Consider a propeller spinning in air. The thrust produced by the propeller is given by T. The density of the air is p. The forward velocity of the air is V. The diameter of the propeller is D. The rotational velocity of the propeller is n. The dynamic viscosity of the air is u. Using Buckingham's pi theorem, find the non-dimensional formulation of T = f (p, V, D, n, µ). Note that the non-dimensional quantities are not sensitive to multiplicative inverses, i.e. and 2 have the same meaning, as does multiplication by a constant, for example, and 2 imply the same non-dimensional group. T pVD V nD T f( PµD pV V nD T pV VD nD =5( T pnD pD V O O

Consider a propeller spinning in air. The thrust produced by the propeller is given by T. The density of the air is p. The forward velocity of the air is V. The diameter of the propeller is D. The rotational velocity of the propeller is n. The dynamic viscosity of the air is u. Using Buckingham's pi theorem, find the non-dimensional formulation of T = f (p, V, D, n, µ). Note that the non-dimensional quantities are not sensitive to multiplicative inverses, i.e. and 2 have the same meaning, as does multiplication by a constant, for example, and 2 imply the same non-dimensional group. T pVD V nD T f( PµD pV V nD T pV VD nD =5( T pnD pD V O O

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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