Question

Which of these formulae is used to calculate the centroid of a polyhedron?

(a) \(\sum_{n=1}^{No. \, of \,pyramids}Centroid_n×Volume_n\)

(b) \(\frac{\sum_{n=1}^{No.  \,of \,pyramids}Centroid_n×Volume_n}{\sum_{n=1}^{No. \, of \,pyramids}Volume_n}\)

(c) \(\frac{\sum_{n=1}^{No.  \,of\, pyramids}Centroid_n×Volume_n}{Volume_n} \)

(d) \(\frac{\sum_{n=1}^{No.  \,of \,pyramids}Centroid_n×Volume_n}{Centroid_n} \)

I had been asked this question during a job interview.

My query is from Types of FVM Elements topic in portion Finite Volume Methods of Computational Fluid Dynamics

Answer 1

The correct answer is:

(b) ∑No.ofpyramidsn=1Centroidn×Volumen / ∑No.ofpyramidsn=1Volumen

This formula is used to calculate the centroid of a polyhedron by considering it as a collection of simpler sub-volumes, like pyramids. The centroid of the entire polyhedron is the weighted average of the centroids of the sub-volumes, weighted by their respective volumes.