Fluid and It’s Properties

Fluid and It’s Properties

Fluid Mechanics

• Fluid statics → Study the behaviour of fluid at rest or at motion study fluid at Rest.
• Fluid kinematics → Study of Fluid at motion without considering pressure.
• Fluid dynamic → Study of fluid at motion with considering pressure.

Fluid:

• Fluid is a substance which deforms continuously under the action of shear stress. The magnitudes of shear stress have no matter.
• Fluid- Gases and liquids
• When shear stress removes, fluid never regain its original shape.
• At rest no shear force act in liquid.
• Fluid is considered to be continuum.
• Continuum fluid- Fluid is a continuous, homogenous matter with no holes that is a continuum.
• Liquid – take shape of container form free surface.
• Gases – Cover the whole volume of container and gases doesn’t form free surface.

Ideal Fluid

Characteristics of Ideal fluid

• Fluid having zero viscosity and zero surface tension.
• Ideal fluid is incompressible.
• There is no ideal fluid but air and water considered as ideal fluid.

Real fluid

Characteristics of real fluid

• Fluid having viscosity and surface tension.
• Real fluids are compressible

Properties of Fluid

Properties of fluid are

1. Extensive
2. Intensive

Intensive properties

• Intensive properties are independent from mass of system.
• Example – Temperature, pressure, density etc.

Extensive properties

• Properties which are depends on size or extent substance.
• Example – Total mass, Total volume, Total momentum etc.

Mass Density (ρ): 

• Mass of fluid per unit volume at a given temperature and pressure.
• Mass density is function of Temperature and Pressure.
• Mass density for gases directly proportional to pressure and inversely proportional to temperature
• Practically, Mass density for liquid is content or little variable with pressure but inversely proportional to temp.
  
  At 4 c and I atm pressure ρ_water = 1000 kg/m³= 1g/cc

Specific weight or weight density [w or r]

• Weight per unit volume known as weight density.
• 
  W for water at 4°C and 1 atm = 1000 × 9.8 KN/m³= 9.8 KN/m³g → acceleration due to gravity.

Note: g (acceleration due to gravity) is function of position on earth (spatial Parameter), so w is also a variable but consider constant [due to little variation].

Specific Volume:

• Specific volume is Reciprocal of specific mass.
• Volume of fluid per unit mass
• Unit of specific volume - 

Specific Gravity or Relative Density

• Specific gravity is the ratio of specific weight of fluid the specific weight of standard fluid.
• 
• Standard fluid
  → Liquid – water
  → Gas – Hydrogen or Air
• Specific gravity have no unit or independent form system of unit
• Specific gravity = Relative density = 

Viscosity

• Viscosity is a quantitative measure of internal resistance of fluid to flow.
• Viscosity relates the strain rate and local stresses in moving fluid.
• Viscosity is measure of Resistance b/w to adjacent layer of fluid at motion.
• Viscosity is due to the internal friction force which caused by
  Cohesive force between fluid molecules.
  Molecular momentum transfer between particles due to collision.

Assume a system having fluid between two plates.

Note: Assume linear variation of velocity

dβ = Angle of deformation during ‘dt’ duration

Velocity at distance y from bottom plate   {from similar triangle }

If consider infinite small element than velocity gradient 

dx = Vdt (Displacement of point p to c during dt duration) ------- (b) eq.

Angular deformation rate is equal to velocity gradient.

According to Newton

• Rate of deformation is proportional to shear stress
  So
  
  μ → Absolute viscosity or Dynamic viscosity or Coefficient of viscosity

unit:

Note: Viscosity of water at 20°c = 1 centriplose

Kinematic Viscosity:

• Kinematic viscosity is the ratio of dynamic viscosity and density (e).
• Kinematic viscosity denoted by (ν)

Unit: 1) 

2) Stoke 

And Stoke 

Classification of fluid according to relation between shear stress and rate of deformation:

Newtonian Fluid:

• Fluid follow the newton’s law of viscosity
  
• Example - Blood

Thixotropic {pseudo –plastic}

• Slope of curve b/w “shear stress and deformation rate” is decreases with increasing in deformation rate.
• Also known as “shear thinning” fluids
• Example – Printer ink

Dilatant:

• Slope of shear “Stress – deformation rate curve” increase with rate of deformation.
• Example – Quick sand
• Also known as shear thickening fluid.

Plastic / Bingham Plastic:

• Having an initial yield stress and then exhibit a linear relationship between 
• Example – Toothpaste

Dependency of Viscosity on temperature:

For Gases:

• In gases, the molecular momentum transfer is predominant over cohesive force.
• So in gases, Viscosity is due to molecular momentum transfer
• With increasing temperature, molecular momentum transfer increases so viscosity increases.

For liquids:

• In liquids the cohesive force between molecules is predominant over molecular momentum transfer.
• With increasing temperature, cohesive force between molecules decreasing so viscosity of liquids decreasing with increasing temperature.

Surface Tension:

Reason:- Cohesive force b/w molecules.

Definition:- Force required to maintain unit length of the film in equilibrium, means force per unit length

Unit:- (N/m)

→ Due to surface tension

• Increasing internal pressure of droplet.
• Tendency of liquid droplet to attain minimum surface area at a given volume, only for this reason, shape of droplet is “Sphere”.

NOTE:-

Minimum surface area at a given volume = surface area of sphere.

Example:

 {from equilibrium in y -direction}

 

Work done, in shifting of wire at (Δn) distance

From this, surface tension defines: -

Perunit change in the surface area of the liquid.

Dependency of surface tension:-

Temperature:-

If temperature increases, cohesive force decreases and this will results in decrease in surface tension

If continuous decreasing in temperature takes place than surface tension becomes zero at “critical point of temperature”.

Additives or {impurities}

Surfactants:-

→ Reduce the surface tension

Ex. Organic solute

Some salt [NaCI] increase the surface tension

• Curved surface indicate pressure difference (mean pressure jump)
  Pressure higher on concave side (in given figure)

Pressure difference between p_i and p₀for

Soap bubble:

Droplet:

Where σ is surface tension and R is the radius of curvature for bubble or droplets

Capillary Effect:-

Reason:- Cohesive force or surface tension and Adhesive forces. (Both force responsible for Capillary effect)

• Curved free surface inside the capillaries is called meniscus.
• Rise or fall of liquid inside the tube is due to contact angle b/w liquid surface and capillary tube.

NOTE:-

if  than

• Level of liquid inside the tube is rise
• Liquid is known as Wetting liquid
• In this case:- 

if  than

• Level of liquid fall inside the tube
• liquid is known as Non-wetting liquid
• In this case:- 

 Angle b/w tangent to the liquid surface and solid surface at contact point.

Height of capillary rise:

By equilibrium:-

Upward force = Downward force (Surface tension= Weight of water)

Observations

• For water –glass interface
   So  this results in

• Height of capillary rise is a function of

• If diameter of tube > 1 cm than Capillary effect negligible

Vapour Pressure and cavitation:-

• Saturation Temperature:
  For a given pressure, the temperature at which a pure substance changes phase is known as saturation temperature
• Saturation Pressure:
  At a given temperature, the pressure at which a pure substance changes phase.

Example: at 1 atm pressure (const. pressure) saturation temperature is 100 c and at constant temp. 100 c saturation pressure for water is 1 atm.

Vapour Pressure:

• For liquid, pressure exerted by its vapour, in phase equilibrium with its liquid at a given temperature
• Vapour pressure increases [with temperature with increases and rate molecules escaping liquid surface increasing]

• When vapour pressure equal to pressure on the liquid – boiling occur.

Cavitation:

• Cavitation is a phenomenon which occurs in a liquid flow system.
• If liquid undergo pressure below vapour pressure during flow, than sudden vaporization takes place
• Vapour bubbles collapse as they are swept from the low pressure region, generating highly destructive pressure waves.
• Cavitation can also occur if a liquid contains dissolved air or other gases, {Reason-SolubilitesDecrease with decreasing pressure}
• Risk of cavitation is greater at higher temperature.

Example: Given a flow system (water) and Temperature is 36 c. Find the minimum pressure to avoid cavitation?

Solution: Minimum pressure to avoid cavitation is equal to vapour pressure of that liquid at given temperature for water

Note:

1. Partial pressure is the pressure exerted by a component in a mixture of gases.
2. for pure substance vapour pressure and saturation pressure both are equal.
3. If external pressure is equal to or less than the vapour pressure, boiling of liquid will start no matter how much temperature.

Bulk Modulus of Elasticity:

• Compressibility of liquid is measured by bulk modulus of elasticity.
• Bulk modulus is represented the compressive stress per unit volumetric strain.
• Bulk modules  k
  
• K → always positive or is a positive quantity having unit of pressure .
• Truly incompressible substance: means 
  So, K (bulk modulus) = ∞

Note:

K increase means Resistance to further compression increases.

• For liquid K increases with decreases in temperature: with decrease in temperature cohesive force between molecules increases, which results in higher resistance to further compression.
• For gases K increases with increases in temperature: With increase in temperature, collision between gas particle increases and results in higher internal pressure so the resistance to further compression increases.