Problem 2.1.12

Calculate viscosity of nitrogen at 80 bar and 300 Kelvin. Nitrogen has the following properties: critical temperature, 126.05 Kelvin, acentric factor, 0.047, critical pressure 33.5 atmospheres, critical mass density 311 kilogram per cubic meter, low pressure viscosity 178.78 micro Poise, compressibility factor 0.392, xi 0.047 (micro Poise)^-1.

Use method of Jossi, Stiel, and Thodos.

Solution:

If a shearing stress is applied to any portion of a confined fluid, the fluid will move and a velocity gradient will be set up within it with a maximum velocity at the point where the stress is applied. If the shear stress per unit area is divided by the velocity gradient, the ratio obtained is defined as the viscosity of the medium. It is a measure of the internal fluid friction. Viscosity is a non-equilibrium property. A poise (P) denotes a viscosity of 0.1 Newton second per meter squared. The kinematic viscosity is the ratio of the viscosity to the density. With viscosity in poises and the density of grams per cubic centimeter, the unit of kinematic viscosity is the stoke, with the units square centimeters per second.

Estimation of low-pressure gas viscosity:

Viscosities of gas mixtures at low pressure:

Effect of pressure on the viscosity of pure gases: The viscosity of a gas is a strong function of pressure near the critical point and at reduced temperatures of 1 to 2 at high pressures.

Viscosity of gas mixtures at high pressures:

In this case the residual viscosity, eta minus eta⁰, is correlated with fluid density. All temperature effects are incorporated in the eta⁰ term. In this method, separate residual viscosity expressions are given for nonpolar and polar gases, but no quantitative criterion is presented to distinguish these classes.

Nitrogen is nonpolar. For the given pressure, temperature and compressibility factor, specific volume is calculated from ZRT over p and is equal to 1.222 ×10^-4 cubic meter per mol. Critical volume is molecular weight over critical mass density. This value is found to be 9.01× 10^-5 cubic meter per mol. Now reduced volume, Vr, can be found t be equal to 1.357. Reciprocal of reduced volume gives reduced density value of 0.737.

Now, we can use Perry’s equation 3-93 for nonpolar gases to obtain residual viscosity for the following table. For a reduced density of 0.737, a value of 2.61 can be interpolated from the table for the dimensionless group (eta minus eta⁰) xi. Inserting the value of xi, we obtain residual viscosity of 64.11 micro poises. Low-pressure viscosity is given as 178.78 micro poises. High-pressure viscosity is found to be 242.8 micro poises.