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

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.5P: Evaluate the dimensionless groups hcD/k,UD/, and cp/k for water, n-butyl alcohol, mercury, hydrogen,...

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