Control components in Hydraulic system

One of the most important functions in any fluid power system is control. If control components are not properly selected, the entire system will fail to deliver the required output. Elements for the control of energy and other control in fluid power system are generally called “Valves”. It is important to know the primary function and operation of the various types of control components. This type of knowledge is not only required for a good functioning system, but it also leads to the discovery of innovative ways to improve a fluid power system for a given application
The selection of these control components not only involves the type, but also the size, the actuating method and remote control capability. There are 3 basic types of valves.
1. Directional control valves
1. Pressure control valves
2. Flow control valves.
Directional control valves are essentially used for distribution of energy in a fluid power system. They establish the path through which a fluid traverses a given circuit. For example they control the direction of motion of a hydraulic cylinder or motor. These valves are used to control the start, stop and change in direction of flow of pressurized fluid.
Pressure may gradually buildup due to decrease in fluid demand or due to sudden surge as valves opens or closes. Pressure control valves protect the system against such overpressure. Pressure relief valve, pressure reducing, sequence, unloading and counterbalance valve are different types of pressure control valves.
In addition, fluid flow rate must be controlled in various lines of a hydraulic circuit. For example, the control of actuator speeds depends on flow rates. This type of control is accomplished through the use of flow control valves.

Directional control valves
As the name implies directional control valves are used to control the direction of flow in a hydraulic circuit. They are used to extend, retract, position or reciprocate hydraulic cylinder and other components for linear motion. Valves contains ports that are external openings for fluid to enter and leave via connecting pipelines, The number of ports on a directional control valve (DCV ) is usually identified by the term “ way”. For example, a valve with four ports is named as four-way valve.



Directional control valves can be classified in a number of ways:
1. According to type of construction :
• Poppet valves
• Spool valves
2. According to number of working ports :
• Two- way valves
• Three – way valves
• Four- way valves.
3. According to number of Switching position:
• Two – position
• Three - position
4. According to Actuating mechanism:
• Manual actuation
• Mechanical actuation
• Solenoid ( Electrical ) actuation
• Hydraulic ( Pilot ) actuation
• Pneumatic actuation
• Indirect actuation

1. Poppet Valves: Directional poppet valves consists of a housing bore in which one or more suitably formed seating elements ( moveable ) in the form of balls, cones are situated. When the operating pressure increases the valve becomes more tightly seated in this design. The main advantage of poppet valves are;
- No Leakage as it provides absolute sealing.
- Long useful life, as there are no leakage of oil flows.
- May be used with even the highest pressures, as no hydraulic sticking (pressure dependent deformation ) and leakages occurs in the valve.
The disadvantages of these valves are;
- Large pressure losses due to short strokes
- Pressure collapse during switching phase due to negative overlap ( connection of pump, actuator and tank at the same time ).

2. Spool valves: The spool valve consists of a spool which is a cylindrical member that has large- diameter lands machined to slide in a very close- fitting bore of the valve body. The spool valves are sealed along the clearance between the moving spool and the housing. The degree of sealing depends on the size of the gap, the viscosity of the fluid and especially on the level of pressure. Especially at high pressures ( up to 350 bar) leakage occurs to such a extent that it must be taken into account when determining the system efficiency. The amount of leakage is primarily dependent on the gap between spool and housing. Hence as the operating pressure increases the gap must be reduced or the length of overlap increased. The radial clearance is usually less than 20 Microns. The grooves between the lands provide the flow passage between ports.

Displacement diagrams

Displacement diagrams: In a cam follower system, the motion of the follower is very important. Its displacement can be plotted against the angular displacement θ of the cam and it is called as the displacement diagram. The displacement of the follower is plotted along the y-axis and angular displacement θ of the cam is plotted along x-axis. From the displacement diagram, velocity and acceleration of the follower can also be plotted for different angular displacements θ of the cam. The displacement, velocity and acceleration diagrams are plotted for one cycle of operation i.e., one rotation of the cam. Displacement diagrams are basic requirements for the construction of cam profiles. Construction of displacement diagrams and calculation of velocities and accelerations of followers with different types of motions are discussed in the following sections

(a) Follower motion with Uniform velocity:

(b) Follower motion with modified uniform velocity:

(c) Follower motion with uniform acceleration and retardation (UARM):

(d) Simple Harmonic Motion:

(e) Cycloidal motion:

Types of follower motion

Cam follower systems are designed to achieve a desired oscillatory motion. Appropriate displacement patterns are to be selected for this purpose, before designing the cam surface. The cam is assumed to rotate at a constant speed and the follower raises, dwells, returns to its original position and dwells again through specified angles of rotation of the cam, during each revolution of the cam.
Some of the standard follower motions are as follows:
They are, follower motion with,
(a) Uniform velocity
(b) Modified uniform velocity
(c) Uniform acceleration and deceleration
(d) Simple harmonic motion
(e) Cycloidal motion

CAMS

CAMS
INTRODUCTION A cam is a mechanical device used to transmit motion to a follower by direct contact. The driver is called the cam and the driven member is called the follower. In a cam follower pair, the cam normally rotates while the follower may translate or oscillate. A familiar example is the camshaft of an automobile engine, where the cams drive the push rods (the followers) to open and close the valves in synchronization with the motion of the pistons. Types of cams Cams can be classified based on their physical shape. a) Disk or plate cam: The disk (or plate) cam has an irregular contour to impart a specific motion to the follower. The follower moves in a plane perpendicular to the axis of rotation of the camshaft and is held in contact with the cam by springs or gravity.
b) Cylindrical cam : The cylindrical cam has a groove cut along its cylindrical surface. The roller follows the groove, and the follower moves in a plane parallel to the axis of rotation of the cylinder.
c) Translating cam The translating cam is a contoured or grooved plate sliding on a guiding surface(s). The follower may oscillate or reciprocate . The contour or the shape of the groove is determined by the specified motion of the follower.
Types of followers:
(i) Based on surface in contact.
(a) Knife edge follower
(b) Roller follower
(c) Flat faced follower
(d) Spherical follower
(ii) Based on type of motion:
(a) Oscillating follower
(b) Translating follower
(iii) Based on line of motion:
(a) Radial follower: The lines of movement of in-line cam followers pass through the centers of the camshafts.
(b) Off-set follower: For this type, the lines of movement are offset from the centers of the camshafts.

Quick return motion mechanisms

Quick return mechanisms are used in machine tools such as shapers and power driven saws for the purpose of giving the reciprocating cutting tool a slow cutting stroke and a quick return stroke with a constant angular velocity of the driving crank. Some of the common types of quick return motion mechanisms are discussed below. The ratio of time required for the cutting stroke to the time required for the return stroke is called the time ratio and is greater than unity.

Kinematic chain

Kinematic chain: A kinematic chain is a group of links either joined together or arranged in a manner that permits them to move relative to one another. If the links are connected in such a way that no motion is possible, it results in a locked chain or structure.

Constrained motion

Constrained motion: In a kinematic pair, if one element has got only one definite motion relative to the other, then the motion is called constrained motion.

(a) Completely constrained motion. If the constrained motion is achieved by the pairing elements themselves, then it is called completely constrained motion.

(b) Successfully constrained motion. If constrained motion is not achieved by the pairing elements themselves, but by some other means, then, it is called successfully constrained motion. Eg. Foot step bearing, where shaft is constrained from moving upwards, by its self weight.

(c) Incompletely constrained motion. When relative motion between pairing elements takes place in more than one direction, it is called incompletely constrained motion. Eg. Shaft in a circular hole.

Types of kinematic pairs

1)Based on nature of contact between elements:

(a) Lower pair. If the joint by which two members are connected has surface contact, the pair is known as lower pair
(b) Higher pair. If the contact between the pairing elements takes place at a point or along a line, such as in a ball bearing or between two gear teeth in contact, it is known as a higher pair.

2) Based on relative motion between pairing elements:
(a) Siding pair. Sliding pair is constituted by two elements so connected that one is constrained to have a sliding motion relative to the other. DOF = 1
(b) Turning pair (revolute pair). When connections of the two elements are such that only a constrained motion of rotation of one element with respect to the other is possible, the pair constitutes a turning pair. DOF = 1
(c) Cylindrical pair. If the relative motion between the pairing elements is the combination of turning and sliding, then it is called as cylindrical pair. DOF = 2
(d) Rolling pair. When the pairing elements have rolling contact, the pair formed is called rolling pair. Eg. Bearings, Belt and pulley. DOF = 1
(e) Spherical pair. A spherical pair will have surface contact and three degrees of freedom. Eg. Ball and socket joint. DOF = 3
(f) Helical pair or screw pair. When the nature of contact between the elements of a pair is such that one element can turn about the other by screw threads, it is known as screw pair. Eg. Nut and bolt. DOF = 1

3) Based on the nature of mechanical constraint.
a) Closed pair. Elements of pairs held together mechanically due to their geometry constitute a closed pair. They are also called form-closed or self-closed pair.
(b) Unclosed or force closed pair. Elements of pairs held together by the action of external forces constitute unclosed or force closed pair .Eg. Cam and follower.

Basics of Fluid Mechanics

Mechanics: It is that branch of scientific analysis which deals with motion, time and force.
Kinematics is the study of motion, without considering the forces which produce that motion. Kinematics of machines deals with the study of the relative motion of machine parts. It involves the study of position, displacement, velocity and acceleration of machine parts.

Dynamics of machines involves the study of forces acting on the machine parts and the motions resulting from these forces.

Plane motion: A body has plane motion, if all its points move in planes which are parallel to some reference plane. A body with plane motion will have only three degrees of freedom. I.e., linear along two axes parallel to the reference plane and rotational/angular about the axis perpendicular to the reference plane. (eg. linear along X and Z and rotational about Y.)The reference plane is called plane of motion. Plane motion can be of three types. 1) Translation 2) rotation and 3) combination of translation and rotation.
Translation: A body has translation if it moves so that all straight lines in the body move to parallel positions. Rectilinear translation is a motion wherein all points of the body move in straight lie paths.

Rotation: In rotation, all points in a body remain at fixed distances from a line which is perpendicular to the plane of rotation.

Translation and rotation: It is the combination of both translation and rotation which is exhibited by many machine parts.

Binary link: Link which is connected to other links at two points.

Ternary link: Link which is connected to other links at three points.

Quaternary link: Link which is connected to other links at four points.

Pairing elements: the geometrical forms by which two members of a mechanism are joined together, so that the relative motion between these two is consistent are known as pairing elements and the pair so formed is called kinematic pair. Each individual link of a mechanism forms a pairing element.

Degrees of freedom (DOF): It is the number of independent coordinates required to describe the position of a body in space.

Second law of thermodynamics:

1. Heat cannot by itself pass from a cold to a hot body.

2. All spontaneous processes are to some extent irreversible and are accompanied by degradation of energy.

3. It is impossible to construct a heat engine that operates continuously in a cycle to produce no effect other than conversion of heat supplied completely into work. This is called Kelvin – Planck statement.

4. It is impossible to construct a heat pump (reverse heat engine) that operates continuously to produce no effect other than transfer of heat from low temperature body to a high temperature body.

Heat capacity

Heat capacity:

Heat capacity of a substance is defined as the heat transfer necessary to bring about a change in the temperature of unit amount of substance by one degree centigrade. Since it is heat transfer which is a path function, it depends upon the way heating is done. For example gases can be heated to increase the temperature by two different methods. The unit quantity of gas taken in container with rigid wall, when heated its volume remains constant. Another method is to have the wall which is flexible. If the piston is movable in the piston and cylinder arrangement, gas when heated pushes piston and pressure will be constant. Even if we take unit amount of gas in both these heating methods, it is observed the heat transfer is not the same.

Thermodynamics Process

Thermodynamic process:

A system in thermodynamic equilibrium is disturbed by imposing some driving force; it undergoes changes to attain a state of new equilibrium. Whatever is happening to the system between these two equilibrium state is called a process. It may be represented by a path which is the locus all the states in between on a p-V diagram as shown in the figure above.

For a system of gas in piston and cylinder arrangement which is in equilibrium, altering pressure on the piston may be driving force which triggers a process shown above in which the volume decreases and pressure increases. This happens until the increasing pressure of the gas equalizes that of the surroundings. If we locate the values of all intermediate states, we get the path on a p-V diagram.

Equilibriums of Thermodynamics

Equilibrium state:

A system is said to be in thermodynamic equilibrium if it satisfies the condition for thermal equilibrium, mechanical equilibrium and also chemical equilibrium. If it is in equilibrium, there are no changes occurring or there is no process taking place.

Thermal equilibrium:

There should not be any temperature difference between different regions or locations within the system. If there are, then there is no way a process of heat transfer does not take place. Uniformity of temperature throughout the system is the requirement for a system to be in thermal equilibrium.

Surroundings and the system may be at different temperatures and still system may be in thermal equilibrium.

Mechanical equilibrium:

There should not be any pressure difference between different regions or locations within the system. If there are, then there is no way a process of work transfer does not take place. Uniformity of pressure throughout the system is the requirement for a system to be in mechanical equilibrium.

Surroundings and the system may be at pressures and still system may be in mechanical equilibrium.

Chemical equilibrium:

There should not be any chemical reaction taking place anywhere in the system, then it is said to be in chemical equilibrium. Uniformity of chemical potential throughout the system is the requirement for a system to be in chemical equilibrium.

Surroundings and the system may have different chemical potential and still system may be in chemical equilibrium.

Basic of Thermodynamics

Introduction:

Thermodynamics deals with heat inter-action and work inter-action with the substances called systems. Work and heat are forms of energy. Transfer of heat or work to a substance brings about certain changes in the substance and whatever change happens is called a process. Thermo means heat. Since work is also a form of energy, thermo is taken to mean heat and work. Dynamics refers to the changes that occur as a result of heat or work transfer.

Biological systems are capable doing work. For example, micro-organism is capable swimming in the body fluid of its host. It needs to do the work. Where does energy for doing this work come from? It is the metabolic activity that converts some form of energy (Nutrition that it takes form host is a form of chemical energy) into work. It is important then to understand how this happens so that we can exploit this to our engineering benefit.

In thermodynamics we have work transfer, heat transfer and then we have a system for interaction which undergoes a process. Let us look at these basic terms.

System:

We need to fix our focus of attention in order to understand heat and work interaction. The body or assemblage or the space on which our attention is focused is called system. The system may be having real or imaginary boundaries across which the interaction occurs. The boundary may be rigid and sometimes take different shapes at different times. If the system has imaginary boundary then we must properly formulate the idea of system in our mind.





Surroundings:

Every thing else apart from system constitutes surroundings. The idea of surroundings gets formulated the moment we define system. System and surroundings together form what is known as universe.

Closed system:

If the system has a boundary through which mass or material cannot be transferred, but only energy can be transferred is called closed system. In an actual system, there may not be energy transfer. What is essential for the system to be closed is the inability of the boundary to transfer mass only.

Open system:

If the system has a boundary through which both energy and mass can transfer, then it is called open system.

Properties:

Variables such as pressure, temperature, volume and mass are properties. A system will have a single set of all these values.


Intensive properties:

The properties that are independent of amount contained in the system are called extensive properties. For example, take temperature. We can have a substance with varying amount but still same temperature. Density is another example of intensive property because density of water is same no matter how much is the water. Other intensive properties are pressure, viscosity, surface tension.






Extensive properties:

The properties that depend upon amount contained in the system are called extensive properties. Mass depends upon how much substance a system has in it therefore mass is an extensive property.

State:

It is defined as condition of a system in which there are one set of values for all its properties. The properties that define the state of a system are called state variables. There is certain minimum number of intensive properties that requires to be specified in order to define the state of a system and this number is uniquely related to the kind of system. This relation is phase rule which we shall discuss little later.

Process:
The changes that occur in the system in moving the system from one state to the other is called a process. During a process the values of some or all state variables change. The process may be accompanied by heat or work interaction with the system.

Heat:

It is a form of energy that exists only in transit. This transit occurs between two points which differ in temperature. Since it exists only in transit, it should be accompanied by changes that occur in the system. The moment this energy cease to move, it appears as internal energy. We shall discuss internal energy when we deal with I law of thermodynamics.

Work:

It is also a form energy that exists only in transit. The work cannot be stored. Work is defined as the product of force and distance through the force moves.

Fluid mechanics

The branch of mechanics that is concerned with the properties of gases and liquids.

Fluid mechanics is the study of how fluids move and the forces on them. (Fluids include liquids and gases.) Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms. The study of fluid mechanics goes back at least to the days of ancient Greece, when Archimedes made a beginning on fluid statics. However, fluid mechanics, especially fluid dynamics, is an active field of research with many unsolved or partly solved problems. Fluid mechanics can be mathematically complex. Sometimes it can best be solved by numerical methods, typically using computers. A modern discipline, called Computational Fluid Dynamics (CFD), is devoted to this approach to solving fluid mechanics problems. Also taking advantage of the highly visual nature of fluid flow is Particle Image Velocimetry, an experimental method for visualizing and analyzing fluid flow.

The term "fluid" in everyday language typically refers only to liquids, but in the realm of physics, fluid describes any gas or liquid that conforms to the shape of its container. Fluid mechanics is the study of gases and liquids at rest and in motion. This area of physics is divided into fluid statics, the study of the behavior of stationary fluids, and fluid dynamics, the study of the behavior of moving, or flowing, fluids. Fluid dynamics is further divided into hydrodynamics, or the study of water flow, and aerodynamics, the study of airflow. Applications of fluid mechanics include a variety of machines, ranging from the water-wheel to the airplane. In addition, the study of fluids provides an understanding of a number of everyday phenomena, such as why an open window and door together create a draft in a room.

Fluid Statics or Hydrostatics

A fundamental characteristic of any fluid at rest is that the force exerted on any particle within the fluid is the same in all directions. If the forces were unequal, the particle would move in the direction of the resultant force. It follows that the force per unit area, or the pressure exerted by the fluid against the walls of an arbitrarily shaped containing vessel, is perpendicular to the interior walls at every point. If the pressure were not perpendicular an unbalanced tangential force component would exist and the fluid would move along the wall.

This concept was first formulated in a slightly extended form by the French mathematician and philosopher Blaise Pascal in 1647. Known as Pascal’s law, it states that the pressure applied to an enclosed fluid is transmitted equally in all directions and to all parts of the enclosing vessel, if pressure changes due to the weight of the fluid can be neglected. This law has extremely important applications in hydraulics.

The top surface of a liquid at rest in an open vessel will always be perpendicular to the resultant forces acting on it. If gravity is the only force, the surface will be horizontal. If other forces in addition to gravity act, then the “free” surface will adjust itself. For instance, if a glass of water is spun rapidly about its vertical axis, both gravity and centrifugal forces will act on the water and the surface will form a parabola that is perpendicular to the resultant force. If gravity is the only force acting on a liquid contained in an open vessel, the pressure at any point within the liquid is directly proportional to the weight of a vertical column of that liquid. This, in turn, is proportional to the depth below the surface and is independent of the size or shape of the container.

The second important principle of fluid statics was discovered by the Greek mathematician and philosopher Archimedes. The so-called Archimedes’ principle states that a submerged body is subject to a buoyancy force that is equal to the weight of the fluid displaced by that body. This explains why a heavily laden ship floats; its total weight equals exactly the weight of the water that it displaces, and this weight exerts the buoyant force supporting the ship.

A point at which all forces producing the buoyant effect may be considered to act is the center of buoyancy and is the center of gravity of the fluid displaced. The center of buoyancy of a floating body is directly above its center of gravity. The greater the distance between these two, the more stable the body.

Archimedes’ principle also makes possible the determination of the density of an object that is so irregular in shape that its volume cannot be measured directly. If the object is weighed first in air and then in water, the difference in weights will equal the weight of the volume of the water displaced, which is the same as the volume of the object. Thus the weight density of the object (weight divided by volume) can readily be determined. In very high precision weighing, both in air and in water, the displaced weight of both the air and water has to be accounted for in arriving at the correct volume and density.

Fluid Dynamics or Hydrodynamics

This branch of fluid mechanics deals with the laws of fluids in motion; these laws are considerably more complex and, in spite of the greater practical importance of fluid dynamics, only a few basic ideas can be discussed here.

Interest in fluid dynamics dates from the earliest engineering application of fluid machines. Archimedes made an early contribution by his invention of the screw pump, the pushing action of which is similar to that of the corkscrewlike device in a meat grinder. Other hydraulic machines and devices were developed by the Romans, who not only used Archimedes’ screw for irrigation and mine pumping but also built extensive aqueduct systems, some of which are still in use. The Roman architect and engineer Vitruvius first described the verticle waterwheel, a technology that revolutionized corn milling, during the 1st century bc.

Despite the early practical applications of fluid dynamics, little or no understanding of the basic theory existed, and development lagged accordingly. After Archimedes, more than 1800 years elapsed before the next significant scientific advance was made by the Italian mathematician and physicist Evangelista Torricelli, who invented the barometer in 1643, and formulated Torricelli’s law, which related the efflux velocity of a liquid through an orifice in a vessel to the liquid height above it. The major spurt in the development of fluid mechanics had to await the formulation of Newton’s laws of motion by the English mathematician and physicist Isaac Newton. These laws were applied to fluids first by the Swiss mathematician Leonhard Euler, who derived the basic equations for a frictionless, or inviscid, fluid.

Euler first recognized that dynamical laws for fluids can only be expressed in a relatively simple form if the fluid is assumed incompressible and ideal, that is, if the effects of friction or viscosity can be neglected. Because, however, this is never the case for real fluids in motion, the results of such an analysis can only serve as an estimate for those flows where viscous effects are small.

Viscous Flows, Laminar and Turbulent Motion

The first carefully documented friction experiments in low-speed pipe flow were carried out independently in 1839 by the French physiologist Jean Leonard Marie Poiseuille, who was interested in the characteristics of blood flow, and in 1840 by the German hydraulic engineer Gotthilf Heinrich Ludwig Hagen. An attempt to include the effects of viscosity into the mathematical equations was made first in 1827 by the French engineer Claude Louis Marie Navier, and independently by the British mathematician Sir George Gabriel Stokes, who in 1845 perfected the basic equations for viscous incompressible fluids. These are now known as the Navier-Stokes equations, and they are so complex that they can be applied only to simple flows. One such flow is that of a real fluid through a straight pipe. Here Bernoulli’s principle is not applicable because part of the total mechanical energy is dissipated as a result of viscous friction, resulting in a pressure drop along the pipe. The equations suggest that this pressure drop for a given pipe and a given fluid should be linear with the flow velocity. Experiments first conducted near the middle of the 19th century showed that this was only true for low velocities; at higher velocities, the pressure drop was more nearly proportional to the square of the velocity. This problem was not resolved until 1883 when the British engineer Osborne Reynolds showed the existence of two types of viscous flows in pipes. At low velocities the fluid particles follow the streamlines (laminar flow) and results match the analytical prediction. At higher velocities the flow breaks up into a fluctuating velocity pattern or eddies (turbulent flow) in a form that cannot be fully predicted even today. Reynolds also established that the transition from laminar to turbulent flow was a function of a single parameter that has since become known as the Reynolds number. If the Reynolds number, which is the product of velocity, fluid density, and pipe diameter, divided by the fluid viscosity, is less than 2100, the pipe flow will always be laminar; at higher values it will normally be turbulent. The concept of a Reynolds number is basic to much of modern fluid mechanics.

Turbulent flows cannot be evaluated solely from computed predictions and depend on a mixture of experimental data and mathematical models for their analysis, with much of modern fluid-mechanics research still being devoted to better formulations of turbulence. The transitional nature from laminar to turbulent flows and the complexity of the turbulent flow can be observed as cigarette smoke rises into very still air. At first it rises in a laminar streamline motion but after some distance it becomes unstable and breaks up into an intertwining eddy pattern.

Boundary Layer Flows

Before about 1860 the engineering interest in fluid mechanics was limited almost entirely to water flows. The development of the chemical industry during the latter part of the 19th century directed attention to other liquids and to gases. Interest in aerodynamics began with the studies of the German aeronautical engineer Otto Lilienthal in the last decade of the 19th century and saw major advances following the first successful powered flight by the American inventors Orville and Wilbur Wright in 1903.

The complexity of viscous flows, especially turbulent flows, severely restricted progress in fluid dynamics until the German engineer Ludwig Prandtl recognized in 1904 that many flows could be divided into two principal regions. The region close to the surface consists of a thin boundary layer where the viscous effects are concentrated and where the mathematical model can be greatly simplified. Outside the boundary layer viscous effects can be disregarded and the simpler mathematical equations for inviscid flows can be used. The boundary-layer theory has made possible much of the development of modern aircraft wings and the design of gas turbines and compressors. The boundary-layer model not only permitted a much simplified formulation of the Navier-Stokes equations in the region close to the body surface but also led to further developments of the flow of inviscid fluids that can be applied outside the boundary layer. Much of the modern development of fluid mechanics was made possible by the boundary-layer concept and it has been carried out by such key contributors as the Hungarian-born American aeronautical engineer Theodore von Kármán, and the German mathematician Richard von Mises, by the British physicist and meteorologist Sir Geoffrey Ingram Taylor.

Compressible Flows

Interest in compressible flows started with the development of steam turbines by the British inventor Charles Algernon Parsons, and the Swedish engineer Carl Gustaf Patrik de Laval during the 1880s. Here high-speed flow of steam within flow passages was first encountered and the need for efficient turbine design led to improved compressible flow analyses. Modern advances, however, had to wait for the stimulus of successful gas turbine and jet engine development in the 1930s. The early interest in high-speed flows over surfaces arose in the study of ballistics, for which an understanding of the motion of projectiles was needed. Major developments started near the end of the 19th century, involving Prandtl and his students, among others, and increased after the introduction of high-speed aircraft and rockets (see Rocket) in World War II.

One of the basic principles of compressible flows is that the density of a gas changes when the gas is subjected to large velocity and pressure changes. At the same time its temperature also changes, leading to more complex means of analysis. The flow behavior of a compressible gas depends on whether the flow velocity is smaller or greater than the velocity of sound. The velocity of sound is the name given to the propagation velocity of a very small disturbance, or pressure wave, within the fluid. For a gas it is proportional to the square root of the absolute temperature. For instance, air at 20° C, or 293° on the Kelvin, or absolute, scale (68° F), has a sound velocity of 344.65 m per sec (1130 ft per sec). If the flow velocity is less than the sound velocity (subsonic flow), pressure waves can be transmitted throughout the whole fluid to adjust the flow that rushes toward an object. Thus the subsonic flow approaching an airplane wing will adjust itself some distance upstream to flow smoothly over the surface. In supersonic flow, pressure waves cannot travel upstream to readjust the flow. As a result, the air rushing toward a wing in supersonic flight will not be prepared for the impending disturbance the wing will cause. Instead, it has to redirect very suddenly in the proximity of the wing, where a sharp compression or shock is coupled with the redirection. The noise associated with this sudden shock causes the sonic boom of aircraft flying at supersonic speeds. Compressible flows are often identified by the Mach number, which is the ratio of the flow velocity divided by the sound velocity. Supersonic flows therefore have a Mach number greater than 1.

Third law of thermodynamics

The third law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. The most common enunciation of third law of thermodynamics is:

As a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.

It can be concluded as 'If T=0K, then S=0' where T is the temperature of a closed system and S is the entropy of the system.

The third law was developed by Walther Nernst, during the years 1906-1912, and is thus sometimes referred to as Nernst's theorem or Nernst's postulate. The third law of thermodynamics states that the entropy of a system at zero is a well-defined constant. This is because a system at zero temperature exists in its ground state, so that its entropy is determined only by the degeneracy of the ground state; or, it states that "it is impossible by any procedure, no matter how idealised, to reduce any system to the absolute zero of temperature in a finite number of operations".

An alternative version of the third law of thermodynamics as stated by Gilbert N. Lewis and Merle Randall in 1923:

If the entropy of each element in some (perfect) crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy; but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.

This version states not only ΔS will reach zero at D = 0 K, but S itself will also reach zero.

Overview

In simple terms, the Third Law states that the entropy of a pure substance approaches zero as the absolute temperature approaches zero. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy.

A special case of this is systems with a unique ground state, such as most crystal lattices. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (if its ground state is singular and unique, whereby log(1) = 0). An example of a system which does not have a unique ground state is one containing half-integer spins, for which time-reversal symmetry gives two degenerate ground states. Of course, this entropy is generally considered to be negligible on a macroscopic scale. Additionally, other exotic systems are known that exhibit geometrical frustration, where the structure of the crystal lattice prevents the emergence of a unique ground state.

Real crystals with frozen defects obey this same law, so long as one considers a particular defect configuration to be fixed. The defects would not be present in thermal equilibrium, so if one considers a collection of different possible defects, the collection would have some entropy, but not actually have a temperature. Such considerations become more interesting and problematic in considering various forms of glass, since glasses have large collections of nearly degenerate states, in which they become trapped out of equilibrium.

Another application of the third law is with respect to the magnetic moments of a material. Paramagnetic materials (moments random) will order as T approaches 0 K. They may order in a ferromagnetic sense, with all moments parallel to each other, or they may order in an antiferromagnetic sense, with all moments antiparallel to each other.

Yet another application of the third law is the fact that at 0 K no solid solutions should exist. Phases in equilibrium at 0 K should either be pure elements or atomically ordered phases.

The Third Law of Thermodynamics is the lesser known of the three major thermodynamic laws. Together, these laws help form the foundations of modern science. The laws of thermodynamics are absolute physical laws - everything in the observable universe is subject to them. Like time or gravity, nothing in the universe is exempt from these laws. In its simplest form, the Third Law of Thermodynamics relates the entropy (randomness) of matter to its absolute temperature.

The Third Law of Thermodynamics refers to a state known as "absolute zero." This is the bottom point on the Kelvin temperature scale. The Kelvin scale is absolute, meaning 0° Kelvin is mathematically the lowest possible temperature in the universe. This corresponds to about -273.15° Celsius, or -459.7 Fahrenheit.

In actuality, no object or system can have a temperature of zero Kelvin, because of the Second Law of Thermodynamics. The Second Law, in part, implies that heat can never spontaneously move from a colder body to a hotter body. So, as a system approaches absolute zero, it will eventually have to draw energy from whatever systems are nearby. If it draws energy, it can never obtain absolute zero. So, this state is not physically possible, but is a mathematical limit of the universe.

In its shortest form, the Third Law of Thermodynamics says: "The entropy of a pure perfect crystal is zero (0) at zero Kelvin (0° K)." Entropy is a property of matter and energy discussed by the Second Law of Thermodynamics. The Third Law of Thermodynamics means that as the temperature of a system approaches absolute zero, its entropy approaches a constant (for pure perfect crystals, this constant is zero). A pure perfect crystal is one in which every molecule is identical, and the molecular alignment is perfectly even throughout the substance. For non-pure crystals, or those with less-than perfect alignment, there will be some energy associated with the imperfections, so the entropy cannot become zero.

The Third Law of Thermodynamics can be visualized by thinking about water. Water in gas form has molecules that can move around very freely. Water vapor has very high entropy (randomness). As the gas cools, it becomes liquid. The liquid water molecules can still move around, but not as freely. They have lost some entropy. When the water cools further, it becomes solid ice. The solid water molecules can no longer move freely, but can only vibrate within the ice crystals. The entropy is now very low. As the water is cooled more, closer and closer to absolute zero, the vibration of the molecules diminishes. If the solid water reached absolute zero, all molecular motion would stop completely. At this point, the water would have no entropy (randomness) at all.

Most of the direct use of the Third Law of Thermodynamics occurs in ultra-low temperature chemistry and physics. The applications of this law have been used to predict the response of various materials to temperature changes. These relationships have become core to many science disciplines, even though the Third Law of Thermodynamics is not used directly nearly as much as the other two.