Optical instrument

The first optical instruments were telescopes used for magnification of distant images, and microscopes used for magnifying very tiny images. Since the days of Galileo and Van Leeuwenhoek, these instruments have been greatly improved and extended into other portions of the electromagnetic spectrum. The binocular device is a generally compact instrument for both eyes designed for mobile use. A camera could be considered a type of optical instrument for storing an image.

Analysis

Another class of optical instrument is used to analyze the properties of light or optical materials. They include:

• Interferometer for measuring the interference properties of light waves
• Photometer for measuring light intensity
• Polarimeter for measuring dispersion or rotation of polarized light
• Reflectometer for measuring the reflectivity of a surface or object
• Refractometer for measuring refractive index of various materials, invented by Ernst Abbe
• Spectrometer or monochromator for generating or measuring a portion of the optical spectrum, for the purpose of chemical or material analysis.
• Autocollimator which is used to measure angular deflections.
• Vertometer which is used to determine refractive power of lenses such as glasses, contact lenses and magnifier lens click here
  

DNA sequencers can be considered optical instruments as they analyse the color and intensity of the light emitted by a fluorochrome attached to a specific nucleotide of a DNA strand.

Height-velocity diagram or volocity of hight

The Height-Velocity diagram or H/V curve is a graph charting the safe/unsafe flight profiles relevant to a specific helicopter. As operation outside the safe area of the chart can be fatal in the event of a power or transmission failure it is sometimes referred to as the dead man's curve or Coffin Corner by helicopter pilots.

In the simplest explanation, the H/V curve is a diagram where the shaded areas should be avoided, as the average pilot may be unable to complete an autorotation landing without damage. The H/V curve will usually contain a take-off profile, where the diagram can be traversed from 0 height and 0 speed to cruise, without entering the shaded areas or with minimum exposure to shaded areas.

The portion in the upper left of this diagram demonstrates a flight profile which will likely not allow the pilot to successfully complete an autorotation, primarily due to having insufficient airspeed to enter an autorotative profile in time to avoid a crash. The shaded area on the lower right is dangerous due to the airspeed and proximity to the ground resulting in dramatically reduced reaction time for the pilot in the case of mechanical failure, or other in-flight emergencies. This shaded area at the lower right is not portrayed in H/V curves for multiengine helicopters capable of safely hovering and flying with a single engine failure.

The following examples further illustrate the relevance of the H/V curve to a single engine helicopter.

At low heights with low airspeed, such as a hover taxi, the pilot can simply cushion the landing with collective, converting rotational inertia to lift. The aircraft is in a safe part of the H/V curve. At the extreme end of the scale (say a three-foot hover taxi at walking pace) even a complete failure to recognise the power loss resulting in an un-cushioned landing would probably be survivable.

As the airspeed increases without an increase in height, there comes a point where the pilot's reaction time would be insufficient to react with a flare in time to prevent a high-speed, and thus probably fatal, ground impact. Even small increases in height give the pilot much greater time to react, thus the bottom right part of the H/V curve is usually a shallow gradient. If above ideal autorotation speed, the pilot's instinct is usually to flare to convert speed to height and increase rotor RPM through coning; which also immediately gets them out of the dead man's curve.

Bell 204B Height-Velocity Diagram

Conversely, an increase in height without a corresponding increase in airspeed will put the aircraft above a survivable un-cushioned impact height, and eventually above a height where rotor inertia can be converted to sufficient lift to enable a survivable landing. This occurs abruptly with airspeeds much below the ideal autorotative speed (typically 40-80 knots). The pilot must have enough time to accelerate to autorotation speed in order to be able to successfully autorotate; this directly relates to a requirement for height. Above a certain height the pilot can achieve autorotation speed even from a 0-knot start, thus putting "high hovers" outside the curve.

The typical safe takeoff profile will involve initiation of forward flight from a low hover, only gaining height as airspeed approaches a safe autorotative speed but keeping above the lower right area of the H/V curve.

Wind wave or theory of hight

In fluid dynamics, wind waves or, more precisely, wind-generated waves are surface waves that occur on the free surface of oceans, seas, lakes, rivers, and canals or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Some waves in the oceans can travel thousands of miles before reaching land. Wind waves range in size from small ripples to huge rogue waves.^[1] When directly being generated and affected by the local winds, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swell. Or, more generally, a swell consists of wind generated waves that are not — or hardly — affected by the local wind at the same moment. They have been generated elsewhere, or some time ago.^[2] Wind waves in the ocean are called ocean surface waves.

Tsunamis are a specific type of wave not caused by wind but by geological effects. In deep water, tsunamis are not visible because they are small in height and very long in wavelength. They may grow to devastating proportions at the coast due to reduced water depth.

Contents 1 Wave formation 2 Types of wind waves 3 Wave breaking 4 Science of waves 5 Wind wave models 6 See also 7 Notes 8 References 9 External links

Wave formation

NOAA ship Delaware II in bad weather on Georges Bank.

The great majority of large breakers one observes on a beach result from distant winds. Four factors influence the formation of wind waves:^[3]

• Wind speed
• Distance of open water that the wind has blown over (called the fetch)
• Width of area affected by fetch
• Time duration the wind has blown over a given area
• Water depth

All of these factors work together to determine the size of wind waves. The greater each of the variables, the larger the waves. Waves are characterized by:

• Wave height (from trough to crest)
• Wavelength (from crest to crest)
• Period (time interval between arrival of consecutive crests at a stationary point)
• Wave propagation direction

Waves in a given area typically have a range of heights. For weather reporting and for scientific analysis of wind wave statistics, their characteristic height over a period of time is usually expressed as significant wave height. This figure represents an average height of the highest one-third of the waves in a given time period (usually chosen somewhere in the range from 20 minutes to twelve hours), or in a specific wave or storm system. Given the variability of wave height, the largest individual waves are likely to be about twice the reported significant wave height for a particular day or storm.

Types of wind waves

Three different types of wind waves develop over time:

• Capillary waves, or ripples
• Seas
• Swells

Ripples appear on smooth water when the wind blows, but will die quickly if the wind stops. The restoring force that allows them to propagate is surface tension. Seas are the larger-scale, often irregular motions that form under sustained winds. They tend to last much longer, even after the wind has died, and the restoring force that allows them to persist is gravity. As seas propagate away from their area of origin, they naturally separate according to their direction and wavelength. The regular wave motions formed in this way are known as swells.

Individual "rogue waves" (also called "freak waves", "monster waves", "killer waves", and "king waves") sometimes occur, up to heights near 30 meters, and being much higher than the other waves in the sea state. Such waves are distinct from tides, caused by the Moon and Sun's gravitational pull, tsunamis that are caused by underwater earthquakes or landslides, and waves generated by underwater explosions or the fall of meteorites — all having far longer wavelengths than wind waves.

Wave breaking

Big wave breaking

Surf in a rocky irregular bottom. Porto Covo, west coast of Portugal

See also: surf wave and breaking wave

Some waves undergo a phenomenon called "breaking". A breaking wave is one whose base can no longer support its top, causing it to collapse. A wave breaks when it runs into shallow water, or when two wave systems oppose and combine forces. When the slope, or steepness ratio, of a wave is too great, breaking is inevitable.

Individual waves in deep water break when the wave steepness — the ratio of the wave height H to the wavelength λ — exceeds about 0.17, so for H > 0.17 λ. In shallow water, with the water depth small compared to the wavelength, the individual waves break when their wave height H is larger than 0.8 times the water depth h, that is H > 0.8 h.^[4] Waves can also break if the wind grows strong enough to blow the crest off the base of the wave.

Three main types of breaking waves are identified by surfers or surf lifesavers. Their varying characteristics make them more or less suitable for surfing, and present different dangers.

• Spilling, or rolling: these are the safest waves on which to surf. They can be found in most areas with relatively flat shorelines. They are the most common type of shorebreak
• Plunging, or dumping: these break suddenly and can "dump" swimmers—pushing them to the bottom with great force. These are the preferred waves for experienced surfers. Strong offshore winds and long wave periods can cause dumpers. They are often found where there is a sudden rise in the sea floor, such as a reef or sandbar.
• Surging: these may never actually break as they approach the water's edge, as the water below them is very deep. They tend to form on steep shorelines. These waves can knock swimmers over and drag them back into deeper water.

Science of waves

Shallow water wave (Animation)click here

Deep water wave (Animation)

Motion of a particle in a wind wave.
A = At deep water. The orbital motion of fluid particles decreases rapidly with increasing depth below the surface.
B = At shallow water (sea floor is now at B). The elliptical movement of a fluid particle flattens with decreasing depth.
1 = Propagation direction.
2 = Wave crest.
3 = Wave trough.

See also: Airy wave theory

Wind waves are mechanical waves that propagate along the interface between water and air; the restoring force is provided by gravity, and so they are often referred to as surface gravity waves. As the wind blows, pressure and friction forces perturb the equilibrium of the water surface. These forces transfer energy from the air to the water, forming waves. In the case of monochromatic linear plane waves in deep water, particles near the surface move in circular paths, making wind waves a combination of longitudinal (back and forth) and transverse (up and down) wave motions. When waves propagate in shallow water, (where the depth is less than half the wavelength) the particle trajectories are compressed into ellipses.^[5][6]

As the wave amplitude (height) increases, the particle paths no longer form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift.^[7][8]

For intermediate and shallow water, the Boussinesq equations are applicable, combining frequency dispersion and nonlinear effects. And in very shallow water, the shallow water equations can be used.

As the depth below the free surface increases, the radius of the circular motion decreases. At a depth equal to half the wavelength λ, the orbital movement has decayed to less than 5% of its value at the surface. The phase speed of the surface wave (also called the celerity) is well approximated by

where

c = phase speed;

λ = wavelength;

d = water depth;

g = acceleration due to gravity at the Earth's surface.

In deep water, where , so and the hyperbolic tangent approaches 1, the speed c, in m/s, approximates , when λ is measured in meters. This expression tells us that waves of different wavelengths travel at different speeds. The fastest waves in a storm are the ones with the longest wavelength. As a result, after a storm, the first waves to arrive on the coast are the long–wavelength swells.

When several wave trains are present, as is always the case in nature, the waves form groups. In deep water the groups travel at a group velocity which is half of the phase speed.^[9] Following a single wave in a group one can see the wave appearing at the back of the group, growing and finally disappearing at the front of the group.

As the water depth d decreases towards the coast, this will have an effect: wave height changes due to wave shoaling and refraction. As the wave height increases, the wave may become unstable when the crest of the wave moves faster than the trough. This causes surf, a breaking of the waves.

The movement of wind waves can be captured by wave energy devices. The energy density (per unit area) of regular sinusoidal waves depends on the water density ρ, gravity acceleration g and the wave height H (which is equal to twice the amplitude, a):

The velocity of propagation of this energy is the group velocity.

Wind wave models

Main article: Wind wave model

Surfers are very interested in the wave forecasts. There are many websites that provide predictions of the surf quality for the upcoming days and weeks. Wind wave models are driven by more general weather models that predict the winds and pressures over the oceans, seas and lakes.

Wind wave models are also an important part of examining the impact of shore protection and beach nourishment proposals. For many beach areas there is only patchy information about the wave climate, therefore estimating the effect of wind waves is important for managing littoral environments.

Physical optics

In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory.

The physical optics approximation

Physical optics is also the name of a high frequency approximation (short-wavelength approximation) commonly used in optics, electrical engineering and applied physics. In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometric or ray optics and not that it is an exact physical theory.

This approximation consists of using ray optics to estimate the field on a surface and then integrating that field over the surface to calculate the transmitted or scattered field. This resembles the Born approximation, in that the details of the problem are treated as a perturbation.

In optics, it is a standard way of estimating diffraction effects. In radio, this approximation is used to estimate some effects that resemble optical effects. It models several interference, diffraction and polarization effects but not the dependence of diffraction on polarization. Since it is a high frequency approximation, it is often more accurate in optics than for radio.

In optics, it typically consists of integrating ray estimated field over a lens, mirror or aperture to calculate the transmitted or scattered field.

In radar scattering it usually means taking the current that would be found on a tangent plane of similar material as the current at each point on the front, i. e. the geometrically illuminated part, of a scatterer. Current on the shadowed parts is taken as zero. The approximate scattered field is then obtained by an integral over these approximate currents. This is useful for bodies with large smooth convex shapes and for lossy (low reflection) surfaces.click here

The ray optics field or current is generally not accurate near edges or shadow boundaries, unless supplemented by diffraction and creeping wave calculations.

The theory of physical optics has some defects in the evaluation of the scattered fields.^[1] For example the diffracted fields, which are created by the edge discontinuities, are obtained by the edge point contributions of the physical optics integrals. Y. Z. Umul has proposed a modified theory that leads to exact solutions to wave diffraction problems for comments composemind@gmail.com

Unit of alcohol

In the United Kingdom, units of alcohol are used as a guideline for the consumption of alcoholic beverages. A unit of alcohol is defined as 10 millilitres of pure alcohol (ethanol) — it is not the same thing as a standard drink. The size of standard drinks varies significantly from country to country.

In Australia, a unit of alcohol is 12.7 millilitres, which is one Australian standard drink.^[1]

A unit of alcohol is approximately the amount of alcohol that an average healthy adult can break down in an hour.^[2] The number of units contained in a typical alcoholic drink is publicised and marked on bottles.

Contents 1 Formulae 2 Quantities 2.1 Beers 2.2 Wines 2.3 Fortified wines 2.4 Spirits 2.5 Alcopops 3 Limits 4 See also 5 References

Formulae

The number of units of alcohol in a drink can be determined by multiplying the volume of the drink (in millilitres) by its percentage ABV, and dividing by 1000. Thus, one pint (568 ml) of beer at 4% ABV contains:

The formula uses the quantity in millilitres divided by 1000; this has the result of there being exactly one unit per percentage point per litre of any alcoholic beverage.

As the volume of alcoholic drinks is becoming increasingly shown in centilitres, discerning the number of units in a drink can be as simple as multiplying volume by percentage (converted into a fraction of 1). Thus, 75 centilitres of wine at 13 % ABV contains:

Quantities

It is often misleadingly stated that a unit is supplied by a small glass of wine, half a pint of beer, or a single measure of spirits.^[3] Such statements are misleading because they do not reflect the large differences in strengths and measures of wines, beers and spirits.^{[4] [5]}

Beers

• A half pint (284 ml) of beer that has a strength of 3.5% abv contains almost exactly one unit. However, most beers are stronger. In pubs, beers generally range from 4% to 5.5% abv with continental lagers starting at around 5% abv. A pint of such lager (568 ml at 5.2% for example) is almost 3 units of alcohol, rather than the often-quoted value of 2 units per pint.
• A 500 ml can/bottle of standard lager (5%) contains 2.5 units.
• 'Super-strength' or strong pale lager may contain as much as two units per half pint.
• One litre of typical Oktoberfest beer (5.5% to 6%) contains 5.5 to 6 units of alcohol.

Wines

• A small glass (125 ml) of 8% abv wine contains one unit of alcohol. However, British pubs and restaurants usually supply larger quantities (medium: 175 ml or large: 250 ml), and few wines are as weak as 8%; 12% is more typical. A standard pub measure (medium glass - 175 ml) of white wine (at 12%) contains around 2 units and a large glass (250 ml) contains 3 units. Red wine, which usually has a higher alcohol content (up to 16%), contains for an average 14% abv an alcohol content of 3.5 units for a large (250 ml glass), approximately one-sixth higher than a typical white wine. Just two bottles of 14% abv red wine a week will supply the maximum intake of alcohol for a man recommended by UK health guidelines.
• A 750 ml bottle of 12% wine contains 9 units. Many wines may contain 14% abv or more, which is just over 10 units of alcohol per bottle.

Fortified wines

• A small glass (50 ml) of sherry, fortified wine, or cream liqueur (approx. 20% abv) contains about one unit.

Spirits

• Most spirits sold in the UK have 40% abv or slightly less. A single pub measure (about 25 ml) of such a spirit contains one unit. However, a larger single measure of 35 ml is now often sold, resulting in the consumption of 1.4 units of alcohol.

Alcopops

• Most alcopops contain 1.4 to 1.5 units per bottle. For example, a regular 275ml bottle of WKD contains 1.4 units^[6], whereas Bacardi Breezer and Smirnoff Ice both contain 1.5 units of alcohol^[7].

Limits

Main article: Recommended maximum intake of alcoholic beverages

Since 1995 the UK government has advised that regular consumption of between three and four units a day for men and between two and three units a day for women would not pose significant health risks, but that consistently drinking four or more units a day (men) or three or more units a day (women) is not advisable^[8]. Previously (from 1992 until 1995) the advice was that men should drink no more than 21 units per week, and women no more than 14.^[9] This was changed because a government study showed that many people were in effect "saving" up their units and "using" them at the end of the week,^{[citation needed]}a phenomenon referred to as binge drinking. The difference between sexes is given due to the (typically) lower weight and water-to-body- click here

A large glass of red wine contains about three units of alcohol. A regular glass such as the one shown may contain about 2

mass-ratio of women.

The Times claimed in October 2007 that these limits had been "plucked out of the air" and have no scientific basis.^[10]

An international study^[11] of almost 6,000 men and 11,000 women found that persons who reported that they drank more than 2 units of alcohol a day had an increased risk of fractures compared to non-drinkers. For example, those who drank over 3 units a day had nearly twice the risk of a hip fracture.

International System of Units or SI unit

The International System of Units (abbreviated SI from the French le Système international d'unités^[1]) is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science.^[2][3]

The older metric system included several groups of units. The SI was developed in 1960 from the old metre-kilogram-second system, rather than the centimetre-gram-second system, which,

Cover of brochure The International System of Units.

in turn, had a few variants. Because the SI is not static, units are created and definitions are modified through international agreement among many nations as the technology of measurement progresses, and as the precision of measurements improves.

The system has been nearly globally adopted. Three principal exceptions are Burma (Myanmar), Liberia, and the United States. The United Kingdom has officially adopted the International System of Units but not with the intention of replacing customary measures entirely.

Realisation of units

It is very important to distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is carefully drawn up so that it is unique and provides a sound theoretical basis upon which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of how the definitions of some important units are realised in practice is given on the BIPM website.^[4]

A coherent SI derived unit can be expressed in SI base units with no numerical factor other than the number 1.^[5] The coherent SI derived unit of resistance, the ohm, symbol Ω, for example, is uniquely defined by the relation Ω = m²·kg·s⁻³·A⁻², which follows from the definition of the quantity electrical resistance. However, "any method consistent with the laws of physics could be used to realise any SI unit."^[6] (p. 111).

History

The metric system was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier, who is known as the "father of modern chemistry") who had been commissioned by Louis XVI of France to create a unified and rational system of measures. After the French Revolution, the system was adopted by the new government.^[7] On 1 August 1793, the National Convention adopted the new decimal metre with a provisional length as well as the other decimal units with preliminary definitions and terms. On 7 April 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms gravet (correctly milligrave) and grave. On 10 December 1799 (a month after Napoleon's coup d'état), the metric system was definitively adopted in France.

Countries by date of metrication

by 1800 1820 1840 1860 1880 1900

1920 1940 1960 1980 unknown

not adopted

The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty which established three international organizations to oversee the keeping of metric standards:

• General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM) - a meeting every four to six years of delegates from all member states;
• International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) - an international metrology centre at Sèvres in France; and
• International Committee for Weights and Measures (Comité international des poids et mesures or CIPM) - an administrative committee which meets annually at the BIPM.

The history of the metric system has seen a number of variations, whose use has spread around the world, to replace many traditional measurement systems. At the end of World War II a number of different systems of measurement were still in use throughout the world. Some of these systems were metric-system variations, whereas others were based on customary systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.

Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units that were recommended are the metre, kilogram, second, ampere, degree Kelvin (later renamed the kelvin), and the candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name: Le Système international d'unités. The seventh base unit, the mole, was added in 1971 by the 14th CGPM.

Future development

ISO 31 contains recommendations for the use of the International System of Units; for electrical applications, in addition, IEC 60027 has to be taken into account. As of 2008^[update], work is proceeding to integrate both standards into a joint standard Quantities and Units in which the quantities and equations used with SI are to be referred as the International System of Quantities (ISQ).^[8]

A readable discussion of the present units and standards is found at Brian W. Petley International Union of Pure and Applied Physics I.U.P.A.P.- 39 (2004).

Units

Main articles: SI base unit, SI derived unit, and SI prefix

The international system of units consists of a set of units together with a set of prefixes. The units of SI can be divided into two subsets. There are seven base units: Each of these base units represents, at least in principle, different kinds of physical quantities. From these seven base units, several other units are derived. In addition to the SI units, there is also a set of non-SI units accepted for use with SI which includes some commonly used units such as the litre.

SI base units^[9][10]

Name	Unit symbol	Quantity	Symbol
metre	m	length	l (a lowercase L)
kilogram	kg	mass	m
second	s	time	t
ampere	A	electric current	I (a capital i)
kelvin	K	thermodynamic temperature	T
candela	cd	luminous intensity	Iv (a capital i with lowercase v subscript)
mole	mol	amount of substance	n

A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.click here

Standard prefixes for the SI units of measure

Multiples	Name		deca-	hecto-	kilo-	mega-	giga-	tera-	peta-	exa-	zetta-	yotta-
	Symbol		da	h	k	M	G	T	P	E	Z	Y
	Factor	100	101	102	103	106	109	1012	1015	1018	1021	1024
Subdivisions	Name		deci-	centi-	milli-	micro-	nano-	pico-	femto-	atto-	zepto-	yocto-
	Symbol		d	c	m	µ	n	p	f	a	z	y
	Factor	100	10−1	10−2	10−3	10−6	10−9	10−12	10−15	10−18	10−21	10−24

SI writing style

• Symbols do not have an appended period/full stop (.).
• Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for variables (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.^[11]
• Symbols for units are written in lower case, except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", whereas the unit itself is written "pascal". All symbols of prefixes larger than 10³ (kilo) are also uppercase.
  • The one exception is the litre, whose original symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many English-speaking countries. The American National Institute of Standards and Technology recommends that "L" be used instead, a usage which is common in the US, Canada and Australia (but not elsewhere). This has been accepted as an alternative by the CGPM since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any standards body. For more information, see litre.
• The SI rule is that symbols of units are not pluralised, for example "25 kg" (not "25 kgs").^[11]
  • The American National Institute of Standards and Technology has defined guidelines for American users of the SI.^[12][13] These guidelines give guidance on pluralising unit names: the plural is formed by using normal English grammar rules, for example, "henries" is the plural of "henry".^[12]:31 The units lux, hertz, and siemens are exceptions from this rule: They remain the same in singular and plural. Note that this rule applies only to the full names of units, not to their symbols.
• A space separates the number and the symbol; e.g., "2.21 kg", "7.3×10² m²", "22 K". This rule explicitly includes the percent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.^[14][15]
• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries as well as most of Asia and the comma in most continental European languages.
• Spaces may be used as a thousands separator (1000000) in contrast to commas or periods (1,000,000 or 1.000.000) in order to reduce confusion resulting from the variation between these forms in different countries. In print, the space used for this purpose is typically narrower than that between words (commonly a thin space).
• Any line-break inside a number, inside a compound unit, or between number and unit should be avoided, but, if necessary, the last-named option should be used.
• Symbols for derived units (formed from multiple units by multiplication) are joined with a centre dot (·), dot (.)^[16], or a non-break space, for example, "N·m", "N.m", or "N m".^[17]
• Symbols formed by division of two units are joined with a solidus (⁄), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s⁻¹", "m·s⁻¹" or . Only one solidus should be used; e.g., "kg/(m·s²)" or "kg·m⁻¹·s⁻²" are acceptable but "kg/m/s²" is ambiguous and unacceptable. Many computer users will type the / character provided on computer keyboards, which in turn produces the Unicode character U+002F, which is named solidus but is distinct from the Unicode solidus character, U+2044.
• In Chinese, Japanese, and Korean language computing (CJK), some of the commonly-used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and Letterlike Symbols subranges for back compatibility, without necessarily recommending future usage.
• When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) are recognised as language-dependent terms, since the value of billion and trillion can vary from language to language. SI, therefore, recommends avoiding these terms.^[18] However, no alternative is suggested by the International Bureau of Weights and Measures (BIPM).click here
  

Spelling variations

• The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.^[19]
• In some English-speaking countries, the unit ampere is often shortened to amp (singular) or amps (plural) in informal writing as well as on many electrical appliances. Secs may sometimes be seen instead of s or seconds.

[edit] Conversion factors

The relationship between the units used in different systems is determined by convention or from the basic definition of the units. Conversion of units from one system to another is accomplished by use of a conversion factor. There are several compilations of conversion factors; see, for example, Appendix B of NIST SP 811.^[12]

Length, mass and temperature convergence

Density (specific mass) is commonly expressed in SI units or in reference to water. Since a cube with sides of 1 decimetre has volume of 1 cubic decimetre, which is 1 litre and, when filled with water, has a approximate mass of 1 kilogram, water has an approximate density of 1 kilogram per litre, which is equal to 1 gram per cubic centimetre and 1 tonne per cubic metre, and will freeze at approximately 0 degrees Celsius at 1 atmosphere of pressure.

Note that this is only an approximate definition of the kilogram, as the density of water can change with temperature; the actual definition is based on a specific platinum-iridium cylinder held in a vault at the BIPM in Sèvres, France.

Cultural issues

The near-worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardise the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. For use in science, it simplifies dealing with very large and small quantities, since it lines up so well with the decimal numeral system.

Many units in everyday and scientific use are not derived from the seven SI base units (metre, kilogram, second, ampere, kelvin, mole, and candela) combined with the SI prefixes. In some cases these deviations have been approved by the BIPM.^[20] Some examples include:

• The many units of time (minute, min; hour, h; day, d) in use besides the SI second, and are specifically accepted for use according to table 6.^[21]
• The year is specifically not included but has a recommended conversion factor.^[22]
• The Celsius temperature scale; kelvins are rarely employed in everyday use.
• Electric energy is often billed in kilowatt-hours instead of megajoules.
• The nautical mile and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 International nautical mile = 1852 m or approximately 1 minute of latitude). In addition to these, Annex 5 of the Convention on International Civil Aviation permits the "temporary use" of the foot for altitude.
• Astronomical distances measured in astronomical units, parsecs, and light-years instead of, for example, petametres (a light-year is about 9.461 Pm or about 9461000000000000 m).
• Atomic scale units used in physics and chemistry, such as the ångström, electron volt, atomic mass unit and barn.
• Some physicists prefer the centimetre-gram-second (CGS) units, with their associated non-SI electric units.
• In some countries, the informal cup measurement has become 250 ml. Likewise, a 500 g metric pound is used in many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (for example, pints for beer and cider in glasses in the UK —although pint means 568 ml; champagne in Jeroboams in France).
• A metric mile of 10 km is used in Norway and Sweden. The term metric mile is also used in some English speaking countries for the 1500 m foot race.
• In the US, blood glucose measurements are recorded in milligrams per decilitre (mg/dL), which would normalise to cg/L; in Canada, Australia, New Zealand, Oceania and Europe, the standard is millimole per litre (mmol/L) or mM (millimolar).
• Blood pressure and atmosphere pressure are measured in mmHg instead of Pa.

The fine-tuning that has happened to the metric base-unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the US customary units, are nowadays defined in SI units,^[23] any change in the definition of the SI units results in a change of the definition of the older units, as well.

International Trade

One of the European Union's (EU) objectives is the creation of a single market for trade. In order to achieve this objective, the EU standardised on using SI as the legal units of measure. At the time of writing (2009) it had issued two units of measurement directives which catalogued the units of measure that might be used for, amongst other things, trade: the first was Directive 71/354/EEC^[24] issued in 1971 which required member states to standardise on SI rather than use the variety of cgs and mks units then in use. The second was Directive 80/181/EEC^{[25][26][27][28][29]} issued in 1979 which replaced the first and which gave the United Kingdom and the Republic of Ireland a number of derogations from the original directive.

The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty or which were in universal use in worldwide trade. They also permitted the use of supplementary indicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, supplementary indicators have been allowed indefinitely.

[edit] See also

SI derived unit Dimensional analysis History of measurement		List of international common standards Orders of magnitude Long and short scales
Organisations
Institute for Reference Materials and Measurements (IRMM)		CODATA
Standards and conventions
Coordinated Universal Time (UTC)		ISO 1000

Systems of measurement Metric systems International System of Units · metre-kilogram-second · centimetre-gram-second · metre-tonne-second · gravitational system Natural units Geometric · Planck · Stoney · Lorentz–Heaviside · "Schrödinger" · Atomic · Electronic · Quantum chromodynamical Conventional systems Astronomical · Electrical · Temperature Customary systems Avoirdupois · Apothecaries' · Burmese · Canadian · Chinese · Danish · Dutch · English · Finnish · French · German · Hindu · Hong Kong · Imperial · Irish · Japanese · Maltese · Norwegian · Pegu · Polish · Portuguese · Romanian · Russian · Scottish · Spanish · Swedish · Taiwanese · Tatar · Turkish · Troy · United States Ancient systems Greek · Roman · Egyptian · Hebrew · Arabic · Mesopotamian · Persian · Indian Other systems Non-standard · Mesures usuelles · N-body for comments composemind@gmail.com

measurement of physical quantitics

Article

Dependence of thermal diffusion effects in liquids on the physical properties of the dispersing phase

F. S. Gaeta 1, A. Di Chiara 2

1International Institute of Genetics and Biophysics, C.N.R., Naples, Italy 2International Institute of Genetics and Biophysics, C.N.R., and Faculty of Engineering of the University of Naples, Naples, Italy

Abstract

1. A generalization of the radiation-pressure theory of thermal diffusion in liquids explains the genesis of the forces acting in a condensed phase when heat flows through it. The analytical expressions obtained make it possible to connect such forces originated by the radiation pressure of thermal waves with the transport of matter taking place in solutions or suspensions of particles and also with the ultimate result of this transport, that is, the steady-state concentrations of the dispersed phase in the hot and in the cold regions of the nonisothermal solution. The form in which the theoretical results are laid down lends itself to direct and unambiguous experimental verification. The confrontation with a few data found in the literature lends support to the theory. click here

MOTION IN A STRAIGHT LINE

In mechanics we are interested in trying to understand the motion of objects. In this chapter, the motion of objects in 1 dimension will be discussed. Motion in 1 dimension is motion along a straight line.

2.1. Position

The position of an object along a straight line can be uniquely identified by its distance from a (user chosen) origin. (see Figure 2.1). Note: the position is fully specified by 1 coordinate (that is why this a 1 dimensional problem).

Figure 2.1. One-dimensional position.

Figure 2.2. x vs. t graphs for various velocities.

For a given problem, the origin can be chosen at whatever point is convenient. For example, the position of the object at time t = 0 is often chosen as the origin. The position of the object will in general be a function of time: x(t). Figure 2.2. shows the position as a function of time for an object at rest, and for objects moving to the left and to the right.

The slope of the curve in the position versus time graph depends on the velocity of the object. See for example Figure 2.3. After 10 seconds, the cheetah has covered a distance of 310 meter, the human 100 meter, and the pig 50 meter. Obviously, the cheetah has the highest velocity. A similar conclusion is obtained when we consider the time required to cover a fixed distance. The cheetah covers 300 meter in 10 s, the human in 30 s, and the pig requires 60 s. It is clear that a steeper slope of the curve in the x vs. t graph corresponds to a higher velocity.

Figure 2.3. x vs. t graphs for various creatures.

2.2. Velocity

An object that changes its position has a non-zero velocity. The average velocity of an object during a specified time interval is defined as:

If the object moves to the right, the average velocity is positive. An object moving to the left has a negative average velocity. It is clear from the definition of the average velocity that depends only on the position of the object at time t = t₁ and at time t = t₂. This is nicely illustrated in sample problem 2-1 and 2-2.

Sample Problem 2-1

You drive a beat-up pickup truck down a straight road for 5.2 mi at 43 mi/h, at which point you run out of fuel. You walk 1.2 mi farther, to the nearest gas station, in 27 min (= 0.450 h). What is your average velocity from the time you started your truck to the time that you arrived at the station ?

The pickup truck initially covers a distance of 5.2 miles with a velocity of 43 miles/hour. This takes 7.3 minutes. After the pickup truck runs out of gas, it takes you 27 minutes to walk to the nearest gas station which is 1.2 miles down the road. When you arrive at the gas station, you have covered (5.2 + 1.2) = 6.4 miles, during a period of (7.3 + 27) = 34.3 minutes. Your average velocity up to this point is:

Sample Problem 2-2

Suppose you next carry the fuel back to the truck, making the round-trip in 35 min. What is your average velocity for the full journey, from the start of your driving to you arrival back at the truck with the fuel ?

It takes you another 35 minutes to walk back to your car. When you reach your truck, you are again 5.2 miles from the origin, and have been traveling for (34.4 + 35) = 69.4 minutes. At that point your average velocity is:

After this episode, you return back home. You cover the 5.2 miles again in 7.3 minutes (velocity equals 43 miles/hour). When you arrives home, you are 0 miles from your origin, and obviously your average velocity is:

The average velocity of the pickup truck which was left in the garage is also 0 miles/hour. Since the average velocity of an object depends only on its initial and final location and time, and not on the motion of the object in between, it is in general not a useful parameter. A more useful quantity is the instantaneous velocity of an object at a given instant. The instantaneous velocity is the value that the average velocity approaches as the time interval over which it is measured approaches zero:

For example: see sample problem 2-5.

The velocity of the object at t = 3.5 s can now be calculated:

2.3. Acceleration

The velocity of an object is defined in terms of the change of position of that object over time. A quantity used to describe the change of the velocity of an object over time is the acceleration a. The average acceleration over a time interval between t₁ and t₂ is defined as:

Note the similarity between the definition of the average velocity and the definition of the average acceleration. The instantaneous acceleration a is defined as:

From the definition of the acceleration, it is clear that the acceleration has the following units:

A positive acceleration is in general interpreted as meaning an increase in velocity. However, this is not correct. From the definition of the acceleration, we can conclude that the acceleration is positive if

This is obviously true if the velocities are positive, and the velocity is increasing with time. However, it is also true for negative velocities if the velocity becomes less negative over time.

2.4. Constant Acceleration

Objects falling under the influence of gravity are one example of objects moving with constant acceleration. A constant acceleration means that the acceleration does not depend on time:

Integrating this equation, the velocity of the object can be obtained:

where v₀ is the velocity of the object at time t = 0. From the velocity, the position of the object as function of time can be calculated:

where x₀ is the position of the object at time t = 0.

Note 1: verify these relations by integrating the formulas for the position and the velocity.

Note 2: the equations of motion are the basis for most problems (see sample problem 7).

Sample Problem 2-8

Spotting a police car, you brake a Porsche from 75 km/h to 45 km/h over a distance of 88m. a) What is the acceleration, assumed to be constant ? b) What is the elapsed time ? c) If you continue to slow down with the acceleration calculated in (a) above, how much time would elapse in bringing the car to rest from 75 km/h ? d) In (c) above, what distance would be covered ? e) Suppose that, on a second trial with the acceleration calculated in (a) above and a different initial velocity, you bring your car to rest after traversing 200 m. What was the total braking time ?

a) Our starting points are the equations of motion:

(1)

(2)

The following information is provided:

* v(t = 0) = v₀ = 75 km/h = 20.8 m/s

* v(t₁) = 45 km/h = 12.5 m/s

* x(t = 0) = x₀ = 0 m (Note: origin defined as position of Porsche at t = 0 s)

* x(t₁) = 88 m

* a = constant

From eq.(1) we obtain:

(3)

Substitute (3) in (2):

(4)

From eq.(4) we can obtain the acceleration a:

(5)

b) Substitute eq.(5) into eq.(3):

(6)

c) The car is at rest at time t₂:

(7)

Substituting the acceleration calculated using eq.(5) into eq.(3):

(8)

d) Substitute t₂ (from eq.(8)) and a (from eq.(5)) into eq.(2):

(9)

e) The following information is provided:

* v(t₃) = 0 m/s (Note: Porsche at rest at t = t₃)

* x(t = 0) = x₀ = 0 m (Note: origin defined as position of Porsche at t = 0)

* x(t₃) = 200 m

* a = constant = - 1.6 m/s²

Eq.(1) tells us:

(10)

Substitute eq.(10) into eq.(2):

(11)

The time t₃ can now easily be calculated:

(12)

2.5. Gravitational Acceleration

A special case of constant acceleration is free fall (falling in vacuum). In problems of free fall, the direction of free fall is defined along the y-axis, and the positive position along the y-axis corresponds to upward motion. The acceleration due to gravity (g) equals 9.8 m/s² (along the negative y-axis). The equations of motion for free fall are very similar to those discussed previously for constant acceleration:

where y₀ and v₀ are the position and the velocity of the object at time t = 0.

Example

A pitcher tosses a baseball straight up, with an initial speed of 25 m/s. (a) How long does it take to reach its highest point ? (b) How high does the ball rise above its release point ? (c) How long will it take for the ball to reach a point 25 m above its release point.

Figure 2.4. Vertical position of baseball as function of time.

a) Our starting points are the equations of motion:

The initial conditions are:

* v(t = 0) = v₀ = 25 m/s (upwards movement)

* y(t = 0) = y₀ = 0 m (Note: origin defined as position of ball at t = 0)

* g = 9.8 m/s²

The highest point is obtained at time t = t₁. At that point, the velocity is zero:

The ball reaches its highest point after 2.6 s (see Figure 2.4).

b) The position of the ball at t₁ = 2.6 s can be easily calculated:

c) The quation for y(t) can be easily rewritten as:

where y is the height of the ball at time t. This Equation can be easily solved for t:

Using the initial conditions specified in (a) this equation can be used to calculate the time at which the ball reaches a height of 25 m (y = 25 m):

t = 1.4 s

t = 3.7 s

Figure 2.5. Velocity of the baseball as function of time.

The velocities of the ball at these times are (see also Figure 2.5):

v(t = 1.4 s) = + 11.3 m/s

v(t = 3.7 s) = - 11.3 m/s

At t = 1.4 s, the ball is at y = 25 m with positive velocity (upwards motion). At t = 2.6 s, the ball reaches its highest point (v = 0). After t = 2.6 s, the ball starts falling down (negative velocity). At t= 3.7 s the ball is located again at y = 25 m, but now moves downwards.SENT COMMENTS ON composemind@gmail.com