Chapter 8, Problem 27P

Viscosity is a property of gases and fluids that characterizes their resistance to flow. For most materials viscosity is highly sensitive to temperature. For gases, the variation of viscosity with temperature is frequently modeled by an equation of the form

s $\mu =\frac{C{T}^{3/2}}{T+S}$ where $\mu$ is the viscosity, T is the absolute temperature, and C and S are empirical constants. Below is a table that gives the viscosity of air at different temperatures (data from B.R. Munson, D.F. Young, and T.H. Okiishi, Fundamentals of Fluid Mechanics, 4th ed., John Wiley and Sons, 2002).

T (°C)	-20	0	40	100	200	300	400	500	1,000
$\mu \left(\text{N}{\text{s/m}}^2\right)\left(\times {10}^{-5}\right)$	1.63	1.71	1.87	2.17	2.53	2.98	3.32	3.64	5.04

Determine the constants C and S by curve-fitting the equation to the data points. Make a plot of viscosity versus temperature (in °C). In the plot show the data points with markers and the curve-fitted equation with a solid line.

The curve fitting can be done by rewriting the equation in the form $\frac{T^{3/2}}{\mu }=\frac{1}{C}T+\frac{S}{C}$ and using a first-order polynomial.