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• Difference between Dynamic Viscosity Kinematic Viscosity

• Pressure and Temperature Dependence of Viscosity• Problem on above topic• Summary of Topics we have covered today• Assignment

• What is Today?

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• Dynamic viscosity is the quantitative expression of fluid’s resistance to flow, while Kinematic viscosity is the ratio of the fluid’s viscous force to the inertial force.

• Dynamic viscosity is symbolized by either ‘µ’ or ‘η’, while Kinematic viscosity is mathematically symbolized by ‘υ’.

• In a cgs unit system, dynamic viscosity is in a unit called ‘poise’, which is taken from the name of Jean Louis Marie Poiseuille, while Kinematic viscosity is expressed in ‘stokes’ (St) or centistokes (ctsk or cSt), which are named after George Gabriel Stokes.

• Dynamic viscosity is sometimes referred to as absolute viscosity, or just viscosity, while Kinematic viscosity is sometimes called the diffusivity of momentum.

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Pressure and Temperature Dependence of Viscosity

• Importance of Viscosity in Fluid Mechanics• How to get Data on Viscosity • Viscosity Data for pure gases and liquids Viscous

Science and Engineering Books• Estimation by empirical methods

• Corresponding-states correlation used for estimation of viscosity and show the general trends of viscosity with Temperature and Pressure for ordinary fluids.

• Figure-1 gives a global view of the pressure and temperature dependence of viscosity.

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Figure-1.Reduced viscosityμr = μ / μc as afunction of reducedtemperature for severalvalues of the reducedPressure (pr)

A "reduced quantity” is one that has been made dimensionless by dividing by the corresponding quantity at the critical point.

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Experimental values of the critical viscosity μc are seldom available. However, μc may be estimated in one of the following ways:(1)if a value of viscosity is known at a given reduced pressure and temperature, preferably at conditions near to those of interest, then μc can be calculated from μc = μ /μr; or(2)if critical p-V-T data are available, then μc, may be estimated from these empirical relations

Here μc is in micropoises, pc in atm, Tc in K, and in Vc cm3/g-mole

Pressure and Temperature Dependence of Viscosity

(1)

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Figure-1 can also be used for rough estimation of viscosities of mixtures. For N-component fluids with mole fractions xa the "pseudocritical" properties are:

Pressure and Temperature Dependence of Viscosity

That is, one uses the chart exactly as for pure fluids, but with the pseudocritical properties instead of the critical properties.This empirical procedure works reasonably well unless there are chemically dissimilar substances in the mixture or the critical properties of the components differ greatly.

(2)

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Problem: Estimate the viscosity of N2 at 50°C and 854 atm, given M = 28.0 g/g-mole, pc = 33.5 atm, and Tc = 126.2 K.

Pressure and Temperature Dependence of Viscosity

Solution:Using Eq. (1), we get

6/13/22/1 )2.126()5.33()0.28(70.7 c= 189 micropoises =189 ×10-6 poise

Reduced temperature and pressure are

56.22.126

502.273

rT 5.25

5.33

854rP

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Pressure and Temperature Dependence of Viscosity

From Fig.1, we obtain μr = μ/μc= 2.39.

Hence, the predicted value of the viscosity is

μ= μc (μ/μc)=(189×10-6)(2.39)=452×10-6 poise

The measured value6 is 455×l0-6 poise.

This is unusually good agreement

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What we have done till today? General introduction to Transport Phenomena Transport Coefficients and their estimation methods Brief study of Newton’s law of viscosity, Fourier Law of

Thermal Conductivity and Fick’s Law of Diffusivity. Introduction to Momentum Transport Convective and Molecular Momentum (class assignment) Equation of Continuity Equation of Motion and its applications Pressure and Temperature Dependence of Viscosity

The rest of topics you have to done yourself?

Generalization of Newton’s law of viscosity Molecular theory of the viscosity of gases at low density Molecular theory of the viscosity of liquids

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Assignment Marks = 04 [=05 for those who have taken Zero marks

out of 1 in Surprise Class Test OR absent on that day] Mode: Group assignment (Maximum 05 students in each

group) Activity:

Pick any research paper from www.sciencedirct.com regarding the above mentioned topics.

Make the presentation on the work conducted in research paper.

Present your findings with equal contribution of all the students

Date of Presentation: Decide yourself and communicate to me on coming Monday

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