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Chapter 2: Problem 38

The variation with temperature of the viscosity of air is correlated well by the empirical Sutherland equation \\[\mu=\frac{b T^{1 / 2}}{1+S / T}\\] Best-fit values of \(b\) and \(S\) are given in Appendix A for use with SI units. Use these values to develop an equation for calculating air viscosity in British Gravitational units as a function of absolute temperature in degrees Rankine. Check your result using data from Appendix A.

Short Answer

Expert verified
The Sutherland's equation in BG units is \\ \[\mu' = \frac{b' T'^{1 / 2}}{1 + S' / T'}\] \\ where \(T' = T / 1.8 (R)\), \(\mu' = \mu / 10 (P)\), \(b' = b / 10 (P R^{1/2})\), and \(S' = S / 1.8 (R)\). To check the validity of this equation, convert the given SI data from Appendix A to BG units and substitute into the equation. If done correctly, the computed value of viscosity in Poise should match with the given value in Pascal seconds converted to Poise.

Step by step solution

01

Identifying BG units for Temperature and Viscosity

The SI unit for temperature in the Sutherland's equation is Kelvin (K), which corresponds to degree Rankine (R) in BG units. As for viscosity, the SI unit is Pascal second (Pa.s) and its BG equivalent is Poise (P). We must remember that \[1 K = 1.8 R\] and \[1 Pa.s = 10 P\].
02

Convert The Sutherland Equation to BG Units

Substituting the BG units into the Sutherland's equation gives: \\ \[\mu = \frac{b' T'^{1 / 2}}{1 + S' / T'}\] \\ where \\ \(T' = T / 1.8 (R)\), \\ \(\mu' = \mu / 10 (P)\), \\ \(b' = b / 10 (P R^{1/2})\), and \\ \(S' = S / 1.8 (R)\)\
03

Check the Result Using Data from Appendix A

The given values of \(b\), \(S\), \(T\), and \(\mu\) in SI units from Appendix A should be converted to BG units and substituted into the new Sutherland's equation. The computed value of \(\mu'\) should match with the given value of \(\mu\) converted to BG units.

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