fluid property>viscosity>definition>phenomenon>Newton's law of viscosity>experimental data>unit

                Fluid property
                    Viscosity

•  viscosity is the property which resist the flow of fluid layer motion

• Inverse of the viscosity property is known as the fluidity

• due to temperature increase liquid viscosity decrease and due to temperature increase gas viscosity increase

• in the case of liquid viscosity property is mainly depend upon cohesion

• but, in the case of gas viscosity property is mainly depend upon collision between molecules/momentum transfer

• resistance of flow relative property is known as the viscosity

Newton's law of viscosity

1. according to Newton's law of viscosity shear stress on a particular layer is directly proportional to the shear stress rate /rate of angular deformation
2. validity of Newton's law of viscosity is only laminear flow condition and by experimental data rate of shear strain is almost equal to the velocity  gradient

• experimental data,

(du/dy)=(dө/dt)

τ ∝(dө/dt){original}

τ∝du/dy{up to laminear flow}

τ=μ×(du/dy)

where ,τ=shear stress

μ=absolute/dynamic viscosity coefficient

(du/dy)=velocity gradient

• (du/dy)=0 then rest,

     viscosity=can't say

unit of viscosity and Newton's law of viscosity property in terms of shear force/tangential force

τ=μ×(du/dy)

• F/A=μ×(du/dy)
• unit of viscosity

1. unit of dynamic viscosity/absolute viscosity

F/A=μ×(du/dy)
μ=(F×dy)/(du×A)
S.I system
μ=(N×m×s)/(m×m² )
  =N-s/m² 
in C.G.S system
μ=(dyne×cm×s)/(cm×cm²)
   =dyne-s/cm²
NOTE
relation between S.I and C.G.S unit of dynamic viscosity
1 S.I=____C.G.S
1N-S/m² =(10^5dyne-s)/(10^4cm2)
1S.I=10(dyne-s/cm2)
1S.I=10POISE

2.kinematics viscosity/momentum         diffusivity
v=μ/D
where,v=kinematics viscosity
μ=dynamic viscosity
D=density
in S.I unit system
v=μ/D
v=N-s/(m² ×kg/m3 )
v=(kg-m-s)/(s2×m² ×kg/m3 )
v=m² /sec
in C.G.S unit system
v=cm²/sec
or,v=stoke
relation betweenS.I and C.G.S unit of kinematics viscosity
1S.I=______C.G.S
m² /sec=10^4cm²/sec
1S.I= 10^4 C.G.S

determine the dimensions of viscosity dynamic and kinematics viscosity

1.dynamics/absolute viscosity

in S.I unit system

[μ]=N-S/m² 

where,[F]=N=[M L T^-2]

[μ]=[M L T^-2]×[T]/[L^2]

[μ]=[M L^-1 T^-1]

2.Kinematics viscosity(v)

in S.I unit system
[v]=m² /sec
[v]=[L^2 T^-1]
[v]=[M^0 L^2 T^-1 ]