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2021-08-24 13:53:54 Revision Notes on Flow of Liquids and Viscosity (2/3)


Viscosity:- Viscosity is the property of fluids by virtue of which they tend to destroy any relative motion between their layers.

Velocity gradient:- Velocity gradient is defined as the rate of change of velocity with respect to distance.

(a) Velocity gradient = dv/dr
(b) Dimension of velocity gradient = [dv/dr] = [T-1]
(c) Direction of velocity gradient is perpendicular to the direction of flow, directed in the direction of increasing velocity.
(d) Average velocity gradient:- Average velocity gradient is the difference between velocities of two layers separated a unit distance apart.

Average velocity gradient = Δv/Δr

Newton’s law of viscosity:-

In accordance to Newton’s law of viscosity, the viscous drag force depends upon the nature of fluid along with following factors:-

(a) F∝A (common area of two layers)

(b) F∝dv/dr (velocity gradient)

(c) So, F =ηA (dv/dr)

Here η is called coefficient of viscosity of fluid.

Coefficient of viscosity of fluid (ηv) or fugitive elasticity:-

ηv = shear stress/velocity gradient = (F/A)/(dv/dr)

Modulus of rigidity(ηr):-

ηr = shear stress/shear strain = (F/A)/(θ) = (F/A)/(dx/dr)

Here, θ = dx/dr = displacement gradient

Coefficient of viscosity (Absolute viscosity or Dynamic viscosity):-

F= ηA (dv/dr) if A = 1, dv = 1, dr =1, F = η

Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain (or resist) a unit relative velocity between two layers a unit distance apart.

Or

Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain a unit velocity gradient between its layers.

Unit of η:-

S.I:- η = 1 deca poise = 1 N sec/m2

Co-efficient of viscosity of a fluid is said to be one deca-poise if a tangential force of 1 N per meter square is required to maintain a relative velocity of 1 ms-1 between its layer 1 m apart.

C.G.S:- η = 1 poise = 1 dyn sec/cm2

Coefficient of viscosity of a fluid is said to be one poise if a tangential force of 1 dyn per square cm is required to maintain a relative velocity of 1 cms-1 between its layers 1 cm apart.

Relation between deca-poise and poise:-

1 deca-poise = 10 poise

Dimension formula for η:-

η = Fdr/Adv = [M1L-1T-1]

Fluidity:- Reciprocal of coefficient of viscosity of a fluid is called its fluidity.

Fluidity = 1/η

Unit of fluidity: poise-1

Dimension of fluidity: [M-1L1T1]

Kinematic viscosity:- Kinematic viscosity of a fluid is defined as the ration between its coefficient of viscosity to the density of fluid.

Kinematic viscosity = η/ρ

Units of kinematic viscosity:- C.G.S – 1 stoke = cm2 s-1

Kinetic viscosity of a fluid having its dynamic viscosity one poise and density one g cm-3 is said to be 1 stoke.

Dimensional formula of kinematic viscosity = η/ρ = [M0L2T-1]

Critical velocity (Reynold’s Number):- Critical velocity (vc) is the maximum velocity of the flow of liquid flowing in a streamlined flow.

vc = NR η/ρD

Here η is the coefficient of viscosity of liquid, ρ is the density of liquid and D is the diameter of the tube.

Reynold’s Number, NR = ρvcD/ η

Stokes law:- In accordance to Stoke’s law, force of viscosity F depend upon,

(a) Co-efficient of viscosity of fluid η

(b) Radius of the moving body r

(c) Velocity of body v

So, force of viscosity, F = 6π η r v

Terminal velocity:- v = 2/9 [r2 (ρ-σ)/η]

η = 2/9 [r2 (ρ-σ)g/v]

Variation of viscosity with a change in temperature and pressure:-

(a) Effect of temperature:-

η= A /(1+Bt)c

Here A, B and C are constants.

Again, ηv1/2 = Aec/vt

Here, A and C are constants and v is the relative velocity.

(b) Effect of pressure:- Co-efficient of viscosity of liquids increases due to an increase in pressure but there is no relation, so far, to explain the effect.

Change in viscosity of gases:-

(a) Effect of temperature:- Co-efficient of viscosity of a gas at a given temperature is given by,

η= η0AT1/2

Here T is the absolute temperature of gas. Open / Comment

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2021-08-22 11:43:12 Endoplasmic Reticulum Structure, Types and Functions

In 1897, observed by Garnier and named it as ergastoplasm
In 1945, first described by Porter, Claude and Fullman
In 1953, term given by porter
Present in all eukaryotes
All cells do not have Endoplasmic reticulum. It is generally absent in egg and embryonic cells

Endoplasmic Reticulum Structure
Components of endoplasmic reticulum

Cisternae
Formed by projection of nuclear membrane
They bear ribosomes on the surface
Contain ribophorin that bind the ribosomes

Vesicles
They are oval or rounded, vacuole like element
Many vesicles are free in the cytoplasm

Tubules
They are tube like extensions
Tubules are irregular and branched
Free of ribosomes


Types of Endoplasmic Reticulum

I) Rough Endoplasmic Reticulum
Ribosomes binds with help of ribophorin protein
Mainly composed of cisternae
Abundantly occurs in cell which are engaged in protein synthesis and secretion
Mass of RER in cyton of nueron is called missals granules
e.g. Liver, pancreas and goblet cells

II) Smooth Endoplasmic Reticulum
Ribosomes and ribophorins are absent
Mainly composed of tubules
Occurs especially in those cells which are almost inactive in protein synthesis
It is well developed in cells that synthesis lipids
Mass of SER in retinal cell is called myeloid bodies

Functions of Endoplasmic Reticulum
It gives mechanical support so also called cytoskeleton of cell
Intracellular exchange: Transport of materials in cytoplasm from one place to another through the ER
Provides site for protein synthesis, because rough ER has ribosome’s
Lipids synthesized by smooth ER
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