The viscosity of fluid

FLUID MECHANICS

• solid • liquid

• gas•Fluids can be a liquid or a gas• A fluid is anything that flows: • e.g. liquid (water, mercury at room temp) gas (steam, air, CO2)

• Properties depend on temperature•

• Molecular Structures Of different States Of Matter

The viscosity of fluid

• Definition• Mathematical Statement

• Newton’s law of Viscous Drag

• Unit

•The definition of Viscosity

Its Concept

Viscosity is an internal property of a fluid that offers resistance to flow.

Origin Of Its Name

• The word Viscosity derives from the latin word Viscum Al Ba for misletoe(common name for group of hemi parastic plants).A viscous glue was made from misletoe berries and used for lime-twigs to catch birds.

A Physical Interpretation to Viscosity:

When a fluid flows over a surface then the different layers of the liquid moves with different velocities.Two layers in contact with different velocities try to destroy the relative velocity between them. The property due to which it opposes the relative velocity betwwen different layers is known as VISCOSITY or FLUID FRICTION.

• It states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear strain (du/dy) .The constant of proportionality is called the co-efficient of

viscosity (μ).Mathematically,it is expressed as--

•

τ = μ(du/dy)•

Mathematical Statement

Newton’s law of viscous Drag

M u+du

N

•J u K

y+dy y

B C

Suppose,velocity of a layer JK at a distance “ y ” from the fixed layer BC is “ u ” and that of another layer at a distance “ y+dy ” MN is “ u+du ” .The viscous drag between these two layers of common area “ A ” at constant temperature

F α ( du/dy )

α A

or F = -μ A(du/dy)

where,the constsnt of proportionality μ is called the co-efficient of viscosity of the fluid.The –ve sign shows that the viscous force on a liquid layer acts in a direction opposite to the direction of relative velocity.

Geometrical Derivation of Newton’s Law of

Viscous Drag• • 1 2 3 4 u• F

• b y dɵ

• distance = velocity ˟ time

• = velocity ˟ unit time• =velocity ˟ 1• So, distance = velocity = u

• tan ɵ = (u/b)=dɵ• But,we know • b dɵ = u dt

• From which we can get,τ= μ (du/dy)

• Dimensional formula [μ] =[ M L-2T-1 ]

• Unit of Co-efficient of Viscosity ( μ ) :

• S.I. unit of “ μ ” is Nm-2s or Pa s or poissuli

• c.g.s unit of “ μ ” is dyne cm-2 s or poise

1 poissuli = 10 poise

• Some points:

• Viscosity of a fluid depends upon the nature of the fluid & its temperature and is independent of the velocity gradient & area.

• In case of liquids viscosity increases with density while for gases it decreases with increase of density.

• With rise of temperature viscosity of a liquid increases and that of gas decreases.

• Viscosity of liquids is much greater than the viscosity of gases.

The viscosities of common

substances and lavas: Substance Viscosity (Pa s)

Air (at 18 oC) 1.9 x 10-5 (0.000019)Water (at 20 oC) 1 x 10-3 (0.001)Canola Oil at room temp. 0.1Motor Oil at room temp. 1Corn syrup at room temp. 8Pahoehoe lava 100 to 1,000A'a lava 1000 to 10,000Andesite lava 106 to 107

Rhyolite lava 1011 to 1012

Thank you!