Properties of fluids, Physical properties of fluids, Viscosity, Kinametics viscosity, Learn with Ashiso, learnwithashiso

 Mass- Density:-

Mass density of a fluid is the ratio of mass of fluid to its volume.

It is denoted by ρ (rho).

ρ= mass of fluid/ volume of fluid

   = m/v

ρ = kg/m^3

• Density of water is 1000Kg/m^3 or 1g/cm^3.
• The variation in density of water with the variation of pressure and temperature is so small that is generally considered as neglected for all purpose. 

2. Specific weight:-

Specific weight of fluid is ratio between the weight of fluid to its volume. 


It is denoted by ω.


 ω= weight of fluid/ volume of weight 
    
      ω= (m×g)/ volume of fluid
      ω= ρ×g


Unit= N/m^3.
• Specific weight of water is 9.81 KN/m^3.
• Specific weight of fluid changes from one place to another place because of change in gravitational acceleration. 

3. Specific Volume:-

Specific weight of fluid is the volume per unit mass of the fluid. 


Specific volume=volume of fluid/ mass of fluid. 
        
           =1/(mass of fluid/volume of fluid)


            =1/ρ


   Unit= m^3/Kg 

4. Specific gravity:-

• It is also called relative density. 
• It is defined as the ratio of specific weight of fluid to that of standard fluid.
• The standard fluid is assumed as water and gasses. 
• It is denoted by S.


    S=ω of fluid /ω of water or air.


• It is dimension less. 


ω of fluid= S of fluid × ω of water.
                 = S × ρ × g
                = S × 1000× 9.81
                = S × 9.81 KN/m^3.



Specific gravity of mercury is 13.6 means that it's weight(or mass) is 13.6 times that of same volume of water. 

In other words mercury is 13.6 times heavier that water. 

Surface tension :-

Surface tension is a property if surface odd a liquid that cause it to behave as an elastic sheet.  It I'd define as the force required to maintain unit length of the sheet in complete equilibrium and is equal to the surface tension co- efficient and the length of free surface. 

• It is denoted by sigma( σ ).
• Its S.I. unit is  N/m.
• M.K.S unit=kgf/m.
• C.G.S unit= dyne/cm.

• The value of surface tension of water in contact of air is vary from 0.073N/m at 20°C to 0.06N/m at 100°C.
• Hence we're say that increasing the temperature of water it's surface tension is decreases. 

Capillarity:-

Capillarity is defined as the phenomenon of rise or fall of a liquid in a thin tube ( capillary tube ) relative to the adjacent general level of liquid. 

Capillarity is due to both cohesion and adhesion. 

• Rise of liquid surface is known as capillary rise and fall of liquid surface is known as capillary depression. 
• Capillarity is expressed in cm or mm. 

 

Let,

        σ = Surface Tension

          d = Diameter of capillary tube

          ω = specific weight

         θ = angle of contact

           h = Rise and Fall of liquid in capillary tube. 

Weight of liquid raised or lowered in the capillary tube = ( area of tube × rise or fall ) × ω

                          = π / 4 × d^2 × h × ω

Vertical component of surface tension force

            = σ Cosθ × circumference of tube

               = σ Cosθ × πd

            = πdσ Cosθ .

Aay equilibrium condition, the eight of liquid column 'h' is balanced by the vertical component of surface tension force. 

         

              π / 4 × d^2 × h × ω = πdσ Cosθ .

         h = 4σ Cosθ / ωd.          ----- i.

 

Equation 1st is also known as Ascent formula. 

Viscosity:-

Viscosity is the property of a fluid by a virtue of which it offer resistance to shear stresses.

It is caused due to cohesion and molecular interaction between the fluid layers. 

In other words viscosity is a measure of resistance to relative translation motion of adjacent layer. 

Eg:-  coltar and bitumen or mercury are highly viscous whereas, water and alcohal have very low viscosity. 

• When a liquid flows over a solid surface the velocity is not uniform at any cross- section, velocity if the layer in contact with solid surface is zero and the velocity of the layers goes on increasing. The layer far away from solid surface has maximum velocity. 
• Let us consider two layers PQ and RS at a distance dy apart and moving with velocity u and u+du respectively. 
• The upper layer drag the lower layer by applying a force F and lower layer restrict the motion of upper layer by applying an equal and opposite force. 
• Hence, two equal and opposite force induce a shear resistance Tau ( τ ) between two layers. 

                             τ = F/A

• The shear resistance or shear stress developed between two layers is found to be proportional to the rate of change of velocity in a direction perpendicular to the layers with respect to distance y.

             

                     τ ∝ du/dy

     

                  τ = µ × du/dy.                      -------   i.

Where, 

            µ =  constant of proportionality and is also known as dynamic viscosity or absolute viscosity or simple viscosity.

              du/dy is known as velocity profile. And its unit is sec^-1.

• Eqn 1st is also known as Newton's Law of Viscosity. 

Kinematic viscosity:-

Kinematic viscosity is the ratio if dynamic viscosity to the mass density.

It is denoted by nu( v ).

        v = dynamic viscosity / density 

           = µ /  ρ .

 S.I. unit = m^2/ sec

 M.K.S unit = m^2/ sec

C.G.S unit = cm^2/ sec.