transport phenomena notes

1. Transport Phenomena

2. VELOCITY GRADIENT AND RATE OF
SHEAR
Fs= Shear force equal in
magnitude but opposite in
direction
At the wall maximum velocity gradient
𝑑𝑢
𝑑𝑦

3. SHEAR STRESS
Momentum flux=
𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑠𝑡𝑟𝑒𝑠𝑠
𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎

4. NEWTON’S LAW OF
VISCOSITY
 Newton’s law of viscosity states that;
“Shear stress is directly proportional to the
shear rate.”
 Viscosity “µ” is a constant of proportionality.
 Fluids following this simple linearity are called
Newtonian Fluids.

5. MOMENTUM FLUX
 The units of momentum flux are the same as the
units for shear stress.
 Momentum flux normal to the direction of flow of
the fluid is proportional to the velocity gradient,
with the viscosity as the proportionality factor.

6. VISCOSITY
 Viscosity is that property of a fluid due to
which it offers resistance to the movement of
one layer of fluid over another adjacent layer
of fluid.
 Viscosity (μ) is the measure of the resisting
forces of a fluid which is being deformed.
 Viscosity increases with increase in
temperature in case of gases where as it
decreases in case of liquids.

7. Temperature effect on viscosity
 In the case of gases,
increased temperature
makes the molecular
movement more vigorous
and increases molecular
mixing so that the viscosity
increases.
 In the case of a liquid, as its
temperature increases
molecules separate from
each other, decreasing the
attraction between them, and
so the viscosity decreases.

8. Units of Viscosity
 Unit = Pa.s
= kg/ms
OR
 Unit = P (Poise)
 1 Poise = 1 g/cms

9. KINEMATIC VISCOSITY
 Kinematic viscosity = Viscosity/Density
 Unit = m2/s
OR
 Unit = Stoke (St)
 1 Stoke = 1 cm2/s

10. VISCOSITIES OF GASES
 For gases,
 (for air)
 0.9 (for carbon dioxide and simple
hydrocarbons)
 1.1 (for sulfur dioxide and steam)

11. VISCOSITIES OF GASES
(contd..)
 The viscosity of a gas is almost independent of
pressure in the region of pressures where the gas
laws apply.
 In this region, the viscosity of gases are generally
between 0.01 and 0.1 cP.
 At high pressures, gas viscosity increases with
pressure.

14.  Determine the viscosities of following fluids (at
1 atm);
Air at 180 oF
Air at 30 oC, 100 oC and 200
oC
CO at 0 oC, 300 oC and 600 oC
Helium at 0 oC, 300 oC and
600 oC
F2, Cl2, Br2 and I2 at 20 oC

16. VISCOSITIES OF LIQUIDS
 The viscosities of liquids are generally much greater
than those of gases and cover several orders of
magnitude.
 Liquid viscosities decrease significantly when the
temperature is raised.
 For example, the viscosity of water falls from 1.79 cP
at 0 oC to 0.28 cP at 100 oC.
 The viscosity of a liquid increases with pressure, but
the effect is generally insignificant at pressures less
than 40 atm.
 The absolute viscosities of fluids vary over an
enormous range of magnitudes, from about 0.1 cP for
6

20.  Determine the viscosities of following fluids (at
1 atm);
Water at 10 oC.
100% Glycerol at 60 oC.
Propyl Alcohol at 30 oC.

21. EDDY VISCOSITY
 The relationship between shear stress and
velocity gradient in a turbulent stream is used to
define an eddy viscosity Ev .

22. EDDY VISCOSITY (contd…)
 The total shear stress in a turbulent fluid is the
sum of the viscous stress and the turbulent
stress;

23. Difference between Viscosity and
Eddy viscosity
 The viscosities µ and v are true properties of the
fluid and are the macroscopic result of averaging
motions and momenta of myriads of molecules.
 The eddy viscosity Ev and the eddy diffusivity Ɛm
are not just properties of the fluid but depend on
the fluid velocity and the geometry of the system.
 The eddy viscosity and the eddy diffusivity both
are functions of all factors that influence the
detailed patterns of turbulence and the deviating
velocities, and they are especially sensitive to
location in the turbulent field and the local values
of the scale and intensity of the turbulence.