p0178 - 1.78. CHAPTER 1, PROBLEM 78 83 1.78 Chapter 1,...

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1.78. CHAPTER 1, PROBLEM 78 83 1.78 Chapter 1, Problem 78 Problem: The viscosity of water can be approximated by Andrade’s equation ,v iz . , μ = μ r e T r /T ,whe re μ r and T r are empirical viscosity and temperature scales, respec- tively, and T is absolute temperature. (a) Using values from Tables A.3 and A.7 for T =10 o Cand T =90 o C, determine μ r and T r . (b) Using the values of μ r and T r determined in Part (a), make a graph comparing the tabulated values of μ with Andrade’s equation for 0 o C T 100 o C . Solution: (a) For water, the text tables give ρ and ν . Values of μ are thus given by μ = ρν .Hence , μ (10 o C) = (1000 kg / m 3 )(1 . 31 · 10 6 m 2 / sec) = 1 . 31 · 10 3 kg / (m · sec) and μ (90 o C) = (965 kg / m 3 )(0 . 33 · 10 6 m 2 / sec) = 3 . 18 · 10 4 kg / (m · sec) .I no r d e r to determine the coefficients μ r and S in Andrade’s equation, we take the natural log of the equation, so that f = f r + T r /T Now, for T o C = 283.15 K, we have f = 6 . 638 and 1 /T = 3.532 · 10 3 .A l s o , for T o C = 363.15 K, we have f = 8 . 053 and 1 /T = 2.754 · 10 3 .T h u s ,w e have the two following linear equations for f r and T r . 3 . 532 · 10 3 T r + f r = 6 . 638 2 . 754 · 10 3 T r + f r = 8 . 053 Subtracting the second equation from the first yields 0 . 778 · 10 3 T r =1 . 415 = T r =1819 Then substituting this value of
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This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

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p0178 - 1.78. CHAPTER 1, PROBLEM 78 83 1.78 Chapter 1,...

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