The structure of matter

Matter primarily consists of protons, neutrons and electrons. There are also a number of other building blocks however these are not stable. All of these particles are characterized by four properties: their electrical charge, their rest mass, their mechanical momentum and their magnetic momentum.

The number of protons in the nucleus is equal to the atom's atomic number. The total number of protons and the number of neutrons are approximately equal to the atom's total mass. This information is a part of the data that can be read off from the periodic system. The electron shell contains the same number of electrons as there are protons in the nucleus. This means the atom is electrically neutral.

The Danish physicist, Niels Bohr, produced a theory as early as 1913 that proved to correspond with reality where he, among others, demonstrated that atoms can only occur in a so-called, stationary state with a determined energy. If the atom transforms from one energy state to another a radiation quantum is emitted, a photon. It is these different transitions that make themselves known in the form of light with different wavelengths. In a spectrograph they appear as lines in the atom's spectrum of lines.

The molecule

The molecule and the different states of matter

Atoms held together by chemical bonding are called molecules. These are so small that, for example, 1 mm3 of air at atmospheric pressure contains approx. 2.55 x 1016 molecules.

All matter can in principle exist in four different states:

  • Solid state
  • Liquid state
  • Gaseous state
  • Plasma state

In the solid state the molecules are tightly packed in a lattice, with strong bonding. At all temperatures above absolute zero a certain degree of molecular movement occurs, in the solid state as a vibration around a balanced position, the faster the greater the temperature becomes.

When a substance in a solid state is heated so much that the movement of the molecules cannot be prevented by the rigid pattern (lattice), they become loose the substance melts and transforms to a liquid.

If the liquid is heated more, the bonding of the molecules is broken, and it transforms into a gaseous state during expansion in all directions and mixes with the other gases in the room. When gas molecules are cooled, they loose speed and bond to each other again, and condensation starts.

However, if the gas molecules are heated further, they are broken down into individual particles and form a plasma of electrons and atomic nuclei.



The force on a square centimeter area of an air column, which runs from sea level to the edge of the atmosphere, is about 10.13 N.

Therefore the absolute atmospheric pressure at sea level is approx. 10.13 x 104 N per square meter, which is also called 1 Pa (Pascal), the SI unit for pressure.

A basic dimension analysis shows that 1 bar = 1 x 105 Pa. The higher above sea level you are the lower the atmospheric pressure and visa versa.


Main principles

Thermodynamics' first main principle is a law of nature that cannot be proved, but is accepted without reservation. It says that energy can neither be created nor destroyed and from that it follows that the total energy in a closed system is constant. Thermodynamics' second main principle says that heat can never of "its own effort" be transferred from one source to a hotter source. This means that energy can only be available for work if it can be converted from a higher to a lower temperature level. Therefore in, for example, a heat engine the conversion of a quantity of heat to mechanical work can only take place if a part of this quantity of heat is simultaneously led off without being converted to work.

Gas Laws

 Boyle's law says that if the temperature is constant so the product of pressure and volume are costant.
The relation reads.

This means if the volume is halved during compression, then the pressure is doubled.
Charle's law says that the volume of gas changes in direct proportion to the cange in temperature.
the relation reads.

The general law of state for gases is a combination of Boyle's and Charle's laws. This states how pressure, volume and temperature affect each other.
When one of these variables is changed, this affects at least of the other two variables.
This can be written.

The constant R is called the individual gas constant and only concerns the properties of the gas.
If the mass m of the gas takes up the volume V, the relation can be written.

Heat transfer

Each heat difference within a body, or between different bodies, always leads to the transfer of heat, so that a temperature balance is obtained. This heat transfer can take place in three different ways: through conductivity, convection or radiation. In reality heat transfer takes place in parallel, in all three ways. Conductivity takes place between solid bodies or between thin layers of a liquid or gas. Molecules in movement emit their kinetic energy to the adjacent molecules. Convection can take place as free convection, with the natural movement that occurs in a medium or as forced convection with movement caused by, for example, a fan or a pump. Forced convection gives significantly more intense heat transfer. All bodies with a temperature above 0°K emit heat radiation. When heat rays hit a body, some of the energy is absorbed and transforms to heat. Those rays that are not absorbed pass through the body or are reflected. Only an absolute black body can theoretically absorb all radiated energy. In practice heat transfer is the sum of the heat transfer that takes place through conductivity, convection and radiation.

Changes in state

You can follow the changes in state for a gas from one point to another in a p/V diagram. It should really need three axes for the variables p, V and T. With a change in state you move along a curve on the surface in space that is then formed. However, you usually consider the projection of the curve in one of the three planes, usually the p/V plane. Primarily a distinction is made between five different changes in state: Isochoric process (constant volume), isobaric process (constant pressure), isothermic process (constant temperature) isentropic process (without heat exchange with the surroundings) and polytropic process (where the heat exchange with the surroundings is stated through a simple mathematical function).

Isochoric Process

Heating a gas in an enclosed container is an example of the isochoric process. The relation for the applied energy of heat is:

Isochoric change of state means that the pressure increases, while the volume constant

Isothermic process

If a gas in a cylinder is compressed isothermally, a quantity of heat that is equal to the applied work must be gradually led off. This is practicaly impossible, as such a slow process can not be realised.

Isothermic change of state means that the temperature of a gas mixture is constant, when the pressure and volume are changed

The relation for the quantity of heat led off is:

Isentropic Process

 Isentropic process An example of an isentropic process is if a gas is compressed in a fully insulated cylinder without heat exchange with the surroundings. Or if a gas is expanded through a nozzle so quickly that no heat exchange with the surroundings has time to take place. The relation for such a process is:


When the entropy is a gas that has been compressed or expanded is constant, no heat exchange with the surroundings takes place. This change in state follows Poisson's law.

Polytropic Process

Polytropic process The isothermic process involves full heat exchange with the surroundings and the isotropic process involves no heat exchange at all. In reality all processes are something between these extremes and this general process is called polytropic. The relation for such a process is:

Gas flow through a nozzle

Gas flow through a nozzle The gas flow through a nozzle depends on the pressure ratio on respective sides of the nozzle. If the pressure after the nozzle is lowered the flow increases, however, only until its pressure before the nozzle is approximately double so high. A further reduction of the pressure after the opening does not bring about an increase in flow. This is the critical pressure ratio and it is dependent on the gas's isentropic exponent (k). The critical pressure ratio occurs when the flow velocity is equal to the sonic velocity in the nozzle's narrowest section. The flow becomes supercritical if the pressure after the nozzle is reduced further, under the critical value. The relation for the flow through the nozzle is:

Flow trough pipes

Flow trough pipes Reynold's number is a dimensionless ratio between inertia and friction in a flowing medium. It is defined as:

In principal there are two types of flow pipe.

With Re<2000 the viscous forces dominate in the media and the flow becomes laminar. This means that different layers of the medium move in relation to each other in good order.
The velocity distribution across the laminar layers is usually parabolic shaped. With R4000 the inertia forces dominate the flowing medium and the flow becomes turbulent, with particles that move randomly in the flow's cross section.
The velocity distribution across a layer with turbulent flow becomes diffuse.
In the critical area, between R<=2000 and R>=4000, the flows conditions are undetermined, either laminar or turbulent or a mixture of the both.The conditions are governedby factors such as the surface smoothness of the pipi or other disturbances.
To start a flow in pipe requires a specific pressure difference or pressure drop, to overcome the friction in the pipe and couplings. The size of the pressure drop depens on the diameter of the pipe, its length and form as well as the surface smoothness and Reynold's number.


Throttling When an ideal gas flows through a restrictor, with a constant pressure before and after the restrictor, the temperature remains constant. However, there occurs a pressure drop across the restrictor, through the inner energy transforming into kinematic energy, which is why the temperature falls. However, for real gases this temperature change becomes lasting, even if the gas's energy content is constant. This is called the Joule Thomson effect. The temperature change is equal to the pressure change across the throttling multiplied by the Joule Thomson coefficient. If the flowing medium has a sufficiently low temperature a temperature drop occurs across the restrictor, but if the flow medium is hotter, a temperature increase occurs. This condition is used in several technical applications, for example, in refrigeration technology and the separation of gases.


Air in general

Air is a colourless, odourless and tasteless gas mixture. It consists of many gases, but primarily oxygen and nitrogen. Air can be considered a perfect gas mixture in most calculation contexts. The composition is relatively constant, from seal level and up to an altitude of 25 kilometres. Air is always more or less contaminated with solid particles, for example, dust, sand, soot and salt crystals. The degree of contamination is higher in populated areas, less in the countryside and at higher altitudes. Air is not a chemical substance, but a mechanically mixed substance. This is why it can be separated into its constituent elements, for example, by cooling.


Moist air

Air can be considered as a mixture of dry air and water vapour. Air that contains water vapour is called moist air, but the air?s humidity can vary within broad limits. Extremities are completely dry air and air saturated with moisture. The maximum water vapour pressure that air can hold increases with rising temperatures. A maximum water vapour pressure corresponds to each temperature. Air usually does not contain so much water vapour that maximum pressure is reached. Relative vapour pressure (also known as relative humidity) is a state between the actual partial vapour pressure and the saturated pressure at the same temperature. The dew point is the temperature when air is saturated with water vapour. Thereafter with a fall in temperature the condensation of water takes place. Atmospheric dew point is the temperature at which water vapour starts to condense at atmospheric pressure. Pressure dew point is the equivalent temperature with increased pressure.


Two basic principles

Two basic principles There are two basic principles for the compression of air (or gas), the displacement principal and dynamic compression. Among displacement compressors are, for example, piston compressors and different types of rotary compressors. They are the most common compressors in most countries. On a piston compressor for example, the air is drawn into a compression chamber, which is closed from the inlet. Thereafter the volume of the chamber decreases and the air is compressed. When the pressure has reached the same level as the pressure in the outlet manifold, a valve is opened and the air is discharged at a constant pressure, under continued reduction of the compression chamber's volume. In dynamic compression air is drawn into a rapidly rotating compression impeller and accelerates to a high speed. The gas is then discharged through a diffuser, where the kinetic energy is transformed to static pressure. There are dynamic compressors with axial or radial flow. All are suitable for large volume rates of flow.

Displacement compressors

Displacement compressors A bicycle pump is the simplest form of a displacement compressor, where air is drawn into a cylinder and is compressed by a moving piston. The piston compressor has the same operation principle, with a piston whose forward and backward movement is accomplished by a connecting rod and a rotating crankshaft. If only one side of the piston is used for compression this is called single acting. If both the piston's top and undersides are used the compressor is called double acting. The difference between the pressure on the inlet side and the pressure on the outlet side is a measurement of the compressor's work. The pressure ratio is the relation between absolute pressure on the inlet and outlet sides. Accordingly, a machine that draws in air at atmospheric pressure and compresses it to 7 bar overpressure works with a pressure ratio of (7 + 1)/1 = 8.

Compressors diagram

The compressor diagram for displacement compressors Figure A (at the bottom of this page) illustrates a theoretical compressor diagram and figure B illustrates a real compressor diagram for a piston compressor. The stroke volume is the cylinder volume that the piston travels during the suction stage. The clearance volume is the area that must remain at the piston?s turning point for mechanical reasons, together with the area required for the valves, etc. The difference between the stroke volume and the suction volume is due to the expansion of the air remaining in the clearance volume before suction can start. The difference between the theoretical p/V diagram and the real diagram is due to the practical design of a compressor, e.g. a piston compressor. The valves are never fully sealed and there is always a degree of leakage between the piston and the cylinder wall. In addition, the valves can not open and close without a delay, which results in a pressure drop when the gas flows through the channels. Due to reasons of design the gas is also heated when it flows into the cylinder.

Dynamic compressors

Dynamic compressors A dynamic compressor is a flow machine where the pressure increase takes place at the same time as the gas flows. The flowing gas accelerates to a high velocity by means of the rotating blades, after which the velocity of the gas is transformed to pressure when it is forced to decelerate under expansion. Depending on the main direction of the flow they are called radial or axial compressors. In comparison with displacement compressors, dynamic compressors have a characteristic where a small change in the working pressure results in a large change in the capacity. Each speed has an upper and lower capacity limit. The upper limit means that the gas's flow velocity reaches sonic velocity. The lower limit means that the counter pressure is greater than the compressor's pressure build-up, which means return flow in the compressor. This in turn results in pulsation, noise and the risk for mechanical damage.

Compression in stages

Compression in serveral stages Theoretically a gas can be compressed isentropically or isothermally. This can take place as a part of a reversible process. If the compressed gas could be used immediately, at its final temperature after compression, the isentropic process would have certain advantages. In reality the gas can rarely be used directly without being cooled before use. Therefore the isothermal process is preferred, as this requires less work. In practice attempts are made to realise this process by cooling the gas during compression. How much you can gain by this is shown, for example, with an effect- ive working pressure of 7 bar that theoretically requires 37% higher output for isentropic compression compared with isothermal compression. A practical method to reduce the heating of the gas is to divide the compression into several stages. The gas is cooled after each stage, to then be compressed further. This also increases the efficiency, as the pressure ratio in the first stage is reduced. The power requirement is at its lowest if each stage has the same pressure ratio. The more stages the compression is divided into the closer the entire process gets to be isothermal compression. However there is an economic limit for how many stages a real installation can be designed with.



Comparison between displacement and centrifugal compressors Comparison between displacement and centrifugal compressors The capacity curve for a centrifugal compressor differs significantly from an equivalent curve for a displacement compressor. The centrifugal compressor is a machine with a variable capacity and constant pressure. On the other hand a displacement compressor is a machine with a constant capacity and a variable pressure. Examples of other differences is that a displacement compressor gives a higher pressure ratio even at a low speed, unlike the more significantly higher speed centrifugal compressors. The centrifugal compressors are well suited to large air flow rates.



Basic terminology

Basic terminology and definitions The alternating current used for example to power lighting and motor operations regularly changes strength and direction in a sinusoidal variation. The current strength grows from zero to a maximum value, then falls to zero, changes direction, grows to a maximum value in the opposite direction to then become zero again. The current has then completed a period. The period T is the time in seconds under which the current has gone through all its values. The frequency states the number of complete cycles per second.

When speaking about current or voltage it is usually the root mean square value that is meant. With a sinusoidal current the relation for the current's respective voltage's root mean square value is:

Voltage under 50V is called extra low voltage. Voltage under 1000V is called low voltage. Voltage over 1000V is called high voltage. Standard voltages at 50Hz are 230/400V and 400/690V.

Ohm's law for alternating current

Ohm's law for alternating current An alternating current that passes a coil gives rise to a magnetic flow. This flow changes strength and direction in the same way as the current. When the flow changes an emf (electromotive force) is generated in the coil, according to the laws of induction. This emf is counter directed to the connected pole voltage. The phenomenon is called self-induction. Self-induction in an alternating current unit partly gives rise to phase displacement between the current and the voltage, and partly to an inductive voltage drop. The unit's resistance to the alternating current becomes apparently greater than that calculated or that measured with direct current. Phase displacement between the current and voltage is represented by the angle j. Inductive resistance (reactance) is represented by X. Resistance is represented by R. Apparent resistance in a unit or conductor is represented by Z. Applicable for impedance is:

Three-phase system

Three-phase system Three-phase alternating current is produced in a generator with three separate windings. All values on the sinusoidal voltage are displaced 120° in relation to each other. Different units can be connected to a three-phase unit. A single phase unit can be connected between the phase and zero. Three-phase units can be connected in two ways, star (Y) or delta (Ä) connection. With the star connection a phase voltage lies between the outlets. With a delta connection a main voltage lies between the outlets.


Power Active power, P, is the useful power that can be used for work. Reactive power, Q, is the useless power and can not be used for work. Apparent power, S, is the power that must be consumed from the mains supply to gain access to active power. The relation between active, reactive and apparent power is usually illustrated by a power triangle.


Power Factor Correction

What is Power Factor Correction? Most loads on an electrical distribution system fall into one of three categories; resistive, inductive or capacitive. In a maunfacturing plant, the most common is likely to be inductive. Typical examples of this include transformers, fluorescent lighting and AC induction motors. Most inductive loads use a conductive coil winding to produce an electromagnetic field, allowing the motor to function. All inductive loads require two kinds of power to operate: Active power (kwatts) - to produce the motive force Reactive power (kvar) - to energise the magnetic field

The operating power from the distribution system is composed of both active (working) and reactive (non-working) elements. The active power does useful work in driving the motor whereas the reactive power only provides the magnetic field. The bad news is that you are charged for both!

As the power factor drops the system becomes less efficient. A drop from 1.0 to 0.9 results in 15% more current being required for the same load. A power factor of 0.7 requires approximately 43% more current; and a power factor of 0.5 requires approximately 100% (twice as much) to handle the same load. The objective, therefore, should be to reduce the reactive power drawn from the supply by improving the power factor.


If an AC motor were 100% efficient it would consume only active power but, since most motors are only 75% to 80% efficient, they operate at a low power factor. This means poor energy and cost efficiency because the Regional Electricity Companies charge you at penalty rates for a poor power factor.

The electric motor

The electric motor The most common electric motor is a three phase, short circuit induction motor. This type of motor can be found within all industries. Silent and reliable, it is a part of most systems, for example, compressors. The electric motor consists of two main parts, the stationary stator and the rotating rotor. The stator produces a rotating magnetic field and the rotor converts this energy to movement, i.e. mechanical energy. The stator is connected to the mains supply's three phases. The current in the stator windings give rise to a rotating magnetic force field, which induces currents in the rotor and gives rise to a magnetic field there too. The interaction between the stator's and the rotor's magnetic fields creates turning torque, which makes the rotor shaft rotate.


Rotation speed

Rotation speed If the motor shaft should rotate at the same speed as the magnetic field, the induced current in the rotor would at the same time be zero. However, due to losses in, for example the bearings, this is impossible and the speed is always approx. 1-5% lower than the magnetic field's synchronous speed (slip). Applicable for this synchronous speed is:


Efficiency Energy conversion in a motor does not take place without losses. These are due to, among others, resistive losses, ventilation losses, magnetisation losses and friction losses. Applicable for efficiency is:

It is always the stated power, P2, stated on the motor's rating plate.

Insulation class

 Insulation class The insulation material in the motor's windings is divided into insulation classes in accordance with IEC 85 (International Electrotechnical Commission). A letter corresponding to the temperature, which is the upper limit for the isolation's calculated application area, designates each class. If the upper limit is exceeded by 10°C the service life of the insulation is shortened by about half.

Protection classes

Protection classes state, according to IEC 34-5, how the motor is protected against contact and water. These are stated with the letters IP and two digits. The first states the protection against contact and penetration by a solid object. The other digit states the protection against water.

For example

IP23 represents:

(2) protect against solid objects greater than 12 mm,
(3) protect against direct sprays of water up to 60° from the vertical. 

IP54 represents:

(5) protection against dust,
(4) protection against water sprayed from all directions.    

IP55 represents:

(5) protection against dust,
(5) protection against low-pressure jets of water from all directions

 Cooling methods

Cooling methods Cooling methods state, according to IEC 34-6, how the motor shall be cooled. This is designated with the letters IC and two digits. For example IC 01 represents: Free circulation, own ventilation and IC 41: Jacket cooling, own ventilation.

Installation method

Installation method The installation method states, according to IEC 34-7, how the motor should be installed. This is designated by the letters IM and four digits. For example IM 1001 represents: two bearings, shaft with free journalled end, stator body with feet. IM 3001: two bearings, shaft with free journalled end, stator body without feet, large flange with plain securing holes.

Star and delta connections

Star and delta connections A three-phase electric motor can be connected in two ways, star (Y) or delta (A). The winding phases in a three-phase motor are marked U, V and W (U1-U2; V1-V2; W1-W2). With the star (Y) connection the "ends" of motor winding's phases are joined together to form a zero point, which looks like a star (Y).


On the motor plate it can, for example, state 690/400 V. This means the star connection is intended for the higher voltage and the delta connection for the lower. The current, which can also be stated on the plate, shows the lower value for the star connected motor and the higher for the delta connected motor.

The main supply is connected to a three-phase motor's terminals marked U,V and W. The phase sequence is L1, L2 and L3. This means the motor will rotate clockwise seen from "D" the drive end. To make the motor rotate anticlockwise, two of the three conductors connected to the starter or to the motor are switched. Check the opperation of the cooling fan when rotating anticlockwise.


Torque An electric motor's turning torque is an expression for the rotor's turning capacity. Each motor has a maximum torque. A load above this torque means that the motor does not have the power to rotate. With a normal load the motor works significantly under its maximum torque, however, the start phase involves an extra load. The characteristics of the motor are usually presented in a torque curve.


The SI-system


Dimensioning an installation

Example of dimensioning compressed air installations Through the following pages, some normal calculations for dimensioning a compressed air installation will be demonstrated. The intention is to show how some of the formulas and data from previous chapters are used. The example is based on a desired compressed air equipment and result in dimensioned data, based on components that can be chosen for the compressed air installation. After the example, there are a few additions that show how special cases can be handled. This chapter contians of following items; 1. Input data 2. Component selection 3. Other diminsioning 4. Addition 1 - At high altitude 5. Addition 2 - Intermittent output 6. Addition 3 - Water borne energy recovery 7. Addition 4 - Pressure drop in the piping Please remember

Input data

Input data The compressed air requirments and the ambient conditions must be established before dimensioning is started. In addition to this requirments, a decision as to whether the compressor shall be oil lubricated or oil-free, and whether the equipment shall be water cooled or air cooled must be made. Requirment Assume that the need consists of three compressed air consumers. They have following data;


Ambient conditions (dimensioning) Dimensioning ambient temperature: 20°C Maximum ambient temperature: 30°C Ambient pressure: 1 bar(a) Humidity: 60% Miscellaneous Air cooled equipment Compressed air quality from an oil lubricated compressor is regarded as sufficient.

Component selection


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