Revision Notes on Flow of Liquids and Viscosity (2/3) | Avccs
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.
