Me130 - Report Viscosity

8/12/2019 Me130 - Report Viscosity

1/17

VISCOSITY

ME130 FLUID MECHANICS


2/17


Viscosity ( )

The property of viscosity is important to engineering practice because it leads to significant energy loss when moving fluidscontact a solid boundary, or when different zones of fluid areflowing at different velocities.

Viscosity (also called dynamic viscosity , or absolute viscosity ) isa measure of a fluids resistance to deformation under shearstress.


3/17


Viscosity ( )

In Solid Mechanics, Shear stress ( ), is the ratio of force/area on asurface when the force is aligned parallel to the area. Shear strainis a change in an interior angle of a cubical element, , that wasoriginally a right angle. The shear stress on a material element insolid mechanics is proportional to the strain, and the constant of

proportionality is the shear modulus:

Shear Stress = Shear Modulus Shear Strain s = S


4/17


Viscosity ( )

In fluid flow, however, the shear stress on a fluid element is proportional to the rate (speed) of strain, and the constant of proportionality is the viscosity:

Shear Stress = Viscosity Rate of Strains = ( / t)


5/17


Viscosity ( )

yt V

yV

t : Rate of Strain

yV

t yt

00

lim


6/17


Viscosity ( )

the rate of strain is related to the velocity gradient bydydV

dy

dV

dydV

A F s

2

2

)( m s N

m smm

N


7/17


Viscosity ( )

Other units for Viscosity:

SI (MKS) CGS English

2m s N

sm

kg

s Pa

2cm sdyne

Poise

2 ft slb

s ft slug


8/17


Kinematic Viscosity (v)

Many equations of fluid mechanics include the ratio / . Becauseit occurs so frequently, this ratio has been given the special namekinematic viscosity . The symbol used to identify kinematicviscosity is v. Units of kinematic viscosity v are m 2/s, as shown.

sm

mkg m s N

v2

3

2


9/17


Kinematic Viscosity (v)

Other units for Kinematic Viscosity:

SI (MKS) CGS English

s ft 2

stoke s

cm 2

sm 2


10/17


11/17


Temperature Dependency

An equation for the variation of liquid viscosity with temperatureis:

where C and b are empirical constants that require viscosity dataat two temperatures for evaluation.

T bCe


12/17



Even when the liquid is at rest, the molecules are in constantmotion, but confined to cells, or cages . The cage or latticestructure is caused by attractive forces between the molecules.The cages may be thought of as energy barriers. When the liquid

is subjected to a rate of strain and thus caused to move, there is ashear stress, , imposed by one layer on another in the fluid. Thisforce/area assists a molecule in overcoming the energy barrier,and it can move into the next hole. The magnitude of theseenergy barriers is related to viscosity, or resistance to sheardeformation. At a higher temperature the size of the energy

barrier is smaller, and its easier for molecules to make the jump,so that the net effect is less resistance to deformation under shear.Thus, an increase in temperature causes a decrease in viscosityfor liquids.


13/17




14/17



An estimate for the variation of gas viscosity with temperature isSutherlands equation :

where 0 is the viscosity at temperature T 0, and S is Sutherlands constant. All temperatures are absolute. Sutherlands constant for airis 111 K. Using Sutherlands equation for air yields viscosities withan accuracy of 2% for temperatures between 170 K and 1900 K. Ingeneral, the effect of pressure on the viscosity of common gases isminimal for pressures less than 10 atmospheres.

S T

S T

T

T 023

00


15/17


Newtonian and Non-Newtonian Fluids

Fluids for which the shear stress is directly proportional to the rate ofstrain are called Newtonian fluids .

For some fluids the shear stress may not be directly proportional tothe rate of strain; these are called Non - Newtonian fluids .


16/17



Real Fluid

Newtonian Non - Newtonian

PseudoplasticShear thinning fluidStress Resistance

DilatantShear thickening fluidStress Resistance

BinghamSmall Shear acts like solidHigher Shear acts like

liquid


17/17



Documents

Me130 - Report Viscosity