes planes is defined by

Further the point is called the center of mass of , where


50.2.2 Flux of a fluid across a surface
  Let represent the velocity field of a fluid flow in space at a point . Let be its density at . Then
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