Explanation Given Information: The pressure difference is a function of soap bubble radius R and surface tension of sop film σ s Δ P = f ( R , σ s ) Concept used: Buckingham Pi theorem Method of repeating variable force-based system of primary dimension. Calculation: No. Of parameters, A = 3 They are, pressure difference, Δ P = P i n s i d e − P o u t s i d e Radius = R Surface tension = σ s Hence, Δ P = f ( R , σ s ) The primary dimension of each parameter, Pressure difference, { Δ P } = { f o r c e a r e a } = { F A } = { F L 2 } { Δ P } = { F 1 L − 2 } Radius, { R } = { L } Surface Tension, { σ s } = { f o r c e l e n g t h } = { F L } = { F L − 1 } No. Of primary dimension, j=2 (F,L) Hence we have to select two repeating parameters. According of Pi's,k=n-j=3-2=1 Considering R and σ s as repeating parameters Now, combining repeating parameters with remaining parameters to produce π Hence, dependant π , ( π 1 ) = Δ P R a 1 σ s b 1 Primary dimensions of above terms, { π 1 } = { f 0 L 0 } { Δ P R a 1

Fluid Mechanics Fundamentals And Applications

3rd Edition

ISBN: 9780073380322

Author: Yunus Cengel, John Cimbala

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 7, Problem 118P

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Chapter 7, Problem 117P

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Fluid Mechanics Fundamentals And Applications

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The dimensional analysis of pressure difference using force based system of repeating variables and to analyze whether we get the same results

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