p0230 - 2.30 CHAPTER 2 PROBLEM 30 143 2.30 Chapter 2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
2.30. CHAPTER 2, PROBLEM 30 143 2.30 Chapter 2, Problem 30 Figure 2.4 shows the geometry of the liquid-air interface. c σ ρ λ . . . ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... . . . . . . . . . . . . . . .... . . . . . . . . . . ......................................... . . . . . . . . . . . Figure 2.4: Geometry of a ripple. The dimensional quantities and their dimensions are [ σ ]= F L = MLT 2 L = M T 2 [ ρ M L 3 , [ c L T , [ λ L There are 4 dimensional quantities and 3 independent dimensions ( M,L,T ) , so that the number of dimensionless groupings is 1. The appropriate dimensional equation is [ c ]=[ ρ ] a 1 [ σ ] a 2 [ λ ] a 3 Substituting the dimensions for each quantity yields LT 1 = M a 1 L 3 a 1 M a 2 T 2 a 2 L a 3 = M a 1 + a 2 L 3 a 1 + a 3 T 2 a 2 Thus, equating exponents, we arrive at the following three equations: 0= a 1 + a 2 1= 3 a 1 + a 3 2 a 2 We can solve the first and third equations immediately for a 1 and a 2 ,v iz . , a 1 = 1 / 2 and a 2 =1 / 2 Substituting into the second equation, we find 3 / 2+ a 3 = a 3 = 1 / 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
144 CHAPTER 2. DIMENSIONAL ANALYSIS Substituting back into the dimensional equation, we have
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/12/2009 for the course AME 309 at USC.

Page1 / 2

p0230 - 2.30 CHAPTER 2 PROBLEM 30 143 2.30 Chapter 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online