• Fluid mechanics is the branch of science which deals with behavior of fluid (gaseous or liquid).
• Fluid Mechanics Divided into:

Physical Properties of Liquid

1. Density or Mass Density:

2. Specific Weight or Weight Density

3. Specific Volume

4. Specific Gravity or Relative Density

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 the fluid.

Types of Viscosity:

1. Dynamic Viscosity
2. Kinematic Viscosity

1. Dynamic Viscosity

It is defined as the resistance offered to a layer of fluid when it moves over another layer of fluid.

 Its unit is Ns/m² .

2. Kinematic Viscosity

It is defined as the ratio of dynamic viscosity to density (mass-density) of a fluid. Its unit is m2/s

Mathematically,

Kinematic Viscosity (Ƞ) =(Dynamic Viscosity(µ))/(Density(ρ))

Note: 1 Stoke = 10^-4  m²/s

Types of Fluid

                   Fluid Types

1. Ideal Fluid

• A fluid which is incompressible and having no viscosity is known as an ideal fluid. It is only an imaginary fluid as all the fluids which exist have some viscosity.

2.  Ideal Plastic Fluid

• A fluid which follows Newton’s law of viscosity.
• Example: Toothpaste can be considered ideal plastic fluid.  

3. Real Fluid

• A fluid which possesses viscosity is known as real fluid.
• All the fluids in actual practice are real fluid.  
• Example: Water, Air etc.

4. Newtonian Fluid

• A real fluid in which shear stress is directly proportional to the rate of shear strain or velocity gradient is known as Newtonian fluid.
• Example: Water, Kerosene, Benzene etc.   

5. Non-Newtonian Fluid

• A real fluid in which shear stress is not directly proportional to the rate of shear strain or velocity gradient is known as a Non-Newtonian fluid.
• Example: Ink, Blood, Honey etc.

6. Incompressible Fluid

• A fluid in which the density of fluid does not change with change in external force or pressure is known as incompressible fluid. All liquid are considered in this category.

7. Compressible Fluid

• A fluid in which the density of fluid changes with change in external force or pressure is known as compressible fluid. All gases are considered in this category.

Graphical representation of different fluids:

Source: https://mechanicalnotes.com/fluid-definition-fluid-mechanics-classification-properties-and-difference/

Tabular representation of fluid types:

Concept of continuum in fluid mechanics

Source: https://en.wikiversity.org/wiki/File:Continuum_assumption_sketch.png

Concept of control volume in fluid mechanics

Control volume is a volume in space of special interest for particular analysis. The surface of the control volume is referred as a control surface and is a closed surface. The surface is defined with relative to a coordinate system that may be fixed, moving or rotating. The control volume may be infinitesimally small or may be large and infinite size. The quality of matter and its identity in control volume may change with time but size and shape of control volume is fixed.

Example: Turbines, Compressors, Nozzle, Diffuser, Pumps etc.

Vapour Pressure and Cavitation

Vapour Pressure

• Vapour pressure is the pressure exerted by the vapour on a liquid.

Consider a liquid which is restricted in a closed vessel. Assume that the temperature of liquid is 20⁰ C and pressure is atmospheric. Then the liquid will vaporise at 100⁰ C  . When it vaporise the molecule escape from the free surface of the liquid. These vapour molecules gets collected in the space between the free liquid surface and top of the vessel. The collection of vapours exerts a pressure on the liquid surface. This pressure is known as vapour pressure.

Source: https://www.hkdivedi.com/2017/12/vapour-pressure-and-cavitation.html

Cavitation

• Cavitation is a phenomenon when liquid passes from low pressure region to high pressure region.

• Consider a flowing liquid in a system and if the pressure at any point in this flowing liquid becomes equal to or less than the vapour pressure, the vaporization of the liquid starts. The bubbles of the vapour are carried by flowing liquid into the region of the high pressure where it collapse and give rise to high impact pressure.

• Due to the pressure developed by collapsing bubbles which so high that the material from the adjoining boundaries gets eroded and cavities are formed on them. This process is known as cavitation.

Newton’s Law of Viscosity

Consider two solid plates separated by a fluid body. Keeping lower plate fixed. The upper plate is applied with a force ‘F’ in x-direction which gives velocity ‘V’.

The experiment shows that:

• F α A where, A is surface area of plate in contact with liquid.
• F α V where, V is velocity.
• F α 1/y where, y is separation of two plates.

Now,

F α (AV)/y

Or, F = µ (AV)/y     {where, µ is called coefficient of dynamic viscosity}

Or, (F)/A = µ(V)/y

Ʈ = µ (V)/y

Cohesion and Adhesion

Cohesion

Cohesion refers to the attraction of molecules for other molecules of the same kind and water molecule have strong cohesive force thanks to their ability to form hydrogen bond with one another. Also, cohesive forces are responsible for surface tension.

Source: https://www.usgs.gov/special-topic/water-science-school/science/adhesion-and-cohesion-water?qt-science_center_objects=0#qt-science_center_objects

Adhesion

Adhesion is the attraction of molecule of one kind for molecules of a different kind, and it can be quite strong for water, especially with other molecules bearing positive or negative changes.

Surface tension

• Surface tension is defined as a tensile force acting on the surface of a liquid in contact with air (gas) or between two immiscible liquid.

• It is denoted by ‘σ’ and its unit is N/m .

Source: http://www.ramehart.com/surface_tension.htm

Surface Tension on Liquid Droplet

Source: https://www.eeeguide.com/surface-tension/

Tensile force = Surface tension * Circumference

Or, Tensile force =  σ*π d

Pressure force = P *  π/4 d²

At equilibrium,

 σ*π* d = P *  π/4 d²

Or,  σ =  (P *  π/4 d²) / πd

  Or,  σ =  Pd / 4

Surface Tension on a Hollow Bubble

Source: https://link.springer.com/article/10.1007/s00162-020-00517-z

Tensile force = 2*(Surface tension * Circumference)

Or, Tensile force = 2* (  σ* πd)

Pressure force = P *π/4 *  d²

At equilibrium,

2* (  σ* π d) = P * π/4 * d²

 σ=   Pd/8

Surface Tension on Liquid Jet

Source: https://www.chegg.com/homework-help/fundamentals-of-fluid-mechanics-7th-edition-chapter-1-problem-121p-solution-9781118116135

Tensile force = σ * 2L

Pressure force = P*L*d

At equilibrium,

σ* 2L= P*L*d

Or, σ  =   (P*L*d)/2L          

 σ =  Pd/2  

Capillarity or Meniscus effect

The phenomenon of rise or fall of a liquid in a small diameter tube is known a capillarity or meniscus effect.

Capillary Rise

It is only in wetting liquid i.e. whose adhesion force is greater. Example: Water.

Source: https://socratic.org/questions/5a5349317c01493f36fa0910

Capillary fall

It is only in non-wetting liquids i.e. inter-molecular force is greater.

Example: Mercury.

Source: https://www.hkdivedi.com/2017/12/capillarity-capillary-action-and.html

Hydrostatic force = Pressure * Area

Or, Hydrostatic force = ρgh*π/4 * d²

Tensile force = Surface tension * Circumference *

Or, Tensile force =σ * πd * cosθ

At equilibrium condition,

ρgh*π/4 * d²  = σ * πd * cosθ

Or, h =(σ * πd * cosθ)/ρg*π/4 * d²

 h=(4σ * πd * cosθ)/ρg

Capillary rise or fall between two vertical parallel plates

Source: https://www.sciencedirect.com/science/article/abs/pii/S0021979715301661

References: 1. A text book of fluid mechanics and hydraulic machines, Dr. RK Bansal, (2008), Laxmi publication(P) LTD.

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