Fluid Mechanics : Fluid Properties Study Notes

By Akhil Gupta|Updated : November 27th, 2021

Fluid Mechanics is very important subject from exam point if view. In this artical we will discuss the basic and most important concept of fluid properties.                                                                                                                                                                                                                                                                                                                              

Fluid Properties

Ideal Fluid

Characteristics of Ideal Fluid

  • The ideal fluid has zero viscosity and zero surface tension.
  • Ideal fluid is incompressible.
  • There is no ideal fluid but air and water considered 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 as follows:

(1). Intensive properties:

  • An intensive property is a property of matter that does not change as the number of matters changes.

  • Example: Temperature, pressure, density, Boiling and Melting point, refractive index, etc.

(2). Extensive properties

  • The extensive property is dependent on the amount of matter that is present in the system and it is considered additive for subsystems.
  • Example – Total mass, Total volume, Total momentum, etc.

Mass Density (ρ):

  • It is the mass of fluid per unit volume at a given temperature and pressure.
  • Mass density is a function of Temperature and Pressure.
  • Mass density for gases directly proportional to pressure and inversely proportional to temperature.
    Since for an ideal gas:
    P =ρRT
    byjusexamprep
  • Practically, Mass density for liquid is content or little variable with pressure but inversely proportional to temperature.
    byjusexamprep
    Unit: byjusexamprep
  • At 4°C and 1 atm pressure: ρwater = 1000 kg/m= 1 g/cc

Specific weight or weight density [w or r]:

  • The specific density of a fluid is defined as the ratio of the weight of the fluid to its volume of the fluid.

    byjusexamprep
    byjusexamprep
    Thus, w = ρg  N/m3
    Where: g → acceleration due to gravity.
    Note: g (acceleration due to gravity) is a function of position on earth (spatial Parameter), so w is also a variable but consider constant [due to little variation].
  • w for water at 4°C and 1 atm = 1000 × 9.8 N/m= 9.8 kN/m3

Specific Volume

  • Specific volume is Reciprocal of specific mass.
  • The volume of fluid per unit mass
  • Unit of specific volume: byjusexamprep

Specific Gravity or Relative Density

  • Specific gravity is the ratio of the specific weight of the fluid to the specific weight of the standard fluid.
    byjusexamprep
  • Standard fluid
    • Liquid – water at 4ºC
    • Gas – Hydrogen or Air
  • Specific gravity has no unit or independent form system of unit
  • Relative density is the ratio of the density of a fluid to the density of another fluid (not necessarily water).
  • Whereas specific gravity is the ratio of the density of a fluid to the density of the standard fluid (i.e., water at 4ºC). 
  • For taking water as standard fluid: byjusexamprep

Viscosity

  • Viscosity is a quantitative measure of the internal resistance of a fluid to flow.
  • Viscosity relates to the strain rate and local shear stresses in moving fluid.
  • Viscosity is a measure of the resistance offered by a fluid layer to an adjacent layer of fluid at motion.
  • Viscosity is due to the internal friction force caused by cohesive force between fluid molecules (dominant in fluid) and molecular momentum transfer between particles due to collision (dominant in gases).

 

 

Newton's Law of viscosity:

  • The rate of deformation is proportional to shear stress, so:
    byjusexamprep
  • The velocity gradient is proportional to Shear stress:
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  • μ → Absolute viscosity or Dynamic viscosity or Coefficient of viscosity.
  • Unit:
    byjusexamprep
    byjusexamprep
    byjusexamprep
    Note: Viscosity of water at 20°C = 1 centipoise
  • Poise is a CGS unit: poise = Dyne-s/cm2
    byjusexamprep

Kinematic Viscosity

  • Kinematic viscosity is the ratio of dynamic viscosity (μ) and density (ρ).
  • Kinematic viscosity denoted by (ν):
    byjusexamprep

Units:

  •  byjusexamprep
  • byjusexamprep

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

Newtonian Fluid:

  • Fluid follows Newton’s law of viscosity.
  • Example: Water, petrol, diesel, alcohol, all gases, etc.

Non-Newtonian Fluid:

  • Thixotropic {pseudo–plastic}
    • The slope of the curve between “shear stress - deformation rate” decreases with increasing in deformation rate.
    • Also known as “shear thinning” fluids
    • Example: Printer ink
  • Dilatant:
    • Slope of shear “shear stress – deformation rate curve” increases with the rate of deformation.
    • Example – Quicksand
    • Also known as "shear thickening" fluid.
  • Ideal Plastic / Bingham Plastic:
    • Having initial yield stress and then exhibit a linear relationship between byjusexamprep
    • Example: Toothpaste, drilling mud, etc.
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The 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, the cohesive force between molecules decreasing so the viscosity of liquids decreasing with increasing temperature.
    byjusexamprep

Surface Tension

  • Reason: Cohesive force between the molecules.
  • Definition: Force required to maintain the unit length of the film in equilibrium, i.e., force per unit length.
  • Unit: (N/m)
  • Due to surface tension
    • Increase in the internal pressure of droplet.
    • The tendency of the liquid droplet to attain minimum surface area at a given volume, only, for this reason, the shape of the droplet is “Sphere”.

The dependency of Surface Tension:

Temperature

  • If temperature increases, the cohesive force decreases, and this will result in a decrease in surface tension.
  • If the continuous decrease in temperature takes place then surface tension becomes zero at the “critical point of temperature”.

Excess Pressure:

  • Due to surface tension pressure inside the bubble become higher than the external atmospheric pressure.
  • Excess Pressure is the difference between internal pressure (pi) and external pressure (p0). 
  • For soap bubble:
    byjusexamprep
  • For Liquid droplet:
    byjusexamprep
    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)
  • The free surface having a Concave or convex top, inside the capillaries is called meniscus.
  • The rise or fall of liquid inside the tube is due to contact angle b/w liquid surface and capillary tube.
    byjusexamprep

NOTE:

If byjusexamprep then:

  • The level of liquid inside the tube is rise.
  • The liquid is known as Wetting liquid
  • In this case: byjusexamprep

If byjusexamprep  then:

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

Φ Angle between the tangent to the liquid surface and solid surface at the contact point.

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Height of capillary rise

  • By equilibrium:
  • Upward force = Downward force (Surface tension= Weight of water)
    byjusexamprep

Observations

  • For water –glass interface
    byjusexamprep 
    So cosΦ=1 this results in:
    byjusexamprep
  • Height of capillary rise is a function of:
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  • If the diameter of the tube > 1 cm then the 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 is known as saturation temperature.

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

Vapour Pressure

  • For liquid, the pressure exerted by its vapor, in phase equilibrium with its liquid at a given temperature is known as vapor pressure.
  • Vapour pressure increases with an increase in temperature as the rate of molecules escaping the liquid surface increases.
  • The temperature at which the vapor pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere – boiling occurs.

Cavitation

  • Cavitation is a phenomenon that occurs in a liquid flow system.
  • If liquid undergoes a pressure below its vapor pressure during flow then sudden vaporization takes place and vapor bubbles formed.
  • Vapor bubbles collapse as they move from the low-pressure region to a high-pressure region, generating highly destructive pressure waves.
  • Cavitation can also occur if a liquid contains dissolved air or other gases, (Reason-Solubility decreases with decreasing pressure, and their bubbles form).
  • The risk of cavitation is greater at a higher temperature.

 

Note:

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

Bulk Modulus of Elasticity

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

Note:

K increase means Resistance to further compression increases.

  • For liquid K increases with decreases in temperature: with a 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 an increase in temperature, a collision between gas-particle increases and results in higher internal pressure so the resistance to further compression increases.

 

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