Viscosity

                 Viscosity

Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of fluid. When two layers of fluid, a distance(dy) apart, move one over the other at different velocities, say u and u + du as shown in fig. 

the viscosity together with relative velocity causes a shear stress acting between the fluidlayers.

 The top layer causes a shear stress on the adjacent lower layer while the lower layer 

causes a shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to y. It is denoted by symbol Ꞇ (tau).

Mathematically, Ꞇ ∞ du/dy

 Ꞇ = μ du/dy

 Where ℳ (called mu) is the constant of proportionality and is known as the coefficient of 

dynamic viscosity or only viscosity. du/dy represents the rate of shear strain or rate of shear 

deformation or velocity gradient.

 μ = Ꞇ/ (du/dy)

The viscosity is also defined as the shear stress required to produce unit rate of shear strain. 

Unit of viscosity:

           In MKS system, force is represented by kgf and length in metre (m)

 In CGS system, force is represented by dyne and length in (cm)

 

In SI system, force is represented by Newton(N) and length in (m).                   

 MKS unit of viscosity = kgf-sec/m2 

 CGS unit of viscosity = dyne-sec/cm2

 N/m2 = Pa = Pascal

 SI unit of viscosity = Newton-sec./m2 = Ns/m2

 The unit of viscosity in CGS is also called Poise,

 Poise = dyne-sec/cm2

The numerical conversion of the unit of viscosity from MKS unit to CGS Unit:

 One kgf-sec/m2 = 9.81 N x sec/m2

 One Newton= one kg(mass) x one (m/sec2

) [acceleration]

 = (1000gm) x (100cm)/sec2 = 1000 x 100 gm - cm/sec2

 One Newton= 1000 x 100 dynes {dynes = gm x cm/sec2

}

 One kgf-sec/m2 = 9.81 x1000 x 100 dynes-sec/m2

 = 9.81 x1000 x 100 dynes-sec/cm2

 100x100

 = 98.1 Poise {Poise = dynes-sec/cm2

}

Note: For solving numerical problems, if viscosity is given in poise, it must be divided by

98.1 to get its equivalent numerical value in MKS.

 One kgf-sec/m2 = 9.81 N x sec/m2 = 98.1 Poise

 1 N x sec/m2 = 98.1 Poise

 9.81

 = 10 Poise

1 Poise = 1 Ns/m2

 10

 Note: i) In SI units second is represented by (s) not by (sec)

 ii) If viscosity is given in poise, it must be divided by 10 to get its equivalent

numerical value in S I units.

 Centipoise a unit of viscosity is also used,

 1 centipoise = 1/100 poise or 1cP= 1/100 P

 The viscosity of water at 200C is 0.01 Poise or 1.0 centipoise

KINEMATIC VISCOSITY: It is defined as the ratio between the dynamic viscosity and

density of fluid. It is denoted by Greek Symbol v called ‘nu’.

 Mathematically, V = viscosity/ density = μ

 ῥ

 units in MKS m2

/sec.

 units in CGS cm2

/sec.

 Kinematic viscosity is also known as stoke,

 One stoke = cm2 /sec. = (1/100)2 m2 

/sec. = 10-4 m2 /sec.  

 Centistoke means = 1/100

NEWTON’S LAW OF VISCOSITY: It states that the shear stress (Ꞇ ) on a fluid element

layer is directly proportional to the rate of shear strain. The constant proportionality is called

the coefficient of viscosity.

 Mathematically, Ꞇ = μ du/dy

Fluids which obey the above relation are known as Newtonian fluids and the fluids which do

not obey the above relation are called Non- Newtonian fluid