p0282 - 2.82. CHAPTER 2, PROBLEM 82 277 2.82 Chapter 2,...

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

View Full Document Right Arrow Icon
2.82. CHAPTER 2, PROBLEM 82 277 2.82 Chapter 2, Problem 82 Problem: The time τ required to drain all of the fluid through a hole of diameter d in the bottom of a tank is a function of initial fluid depth, h o , initial fluid volume, V o , gravitational acceleration, g , and fluid kinematic viscosity, ν . How many dimensionless groupings are there? Determine the dimensionless groupings. Solution: The dimensional quantities and their dimensions are [ τ ]= T, [ d L, [ h o L, [ V o L 3 , [ g L T 2 , [ ν L 2 T There are 6 dimensional quantities and 2 independent dimensions ( L, T ) ,sot h a tth e number of dimensionless groupings is 4. The appropriate dimensional equation is [ τ ]=[ d ] a 1 [ h o ] a 2 [ V o ] a 3 [ g ] a 4 [ ν ] a 5 Substituting the dimensions for each quantity yields T = L a 1 L a 2 L 3 a 3 L a 4 T 2 a 4 L 2 a 5 T a 5 = L a 1 + a 2 +3 a 3 + a 4 +2 a 5 T 2 a 4 a 5 Thus, equating exponents, we arrive at the following two equations. 0= a 1 + a 2 +3 a 3 + a 4 +2 a 5 1= 2 a 4 a 5 We can solve immediately for a 4 from the second equation, viz., a 4 = 1 2 1 2 a 5 Using this value for a 4 in the first equation shows that a 1 + a 2 a 3 1 2 1 2 a 5 a 5 = a 1 = 1 2 a 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
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 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

Page1 / 2

p0282 - 2.82. CHAPTER 2, PROBLEM 82 277 2.82 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