# Background Notes on Measures - 2

 Contents: Density Pressure& Stress Speed FuelConsumption Power

Additional information can be found in the Dictionary of Units

DENSITY
 Properly speaking this should be referred to as 'Volumetric Density' to distinguish it from 'Linear Density' or 'Area Density'. But, in ordinary usage 'Density' is usually understood to mean the first one, and that is what is meant here by the single word 'density'. The other two are generally used only by specialists in certain subjects. For any substance, the density is a measure of the mass of a unit volume of that substance. So, it could be measured in 'pounds per cubic foot'    or    'tons per cubic yard' 'grams per litre'    or    'kilograms per cubic metre' etc. The SI preferred unit of density is kg/cubic metre. However, it is not the most convenient for ordinary use. For instance, in those units: iron is over 7000; wood is about 600 and even something as light as cork is over 200. Most users like to use 'grams/cubic centimetre' or (in SI-speak) g cm-3. This divides all the previous figures by 1000 (to make 7, 0.6 and 0.2 respectively). This unit has the added merit of simplicity in that gm/cc, kg/litre and tonnes/m³ are numerically all the same value - a good illustration of the convenience of the SI or metric system. Another advantage of this unit will be found under 'Relative Density'. The calculator also offers units like pounds/gallon. This fits the definition of density (mass/unit volume) but is not generally thought of in that way. It is much more likely to be used as a measure of concentration. It has been included for the sake of completeness, and it does match up with things like kg/litre. Inverse Density (or Specific Density, as it also known) gives a measure of the volume of a unit mass. Like, for example, 'cubic metres per tonne'. This is useful in storage problems (packing lorries, containers or a ship's hold) where it can be used to find out how much space is needed for a given mass. Relative Density (or Specific Gravity) is a measure of how the density of one substance compares with another. It is a ratio [density(1)/density(2)] and has NO units attached. Most often the comparison is being made with pure water. The density of that is usually taken to be 1 kg/litre. So, given the known density of a particular substance expressed in any units, when that is entered in the correct box on the calculator, the density relative to water can be read off in the kg/litre box. [In this context, it is worth remembering that the kilogram was originally defined as 'the mass of one litre of pure water'. Though the pressure and temperature of the water were specified also.] Example. Would something with a density of 63 pounds/cubic foot float on water? Making the appropriate entry in the calculator we can see that its density relative to pure water is 1.009 (to 4 s.f.)So no, it would not float on water.[Or would it? Be careful! The original question did not say 'pure water'. It would float in sea water!]
Go to the DENSITY Conversion Calculator

PRESSURE & STRESS
 Pressure is NOT the same physical thing as stress, but they do use the same definition and thus produce the same units, so the same calculator can be used for both. They both measure force per unit area. Note that it is 'force' and not 'mass'. It could be 'weight' of course (which is a force) but see the MASS conversion calculator notes for an explanation of that.All of the units are generally used to express pressure, while only a few are used with reference to stress - 'pounds per square inch' and 'kilonewtons/square metre' being obvious examples. The SI unit of pressure is the pascal [abbreviation Pa] which is defined as 1 newton/sq.metre or (in SI terms) N m-2. This is a rather small unit in much practical work and it is the 'kilopascal' [kPa] = 1000 pascals, which is seen most often.The hectopascal [hPa] which is 100 pascals and equal to 1 millibar is used by meteorologists, and other users of barometric pressures.A unit of pressure which is becoming well known is the 'bar' now that recommended tyre-pressures are often given in that unit. Though it does not help that filling-station air-pumps seem to be always calibrated in pounds per square inch!It is a little surprising to find nearly 40 different units listed for measuring pressure, but only the ones more likely to be found now are given in the calculator.
Go to the PRESSURE Conversion Calculator

SPEED
 The concept of speed is familiar enough to most people. It is a measure of the distance moved in a unit ot time. So we read of miles per hour, feet per second, kilometres per hour, and can understand statements like A glacier may move at 10 metres/day. For swifts, speeds of 47 metres/second have been recorded. A snail goes along at about 3 feet/minute. Light travels at nearly 300 000 km/second. The speed record for a steam-driven car is 145 miles/hour The Atlantic liner "Unites States" achieved a speed of 38 knots. The SI preferred unit of speed is metres/second.The 'knot' given in the calculator is the SI defined International knot of 1.852 km/hour. A less familiar measure of speed is the use of a Mach number. This is a ratio and has NO units. It is a measure of how many times faster an object is moving than sound does in the SAME medium and under the SAME conditions of pressure and temperature. Usually the medium is air - but it does not have to be - it could be water.Thus Mach 1 is the same as the speed of sound, Mach 2 is twice as fast and so on. The problem is that the speed of sound is not constant in any given medium. It does vary quite considerably with the pressure and the temperature. In the case of aeroplanes, as they go higher, both the air pressure and temperature become less. So Mach numbers do not give an exact speed unless all the surrounding conditions are known. To get some idea of the size of a Mach number, the conversion done in the calculator is based on the speed of sound being 331.5 metres/second, which it is at sea-level at 0°C. Ernst Mach (1838-1916) was an Austrian physicist.

 So, what is velocity?Well it is more than just another name for speed.Speed is speed. But velocity is speed + direction.If a velocity is to be given then it must (or should) include a reference to direction. For example, an object travelling with a velocity of 34 m/sec in a direction of 045° would mean that the object was moving with that (stated) speed in that (stated) direction. A car driving around a corner at a steady speed of 30 miles/hour would not change its speed, but it would certainly be changing its velocity (all the time it was going around the corner) until it was going along in a straight line again.
Go to the SPEED Conversion Calculator

FUEL CONSUMPTION
 This is a measure which many people use at some time or other, even if it is only in a casual rather than a calculated way. This is in connection with the motor-car, saying how much it "drinks" in miles per gallon (mpg). Here there are two units involved (distance/volume), either or both of which can be changed so we could have 'miles per litre' or 'kilometres per gallon' or 'kilometres per litre' and so on - whatever happens to be convenient. Fuel consumption can also be stated in another way, by saying how much fuel is needed to make the car go a particular distance. This could be put as gallons per mile. However, unless we were describing the fuel consumption of a jumbo-jet, this figure would be rather small. For example, a car doing 35 mpg uses about 0.0286 gallons per mile. To make this figure more "friendly" it is usual to state the amount of fuel needed to go a greater distance - say 100 miles. Now 35 mpg becomes 2.86 gallons per 100 miles. In terms of planning fuel requirements for a trip this form is more directly usable. In fact the metric way of expressing fuel consumption has always been in litres per 100 kilometres.The fuel consumption of 'ordinary' cars in 'ordinary' use varies between 30 and 50 miles per gallon, depending upon care and conditions. The size of the engine (and its condition), the weight of the vehicle, speed (and how much it varies), hills, length of the journey, are just some of the factors that affect how much fuel is needed for a given distance. In very special record-breaking attempts, on a track, in a purpose-built vehicle (holding only one person), petrol consumptions of nearly 8,000 miles per gallon have been achieved! The record breaking attempts of 'ordinary' cars (carefully tuned and driven) on level roads are more usually not much over 100 miles per gallon. Note that all of this is directed towards vehicle movement. Fuel consumption can arise in other circumstances. For example, the fuel-flow to an engine might be measured in terms of mass per unit of time (kg/minute, pounds/hour etc.) or volume per unit of time (litres/second, cubic metres/hour etc.). These are referred to as 'mass rate of flow' and 'volume rate of flow' respectively and are dealt with in separate conversion calculators. Alternatively, an engine (of any type) used to drive a generator might have its fuel consumption measured in terms of fuel used (in gallons, litres, kilograms etc.) per measure of electricity generated (kilowatt-hours etc.)
Go to the FUEL CONSUMPTION Conversion Calculator

POWER
 Power is a measure of the rate of doing work (or using energy) in relation to time. The SI unit of power is the watt [symbol W] which is a rate of 1 joule per second. What does it mean?Imagine a bucket of water being raised from a well which is 40 metres deep. The water weighs 1 kg. This is equivalent to a force of about 9.8 newtons (keep it simple, call it 10). The work that has to be done (or the energy needed) to raise that water through that height is given by Work = Force × Distance moved In this case that is  10 newtons × 40 metres  =  400 joules So, 400 joules of energy are needed, and nothing can alter that. What can be altered, is the time taken to do that amount of work, or deliver that amount of energy. It could be done in 1 second (at least in theory!) or 1 hour or 1 day or any other unit of time.Done in 1 second it needs a power of 400 watts (= 400 joules/sec).Done in 1 hour it needs a power of about 0.111 watts (= 400J/3600 sec)Notice:  Power used × Time taken must equal 400 joules. Putting it another way.A litre of petrol contains about 33,000 kilojoules of energy, and a car travelling at 50 kilometres per hour might use 1 litre of petrol in about 10 minutes. This is a power of 55 kW (or about 70 horsepower). Of course, due to the inefficiencies of the system only about 25% of that is actually delivered to the wheels. (Unfortunately!) Whereas if 1 litre of petrol were burnt in just 1 second, as in an explosion, then it would produce 33,000 kW of power (over 44,000 horsepower).Incidentally, it would be almost 100% efficient! The watt is named after James Watt, a Scottish engineer (1736-1819). Ironically, he himself devised his own unit of power. In 1783 he found a 'strong' horse could raise a mass of 150 pounds through a height of 4 feet in 1 second. From this he defined 1 horsepower as a work rate of 550 ft-lbf per second.
 Caution Some of the units named here have more than one definition!First there are: calories (and kilocalories), British thermal units (and therms). Full details of the different values possible for each can be found under the entry for 'Energy' in the main Dictionary of Units. The values used in the calculator are those of the International Table.Second is horsepower, which can in fact take 5 different values. Again, details are to be found under the entry for 'Power' in the main Dictionary. Generally, the values used in the calculator will serve for most purposes but, for extremely accurate work, care needs to be taken.
Go to the POWER Conversion Calculator

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