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Consider the physical quantities f, g, h, i and j with dimensions: [S] = M² [g] = [h] = MLT-2 [i] = L-3 МI-3 G] = L?T? We would like to use Buckingham's theorem to determine an expression for g in terms of f, h, i and j. Finding dimensionless products of the form fªg°h°idje leads to three equations, one of which is: 0 =a- a +b+ By choosing b and c as arbitrary variables, it can be shown that one of the dimensionless products produced is: hi/f hi What is the exponent of g in the other dimensionless product (to what power is g raised?)

Consider the physical quantities f, g, h, i and j with dimensions: [S] = M² [g] = [h] = MLT-2 [i] = L-3 МI-3 G] = L?T? We would like to use Buckingham's theorem to determine an expression for g in terms of f, h, i and j. Finding dimensionless products of the form fªg°h°idje leads to three equations, one of which is: 0 =a- a +b+ By choosing b and c as arbitrary variables, it can be shown that one of the dimensionless products produced is: hi/f hi What is the exponent of g in the other dimensionless product (to what power is g raised?)

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 1.6CYU: Check Your Understanding Is the equation v=atdimensionally consistent? One further point thin needs...
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Consider the physical quantities f, g. h, i and j with dimensions: [f] = M² (g] = ML-3 [h] = MLT-2 [i] = L-3 [j] = L?T² We would like to use Buckingham's theorem to determine an expression for g in terms of f, h, i and j. Finding dimensionless products of the form fa g'h°id je leads to three equations, one of which is: a + b+ By choosing b and c as arbitrary variables, it can be shown that one of the dimensionless products produced is: hivf hi hij What is the exponent of g in the other dimensionless product (to what power is g raised?)
Transcribed Image Text:Consider the physical quantities f, g. h, i and j with dimensions: [f] = M² (g] = ML-3 [h] = MLT-2 [i] = L-3 [j] = L?T² We would like to use Buckingham's theorem to determine an expression for g in terms of f, h, i and j. Finding dimensionless products of the form fa g'h°id je leads to three equations, one of which is: a + b+ By choosing b and c as arbitrary variables, it can be shown that one of the dimensionless products produced is: hivf hi hij What is the exponent of g in the other dimensionless product (to what power is g raised?)
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