Introduction to fluid Mechanics

Fluid mechanics is defined as branch of science which studies mechanics of fluid and forces on them. It is also defined as branch of science which deals with fluids which at rest or in motion.

Following are the main branches of fluid mechanics
I. Fluid statics
Fluid statics is defined as branch of science which deals with fluid which is at rest.
II. Fluid dynamics

Fluid dynamics is defined as branch of science which deals with forces acting on fluid which is in motion.
There are two types of fluid. One is liquid and other are gases. Generally liquid has called as incompressible fluid and gas has compressible.

Fluid Properties

Following are the basic fluid properties

I. Density – Density is defined as ratio of mass and volume of fluid.
Density is denoted by ‘ρ’
Formula of density = Mass/Volume
Unit of density – kg/m3

II. Viscosity – Viscosity is defined as property of fluid that is resist to shear force on it. Because of viscosity fluid offers resistance to one layer over another adjacent layer.
Viscosity denoted by ‘µ’.
Unit of viscosity is ‘m2/s’.

III. Temperature – Temperature is defined as property of fluid that is define the degree of hotness or coldness fluid.
Temperature is denoted by ‘T’.
Unit of temperature is ‘°C’.

IV. Pressure – Pressure is the ratio of force and unit area of fluid.
Pressure is denoted by ‘P’.
Formula of force, P = F/A
Unit of pressure is ‘N/m2’

V. Specific volume – Specific volume is ratio of volume of fluid and occupied per unit mass.
Specific volume denoted by ‘v’
Formula of Specific volume (v) = V/m
Unit of Specific volume is ‘m3/kg’

VI. Specific weight – Specific weight is defined as weight possessed by per unit volume.
Specific weight denoted by ‘w’
Formula of specific weight (w) = W/V
Unit of specific weight is ‘N/m3’

VII. Specific gravity – Specific gravity is defined as ratio of specific weight of given fluid and specific weight of standard fluid.
Specific gravity denoted by ‘S’
Formula of specific gravity (S) = Specific weight of given fluid/Specific weight of standard fluid
It has no unit.

Fluid Statics

Fluid statics is branch of fluid mechanics that deals with forces acting on fluid at rest.
3.1 Pascal’s law – Pascal’s law states that pressure at any point of static fluid equal towards all directions in plane.

As shown in fig 3.1.1, when force applied on piston 1 it transmits force from static fluid and force applied on piston 2 as per Pascal’s law of static fluid.

Applications of fluid statics
I.  It is useful for hydraulic press and hydraulic jack.
II. It is applied in hydraulic braking system
III. This law is applicable for manometers and used to measure pressure differences
IV. It can be useful for dams
Following is one example applications of fluid static
3.2 Manometer -

Manometer is device used to check pressure difference at any point of fluid. It is used measure pressure of air and gases.

Buoyancy

Buoyancy is defined as force exerted by the fluid in upward direction on the immersed body. It is denoted by ‘B’ or FB. SI unit of buoyancy is N

Buoyancy is depend on differences between pressure acting of different sides of immersed body.
Archimedes principle -   Archimedes principle states that magnitude of buoyant force is equal to weight of fluid it displaces

                                  B = ρ x g x V displaced

As per formula following factors affect on buoyancy.
I. Density of fluid
II. Volume of fluid displayed
III. Local acceleration due to gravity

Internal Flow

There are following types of fluid flow.

I. Steady and Un-steady flow – 
a) Steady flow is defined as flow in which volume of flowing fluid remains constant at any point of flow.
b) Un-steady flow is defined as flow in which volume of flow varies at various point of flow.

II. One, Two and Three dimensional flow – 
a) One dimensional flow – One dimensional flow is defined as flow in which flow parameters expressed as functions of time and one space coordinate only.
b) Two dimensional flow – Two dimensional flow is defined as flow in which parameters expressed as functions of time and two space coordinate.
c) Three dimensional flow – Three dimensional flow is defined as flow in which hydrodynamic parameters functions of time and three space coordinates.

III. Laminar and turbulence flow – 
a) Laminar flow – Laminar flow is defined as flow in which fluid flows in parallel layer and there are no disturbance between layers.
b) Turbulence flow – Turbulence flow is defined as flow in which fluid not travel in layers and it is mixing across the tube.

IV. Uniform and Non-uniform flow – 
a) Uniform flow – Uniform flow is defined as flow in which fluid does not change magnitude of velocity and direction of flow.
b) Non-uniform flow – Non-uniform flow is defined as flow in which fluid changes its direction and velocity at any point.

V. Rotational and Irrotational flow – 
a) Rotational flow – If there are angular momentum of the fluid about any point known as rotational flow.
b) Irrotational flow – If there are no angular momentum of fluid about any point known as Irrotational flow.

VI. Compressible and Incompressible flow – 
a) Compressible flow – Compressible flow is defined as flow in which fluid changes density when force applied on it.
b) Incompressible flow – Incompressible flow is defined as flow in which fluid does not changes its density when force applied on it.

Bernoulli’s Equation

Bernoulli’s principle states that speed of moving fluid increases when the pressure within fluid decreases

Bernoulli’s formula – 
  p + 1/2(ρV2) + (ρ x g x h) = constant
In above formula of Bernoulli’s equation,
 p = Pressure
ρ = Density
V = Velocity
h = Elevation


Example –
I. Venturimeter 
This is restriction type flow meter. Venturimeter works on Bernoulli’s principle. Venturi converts pressure energy into kinetic energy. It helps to calculate flow energy at discharge.

As we see in diagram 10.1.2, Venturimeter consist following parts
a) Converging cone
b) Throat
c) Diverging cone
d) Manometer

Notations in diagram
a) D = Diameter of first pipe
b) D = Diameter of second pipe
c) P1 = Pressure at first pipe
d) P2 = Pressure at second pipe
e) h = Manometric deflection

Applications pf venturimeter,
a) It is widely used in waste water treatment
b) It is also used to measure fluid velocity