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LECTURE NOTES
ON
FLUID DYNAMICS
Mr. Shiva Prasad U
Assistant Professor
Dr. Govardhan D
Professor
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Dundigal – 500043, Hyderabad
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LECTURE NOTES ON FLUID DYNAMICS, Assignments of Fluid Dynamics
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.
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LECTURE NOTES
ON
FLUID DYNAMICS
Mr. Shiva Prasad U
Assistant Professor
Dr. Govardhan D
Professor
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Dundigal – 500043, Hyderabad
MODULE - I
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 vectorquantities.
Eg: Mass, time internal, Distance traveled _ Scalars Weight, Displacement, Velocity _ Vectors
Velocity and Speed: Rate of displacement is called velocity and Rate and distance travelled 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: Kgm/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.
Energy: Capacity of doing work is called energy. Unit: Nm or J
Potential energy = mgh Kinetic energy = ½ mv^2 Power: Rate of doing work is calledPower.
Matter: Anything which possesses mass and requires space to occupy is called matter. States of matter : Matter can exist in the following states Solid state.
Solidstate: In case of solids intermolecular force is very large and hencemolecules
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 FluidState: Liquids and gases together are called fluids. Incase ofliquids Intermolecular force is comparatively small. Therefore liquids exhibit definite volume. But they assume the shape of thecontainer
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 also considered asfluids.
Branches of Mechanics:
I. Fluid Statics deals with action of forces on fluids at rest or inequilibrium.
II. Fluid Kinematics deals with geometry of motion of fluids without considering the cause of motion
Properties of fluids:
1. Mass density or Specific mass(ρ): Mass density or specific mass is the mass per unit volume of the fluid. 2. Weight density or Specific weight(ϒ): Weight density or Specific weight of a fluid is the weight per unit volume. Unit: kg/m3 or kgm
Unit: m3/kg
As the temperature increases volume increases and hence specific volume increases. As the pressure increases volume decreases and hence specific volumedecreases.
Effect of temperature on surface tension ofliquids: In case of liquids, surface tension decreases with increase in temperature. Pressure has no or very little effect on surface tension of liquids.
Problems:
- Whatisthepressureinsidethedropletofwater0.05mmindiameterat20^0 Cifthepressure outside the droplet is 103 kPa Take σ = 0.0736 N/m at 20^0 C.
- liquid bubble 2cm in radius has an internal pressure of 13Pa. Calculate the surface tension of liquid film.
Compressibility: It is the property by virtue of which there will be change in volume of fluid due to change in pressure.
Rheological classification of fluids: (Rheology _ Study of stress – strain behavior).
- Newtonian fluids: A fluid which obeys Newton’s law of viscosity i.e., t = μ. du/dy is called Newtonian fluid. In such fluids shear stress varies directly as shear strain. In this case the stress strain curve is a stress line passing through origin the slope of the line gives dynamic viscosity of the fluid. Eg: Water, Kerosene.
- Non- Newtonian fluid: A fluid which does not obey Newton’s law of viscosity is called non- Newton fluid. For suchfluids,
Ideal fluid: Any fluid for which viscosity is assumed to be zero is called Ideal fluid. Forideal fluid t = 0 for allvaluesof du/dy
5. Real fluid :
Any fluid which posses certain viscosity is called real fluid. It can be Newtonian or non – Newtonian, thixotropic or ideal plastic.
PRESSURE AND ITS MEASUREMENTS:
Fluid is a state of matter which exhibits the property of flow. When a certain mass of fluids is held in static equilibrium by confining it within solid boundaries, it exerts force along direction perpendicular to the boundary in contact. This force is called fluid pressure.
- Pressuredistribution: It is the variation of pressure over the boundary in contact with the fluid. There are two types of pressure distribution.
a) Uniform Pressuredistribution.
b) Non-Uniform Pressuredistribution.
(a) Uniform Pressuredistribution:
If the force exerted by the fluid is same at all the points of contact boundary then the pressure distribution is said to be uniform.
Absolute pressure and GaugePressure: Absolute pressure at a point is the intensity of pressure at that point measured with reference to absolute vacuum or absolute zero pressure. Absolute pressure at a point can never be negative since there can be no pressure less than absolute zero pressure. Absolute pressure at ‘A’
Absolute pressure at a point is the intensity of pressure at that point measured with reference to absolute vacuum or absolute zero pressure. Absolute pressure at a point can never be negative since there can be no pressure less than absolute zero pressure. If the intensity of pressure at a point is measured with reference to atmospheric pressure, then it is called gauge pressure at that point. Gauge pressure at a point may be more than the atmospheric pressure or less than the atmospheric pressure. Accordingly gauge pressure at the point may be positive or negative. Negative gauge pressure is also called vacuum pressure.
From the figure, It is evident that, Absolute pressure at a point = Atmospheric pressure ± Gauge pressure. NOTE: If we measure absolute pressure at a Point below the free surface of the liquid, then, p = g. Y + patm If gauge pressure at a point is required, then atmospheric pressure is taken as zero, then, p = g. Y Pressure Head It is the depth below the free surface of liquid at which the required pressure intensity is available. P = gh h = P/ g For a given pressure intensity ‘h’ will be different for different liquids since, ‘g’ will be different for different liquids. Whenever pressure head is given, liquid or the property of liquid like specify gravity, specific weight, mass density should be given. Eg: (i) 3m ofwater (ii) 10m of oil of S =0.8. (iii) 3m of liquid of g = 15kN/m (iv) 760mm ofMercury. (v) 10m _ notcorrect. NOTE:
1. To convert head of a liquid to head of anotherliquid.
2. Intensity of pressure required at a points is 40kPa. Find corresponding headin
(a) water (b) Mercury (c) oil of specificgravity-0.9.
4. Standard atmospheric pressure is 101.3 kPa Find the pressure head in (i) Meters of water (ii) mm
of mercury (iii) m of oil of specific gravity0.8.
5. An open container has water to a depth of 2m and above this an oil of S = 0.9 for a depth of 1m.
Find the intensity of pressure at the interface of two liquids and at the bottom of thetank.
6. Convert the following absolute pressure to gauge pressure (a) 120kPa (b) 3kPa (c) 15m of H2o
(d) 800mm ofHg.
Types of Simple Manometers Common types of simple manometers are
a) Piezometers
b) U-tubemanometers
c) Single tubemanometers
d) Inclined tubemanometers
a) Piezometers:
Piezometer consists of a glass tube inserted in the wall of the vessel or pipe at the level of point at which the intensity of pressure is to be measured. The other end of the piezometer is exposed to air. The height of the liquid in the piezometer gives the pressure head from which the intensity of pressure can be calculated. To minimize capillary rise effects the diameters of the tube is kept more than 12mm.
Merits _ Simple in construction _ Economical Demerits _ Not suitable for high pressure intensity. _ Pressure of gases cannot be measured.
(b) U-tubeManometers:
A U-tube manometers consists of a glass tube bent in U-Shape, one end of which is connected to gauge point and the other end is exposed to atmosphere. U-tube consists of a liquid of specific of gravity other than that of fluid whose pressure intensity is to be measured and is called manometricliquid.
- Manometricliquids ¨ Manometric liquids should neither mix nor have any chemical reaction with the fluid whose pressure intensity is to be measured. ¨ It should not undergo any thermal variation. ¨ Manometric liquid should have very low vapour pressure. ¨ Manometric liquid should have pressure sensitivity depending upon the magnitude of pressure to be measured and accuracy requirement.
- To write the gauge equation formanometers Gauge equations are written for the system to solve for unknown quantities. Steps: