Fundamental Concepts of Fluid Mechanics

·         Mechanics : Deals with action of forces on bodies at rest or in motion.

·         State of rest and Motion: They are relative and depend on the frame of reference.  If the position with reference to frame of reference is fixed with time, then the body is said to be in a state of rest.  Otherwise, it is said to be in a state of motion.

·         Scalar and heater quantities: Quantities which require only magnitude to represent them are called scalar quantities.  Quantities which acquire magnitudes and direction to represent them are called vector quantities.

Eg: Mass, time internal, Distance traveled à Scalars

            Weight, Displacement, Velocity à Vectors

·         Velocity and Speed: Rate of displacement is called velocity and Rate and distance traveled is called Speed.

Unit: m/s

·         Acceleration: Rate of change of velocity is called acceleration. Negative acceleration is called retardation.

·         Momentum: The capacity of a body to impart motion to other bodies is called momentum.

The momentum of a moving body is measured by the product of mass and velocity the moving body

Momentum = Mass x Velocity

Unit: Kg m/s

·       Newton’s first law of motion: Every body continues to be in its state of rest or uniform motion unless compelled by an external agency.

·       Inertia: It is the inherent property the body to retain its state of rest or uniform motion.

·       Force: It is an external agency which overcomes or tends to overcome the inertia of a body.

·       Newton’s second law of motion: The rate of change of momentum of a body is directly proportional to the magnitudes of the applied force and takes place in the direction of the applied force.

·       Mass:   Measure of amount of matter contained by the body it is a scale of quantity.

                        Unit: Kg.   

                                                                   

·       Weight:  Gravitational force on the body. It is a vector quantity.

                        F = ma

                        W = mg

                        Unit: newton (N)                    g = 9.81 m/s²

·       Volume:  Measure of space occupied by the body.

                        Unit: m³

                                1 m³ = 1000 litres

·       Work:  Work done = Force x Displacement  à Linear motion.

                  Work done = Torques x Angular displacement  à Rotatory motion.

Unit: Nm or J

·       Energy:  Capacity of doing work is called energy.

Unit: Nm or J

FLUID MECHANICS

·       Matter: Anything which possess mass and requires space to occupy is called matter.

·       States of matter:

Matter can exist in the following states

¨      Solid state.

¨      Fluid state.

¨      Solid state: In case of solids intermolecular force is very large and hence molecules are not free to move. Solids exhibit definite shape and volume. Solids undergo certain amount of deformation and then attain state of equilibrium when subjected to tensile, compressive and shear forces.

¨      Fluid State: Liquids and gases together are called fluids. Incase of liquids Intermolecular force is comparatively small. Therefore liquids exhibit definite volume. But they assume the shape of the container

            Liquids offer very little resistance against tensile force.  Liquids offer maximum resistance against compressive forces. Therefore, liquids are also called incompressible fluids. Liquids undergo continuous or prolonged angular deformation or shear strain when subjected to tangential force or shear force. This property of the liquid is called flow of liquid. Any substance which exhibits the property of flow is called fluid. Therefore liquids are considered as fluids.

            In case of gases intermolecular force is very small. Therefore the molecules are free to move along any direction. Therefore gases will occupy or assume the shape as well as the volume of the container.

         Gases offer little resistance against compressive forces. Therefore gases are called compressible fluids. When subjected to shear force gases undergo continuous or prolonged angular deformation or shear strain. This property of gas is called flow of gases. Any substance which exhibits the property of flow is called fluid. Therefore gases are considered as fluids.

FLUID MECHANICS

Fundamental Concepts:

·         Mechanics : Deals with action of forces on bodies at rest or in motion.

·         State of rest and Motion: They are relative and depend on the frame of reference.  If the position with reference to frame of reference is fixed with time, then the body is said to be in a state of rest.  Otherwise, it is said to be in a state of motion.

·         Scalar and heater quantities: Quantities which require only magnitude to represent them are called scalar quantities.  Quantities which acquire magnitudes and direction to represent them are called vector quantities.

Eg: Mass, time internal, Distance traveled à Scalars

            Weight, Displacement, Velocity à Vectors

·         Velocity and Speed: Rate of displacement is called velocity and Rate and distance traveled is called Speed.

Unit: m/s

·         Acceleration: Rate of change of velocity is called acceleration. Negative acceleration is called retardation.

·         Momentum: The capacity of a body to impart motion to other bodies is called momentum.

The momentum of a moving body is measured by the product of mass and velocity the moving body

Momentum = Mass x Velocity

Unit: Kg m/s

·       Newton’s first law of motion: Every body continues to be in its state of rest or uniform motion unless compelled by an external agency.

·       Inertia: It is the inherent property the body to retain its state of rest or uniform motion.

·       Force: It is an external agency which overcomes or tends to overcome the inertia of a body.

·       Newton’s second law of motion: The rate of change of momentum of a body is directly proportional to the magnitudes of the applied force and takes place in the direction of the applied force.

·       Matter: Anything which possess mass and requires space to occupy is called matter.

·       States of matter:

Matter can exist in the following states

¨      Solid state.

¨      Fluid state.

¨      Solid state: In case of solids intermolecular force is very large and hence molecules are not free to move. Solids exhibit definite shape and volume. Solids undergo certain amount of deformation and then attain state of equilibrium when subjected to tensile, compressive and shear forces.

¨      Fluid State: Liquids and gases together are called fluids. Incase of liquids Intermolecular force is comparatively small. Therefore liquids exhibit definite volume. But they assume the shape of the container

            Liquids offer very little resistance against tensile force.  Liquids offer maximum resistance against compressive forces. Therefore, liquids are also called incompressible fluids. Liquids undergo continuous or prolonged angular deformation or shear strain when subjected to tangential force or shear force. This property of the liquid is called flow of liquid. Any substance which exhibits the property of flow is called fluid. Therefore liquids are considered as fluids.

            In case of gases intermolecular force is very small. Therefore the molecules are free to move along any direction. Therefore gases will occupy or assume the shape as well as the volume of the container.

            Gases offer little resistance against compressive forces. Therefore gases are called compressible fluids. When subjected to shear force gases undergo continuous or prolonged angular deformation or shear strain. This property of gas is called flow of gases. Any substance which exhibits the property of flow is called fluid. Therefore gases are considered as fluids. 

Classification of Flows

1. Steady and unsteady flows:

A flow is said to be steady if the properties (P) of the fluid and flow do not change with time (t) at any section or point in a fluid flow.

A flow is said to be unsteady if the properties (P) of the fluid and flow change with time (t) at any section or point in a fluid flow.

Eg: Flow observed at a dam section during rainy season, wherein, there will be lot of inflow with which the flow properties like depth, velocity etc.. will change at the dam section over a period of time representing it as unsteady flow.

2. Uniform and non-uniform flows:

A flow is said to be uniform if the properties (P) of the fluid and flow do not change (with direction) over a length of flow considered along the flow at any instant.

A flow is said to be non-uniform if the properties (P) of the fluid and flow change (with direction) over a length of flow considered along the flow at any instant.

Eg: Flow observed at any instant, at the dam section during rainy season, wherein, the flow varies from the top of the overflow section to the foot of the dam and the flow properties like depth, velocity etc., will change at the dam section at any instant between two sections, representing it as non-uniform flow.

3. One, two and three dimensional flows:

Flow is said to be one-dimensional if the properties vary only along one axis / direction and will be constant with respect to other two directions of a three-dimensional axis system.

Flow is said to be two-dimensional if the properties vary only along two axes / directions and will be constant with respect to other direction of a three-dimensional axis system.

Flow is said to be three-dimensional if the properties vary along all the axes / directions of a three-dimensional axis system.

4. Laminar and Turbulent flows:

When the flow occurs like sheets or laminates and the fluid elements flowing in a layer does not mix with other layers, then the flow is said to be laminar. The Reynolds number (Re) for the flow will be less than 2000.

When the flow velocity increases, the sheet like flow gets mixed up and the fluid elements mix with other layers there by causing turbulence. There will be eddy currents generated and flow reversal takes place. This flow is said to be Turbulent. The Reynolds number for the flow will be greater than 4000.

For flows with Reynolds number between 2000 to 4000 is said to be transition flow.

5. Compressible and Incompressible flows:

Flow is said to be Incompressible if the fluid density does not change (constant) along the flow direction and is Compressible if the fluid density varies along the flow direction

r = Constant (incompressible) and r ¹ Constant (compressible)

6. Rotational and Irrotational flows:

Flow is said to be Rotational if the fluid elements does not rotate about their own axis as they move along the flow and is Rotational if the fluid elements rotate along their axis as they move along the flow direction

KINEMATICS OF FLUID FLOW

Fluid kinematics refers to the features of a fluid in motion. It only deals with the motion of fluid particles without taking into account the forces causing the motion. Considerations of velocity, acceleration, flow rate, nature of flow and flow visualization are taken up under fluid kinematics.

A fluid motion can be analyzed by one of the two alternative approaches, called Lagrangian and Eulerian.

In Lagrangian approach, a particle or a fluid element is identified and followed during the course of its motion with time.

Difficulty in tracing a fluid particle (s) makes it nearly impossible to apply the Lagrangian approach. The alternative approach, called Eulerian approach consists of observing the fluid by setting up fixed stations (sections) in the flow field.

Motion of the fluid is specified by velocity components as functions of space and time. This is considerably easier than the previous approach and is followed in Fluid Mechanics.

Eg: Observing the variation of flow properties in a channel like velocity, depth etc, at a section.

Fluid Mechanics Basic Definitions

• Mechanics : Deals with action of forces on bodies at rest or in motion.

• Velocity and Speed: Rate of displacement is called velocity and Rate and distance traveled is called Speed.

Unit: m/s

• Acceleration: Rate of change of velocity is called acceleration. Negative acceleration is called retardation.

• Momentum: The capacity of a body to impart motion to other bodies is called momentum.

The momentum of a moving body is measured by the product of mass and velocity the moving body

Momentum = Mass x Velocity

Unit: Kg m/s

• Newton’s first law of motion: Every body continues to be in its state of rest or uniform motion unless compelled by an external agency.

• Inertia: It is the inherent property the body to retain its state of rest or uniform motion.

• Force: It is an external agency which overcomes or tends to overcome the inertia of a body.

• Newton’s second law of motion: The rate of change of momentum of a body is directly proportional to the magnitudes of the applied force and takes place in the direction of the applied force.

• Mass: Measure of amount of matter contained by the body it is a scale of quantity.

Unit: Kg.

• Weight: Gravitational force on the body. It is a vector quantity.

F = ma

W = mg

Unit: newton (N) g = 9.81 m/s2

• Volume: Measure of space occupied by the body.

Unit: m3

1 m3 = 1000 litres

• Work: Work done = Force x Displacement  Linear motion.

Work done = Torques x Angular displacement  Rotatory motion.

Unit: Nm or J

• Energy: Capacity of doing work is called energy.

Unit: Nm or J

Potential energy = mgh

Kinetic energy = ½ mv2 or ½ mrw2

Power: Rate of doing work is called Power.

• Matter: Anything which possess mass and requires space to occupy is called matter.

• States of matter:

Matter can exist in the following states

• Solid state.

• Fluid state.

• Solid state: In case of solids intermolecular force is very large and hence molecules are not free to move. Solids exhibit definite shape and volume. Solids undergo certain amount of deformation and then attain state of equilibrium when subjected to tensile, compressive and shear forces.

• Fluid State: Liquids and gases together are called fluids. Incase of liquids Intermolecular force is comparatively small. Therefore liquids exhibit definite volume. But they assume the shape of the container Liquids offer very little resistance against tensile force. Liquids offer maximum resistance against compressive forces. Therefore, liquids are also called incompressible fluids. Liquids undergo continuous or prolonged angular deformation or shear strain when subjected to tangential force or shear force. This property of the liquid is called flow of liquid. Any substance which exhibits the property of flow is called fluid. Therefore liquids are considered as fluids.

In case of gases intermolecular force is very small. Therefore the molecules are free to move along any direction. Therefore gases will occupy or assume the shape as well as the volume of the container.

Gases offer little resistance against compressive forces. Therefore gases are called compressible fluids. When subjected to shear force gases undergo continuous or prolonged angular deformation or shear strain. This property of gas is called flow of gases. Any substance which exhibits the property of flow is called fluid. Therefore gases are considered as fluids.