The property of a fluid to oppose relative motion between its layers is called viscosity. This property can be observed when the flow is steady or the liquid moves with a constant velocity. The flow may be called laminar. The opposition or resistance is due to intermolecular forces (cohesive force). It is clear from the that velocity of layers decrease perpendicular to the flow
∴ Shearing stress F / A ∝ velocity gradient (rate of change of strain)
Or F = - η A dv / dy
Where η is coefficient of viscosity, A is area of cross section and dv / dy is velocity gradient.
Since the coefficient of viscosity is the ratio of shearing stress to the rate of change of change of strain, it may be regarded as transient or fugitive rigidity, Maxwell regarded viscosity as the limiting case of elastic solid. Η is coefficient of viscosity. Its unit is poise (CGS), poiseule (SI) 1 poise = 0.1 velocity.
Critical velocity the velocity at which the steady, laminar or streamline flow changes to turbulent or eddy flow is called critical velocity.
Stake’s formula F = 6πηrv
This formula is valid if Reynolds number for the system is < 1.
Terminal velocity when a drop or a spherical body falls under gravity then
v-terminal = 2r2 (p – σ)g / 9η where r is radius of drop/body and p ---->density of drop/body, σ ---> density of viscous fluid, η ----> coefficient of viscosity
Reynolds’s number R = inertial force/are / viscous drag/area
if D is diameter of the tube then
R = pvD / η = inertial force / viscous drag = 1 / 2 pv2 / ηV / r
For water if v < 20 cm/s or R < 2000 flows is laminar at 20°C.
If v > 30 cm/s or R > 3000 flow is turbulent at 20°C.
Kinematic viscosity is the ratio of η / P its unit is Stokes.
Poiseuille’s equation amount of liquid flowing per second thorough a tube of radius r is given by
dv / dt = π Pr4 / 8 ηI
Where P / I is pressure gradient r is radius of the bue
P = P (h1 – h1) g shows scheme for Poiseuille’s law.
Shows how the rate of flow varies with pressure head.
Where A and C are constant P is density and T is temperature in Kelvin.
That is viscosity of the liquid in general decrease with rise in temperature.
Η = aηoT+1/2 that is coefficient of viscosity increases with temperature where λ is that mean free path and c is rms velocity of the gas molecules.
We can compare the viscosities of two liquids using viscometers.
In gases η = 1 / 3 λPC and variation with temperature is
η1 / η2 = p1t1 / p2 t2
Where p1 and p2 are densities and t1 and t2 are times for the two liquids in which they can vacate the viscometer.
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