Fluid Mechanics - Kinematics of Flow and Ideal Flow

Kinematics is defined as that branch of science which deals with the motion of particles without considering the forces causing the motion. The velocity at any point in a flow field at any time is studied in this branch of fluid mechanics.

Types of Fluid Flow :-

1) Steady and Unsteady Flows :- Steady flow is defined as that type of flow in which the fluid characteristics like velocity , pressure , density etc. at a point do not change with time.
Unsteady Flow is that type of flow , in which the fluid characteristics like velocity , pressure , density etc. at a point change with respect to time.

2) Uniform and Non-Uniform Flow :- Uniform flow is defined as that type of flow in which the velocity at any given time does not Change with respect to time.
Non-uniform Flow is defined as that types of flow in which the velocity at any given time changes with respect to time.

3) Laminar And Turbulent Flow :- Laminar flow is defined as that types of flow in which the fluid particles move along a well-defined path or stream line and all the stream lines are straight and parallel.
Turbulent Flow is defined as that types of flow in which the fluid particles move in a zig-zag way. Due to the movement of fluid particles in a zig-zag way, the Eddies formation takes place which are responsible for high energy loss.

4) Compressible and Incompressible Flows :- Compressible flow is defined as that types of flow in which the density of a fluid changes from point to point or in other words the density is not constant for the fluid.
Incompressible flow is defined as that types of flow in which the density is constant for the fluid flow. Liquids are generally incompressible while gases are compressible.

5) Rotational and Irrotational Flows :- Rotational flow is defined as the that types of flow in which the fluid particles while flowing along a stream lines , also rotate about their own axis.
Irrotational flow is defined as that types of flow in which the fluid particles while flowing along a stream lines , but do not rotate about their own axis.

One-, Two-, and Three - Dimensional Flows :- One - dimensional is that types of flow in which the flow parameters such as velocity is a function of time and one space co-ordinate only , say x.
Two-dimensional flow is that types of flow in which the velocity is a function of time and two rectangular space co-ordinates say x and y.
Three-dimensional flow is that types of flow in which the velocity is a function of time and three mutually perpendicular directions.

- Rate of Flow and Discharge :- It is defined as the quantity of fluid flowing per second through a section of a pipe or a channel.

- Continuity Equation :- The equation based on the principle of conservation of mass is called continuity equation.  Thus for a fluid flowing through the pipe at all the cross-section , the quantity of fluid per second is constant.

Fluid Mechanics - Pressure and its Measurement in terms of fluid flow

Consider a small area dA in large mass of fluid. If the fluid is stationary, than the force exerted by surrounding fluid on the area dA will always be perpendicular to the surface dA. If the F force acting on an area dA than the pressure is defined as the force (F) per unit area is known as the intensity of pressure.

Pascal's Law :- It state that the pressure or intensity of pressure at a point in a static fluid is equal in all directions.

- Absolute Pressure :- Absolute pressure is defined as the pressure which is measured with the reference to absolute vacuum pressure.

- Gauge Pressure :- Gauge Pressure is defined as the pressure which is measured with the help of a pressure measuring instrument , in which the atmospheric pressure is taken as a datum. The atmospheric pressure on the scale is marked as a zero.

- Vacuum Pressure :- Vacuum Pressure is defined as the pressure below the atmospheric pressure.
The relationship between the absolute pressure, gauge Pressure and vacuum pressure are :-

1) Absolute Pressure = Atmospheric Pressure + Gauge Pressure

2) Vacuum Pressure = Atmospheric Pressure - Absolute Pressure

- Measurement Of Pressure :- The pressure of a fluid is measured by the following devices :-

1. Manometers :- Manometers are defined as the devices used for measuring the pressure at a point in a fluid by balancing the column of fluid by the same or another column of the fluid. They are further classified as :-

(A) Simple Manometers :- A simple manometer consist of a glass tube having a one of its end connected to a point where pressure is to be measured and other end remains open to the atmosphere. Common types of simple manometers are :

* Piezometer
* U-tube Manometer
* Single Column Manometer

(B) Differential Manometers :- Differential manometer are the devices used for measuring the difference of pressure between two points in a pipe or in two different pipe. A differential manometer consist of a U-tube , containing a heavy liquid , whose two ends are Connected to a points , whose difference of pressure is to be measured. Most commonly types of differential Manometers are :

* U-tube differential manometer
* Inverted U-tube differential manometer

2. Mechanical Gauges :- Mechanical gauges are defined as the device used for measuring the pressure by balancing the fluid column by the spring or dead weight. The commonly used mechanical pressure gauges are :

(A) Diaphragm Pressure Gauge.
(B) Bourdon tube pressure gauge.
(C) Dead - Weight pressure Gauge.
(D) Bellows pressure Gauge.

Fluid Mechanics

Fluid Mechanics :- Fluid mechanics is that branch of science which deals with the behavior of fluids at a rest as well as in motion. Fluid Mechanics is that science which study the static, kinematic and dynamic behavior of fluids.

Properties of Fluids :-

1. Density or Mass Density :- Density or mass density of a fluid is defined as the ratio of mass of a fluid to its volume . Thus the mass par units volume of a fluid is called Density or mass density. It is denoted by p (rho). It's SI units is kg per cubic meter.

2. Specific weight or weight density :- Specific weight or weight density of a fluid may be defined as a ratio of the weight of fluid to the its volume. Thus the weight per unit volume of a fluid is called specific weight or weight density. It is denoted by 'w'. It's SI unit is Newton per unit cubic meter.

3. Specific Volume :- Specific volume of a fluid is defined as the volume occupied by the volume per unit mass . Thus the volume per unit mass of a fluid is termed as specific volume. It is the reciprocal of density or mass density.

4. Specific Gravity :- Specific gravity of a fluid is defined as the ratio of density of the fluid to the density of the standard fluid. Specific gravity is a dimensionless. It is denoted by 'S'.

Viscosity :- Viscosity is defined as the properties of fluid which offers a resistance to the one layer of the fluid to the another layer of the fluid is defined as the viscosity. It is denoted by 'tau'.

Newton's law of Viscosity :- It states that the shear stress of a liquid surface is directly proportion to the rate of shear strain. The constant of proportionalty is termed as a coefficient of viscosity.

Surface Tension :- Surface tension is defined as the tensile force acting on the surface of a liquid in a contact with the gas or on the surface of miscible two liquid surface. It is denoted by sigma.

Capillarity :- Capillarity is the phenomenon of rise and fall of a liquid surface in a small tube with the adjacent general level of liquid when small tube held in a vertical position in a liquid.

Types of Fluids :-

1. Ideal Fluids :- A fluid, which is incompressible and having no viscosity . It is an imaginary fluids because all fluids have a some viscosity.

2. Real Fluids :- A fluid , which have a viscosity are termed as Real fluids. In actual all fluids are Real fluids because all fluids having some viscosity.

3. Newtonian Fluids :- A real fluid, in which shear stress is directly proportion to the rate of shear strain is termed as a Newtonian fluids.

4. Non-Newtonian Fluids :- A real fluid, in which shear stress is not directly proportional to the rate of shear strain is known as Non-Newtonian fluids.

5. Real Plastics Fluids :- A fluid , in which shear stress is more than yields value and shear stress is directly proportional to the rate of shear strain.

Bulk Modulus of Elasticity :- It is defined as the ratio of compressive stress to volumetric strain. It is denoted by 'K'.

Compressibility :- Compressibility is the reciprocal of the bulk modulus of elasticity.

Kinematic Viscosity :- It is defined as the ratio between the dynamic viscosity and density of fluid. It is denoted by the Greek symbol (v) called 'nu'.