Density, Specific Weight, Specific Gravity & Specific Volume

Density or Mass Density: It is the ratio of the mass to volume. Mass per unit volume. It is denoted by Greek letter ρ.

Concept: Every matter is made up of molecules; and molecules are combination atoms. When the molecules are together they become mass of that substance. Some of the molecules come together leaving voids between them and some are very compact. For example, take pebbles and sand. For the same volume, pebbles will have more voids and sand will have less voids.  Like this the molecule arrangement in some substances will be different from other substance.  Hence we have to find the mass available in particular volume. To make it common we take unit volume.  It may be 1 cm³ or 1m³.

Water is taken as Standard liquid and Air is taken as standard gas.

Specific Weight: Weight per unit volume   w= mg/V (N/m³) =W/V

Specific Gravity: 

Specific weight of a fluid/specific weight of standard fluid (water)

Specific weight of a gas /specific weight of standard gas (air)

This can also be ratios of densities.

Specific Volume: This is inverse of density v =1/ρ (m³/V)

Matter appears in the form of solids, semi-solids, and fluids.  In this we are dealing with only fluids. As already defined, a fluid is substance which deforms continuously under shear or tangential forces. It is also defined as the substance which flows.

Again the fluids are sub-divided into liquids and gases.  Some liquids flow fast and some liquids flow slowly.  Petrol flows faster than water and water flows faster than lubricant oil. This property which gives resistance to flow is called the viscosity, the internal resistance for flow between the layers.

Liquids are treated as incompressible fluid. It means, when compressive forces applied on liquids, the change or reduction in volume will be negligible and for all practical purposes they can be treated as incompressible.

Gases are compressible. When compressive forces applied, the change in volume is appreciable. Since mass did not change, the density changes when compressed. But when the compressive forces are small and flow velocities are small, gases are also considered as incompressible for easy computation.

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Units & Dimensions

As already defined, Unit is a standard quantity. For each fundamental quantity a unit is defined. For example, for mass Kilogram (kg) is taken as unit.  Similarly, Dimension of any physical quantity can be expressed by fundamental dimensions. For example length can be used as dimension for length, area, volume etc.  The following are the Basic units and dimensions.

Fundamental dimensions are L for length, M for mass and T for time. There are other fundamental dimensions, but most of the physical quantities are represented by these dimensions

Basic Unit	Unit/Symbol	Dimension	Physical Quantity
Kilogram	kg	M	Mass
Meter	m	L	Length
Second	s	T	Time
Degree Kelvin	K	θ	Temperature
Ampere	A	I	Current
Candela	cd		Luminous intensity
Mole	mol		Amount of substance

Supplementary Unit	Unit/Symbol	Dimension	Physical Quantity
Radian	Rad	--	Plane angle
Steridian	Sr	--	Solid angle

Derived Unit	Unit / Symbol	Physical Quantity
Newton	N= kg m/s2	Force
Joule	J= N m = kg m2/s2	Energy, work, heat
Watt	W = J/s = N m/s = kg m2/s3	Power
Pascal	Pa = N/m2 = kg /m s2	Pressure, stress
Hertz	Hz = s-1	Frequency
Volt	V = W/A	Potential
Coulomb	C = A s	Charge
Ohm	Ω = V/A =W/A2	Resistance
Farad	F =A s/V =A2 s/W	Capacitance
Weber	Wb =V s =W s/A	Inductance
Henry	H = V s/A =W s/A2	Magnetic flux
Siemen	S =V/A =W/A2	Conductance
Tesla	T = Wb/m2 =V s/m2 =W s/A m2	Magnetic induction
Lumen	Lm =cd sr	Luminous flux
Lux	Lm/m2 =cd sr /m2	Luminance

There are many types of units. Some them are FPS (Foot, Pound and Second) units, MKS (Meter, Kilogram and Second) Units, CGS (Centimeter, Gram and Second) Units etc.  India and most of the countries follow SI units, International Standard or SI units.  Meter, Kilogram and Second are basic units.

RULES TO WRITE UNITS:

1. Leave at least one blank space between the number and units, e.g., 32 kg or 205 N/m² etc.
2. Do not use full stops, dots, dashes or plurals for units. Write Nm, not as N.m, N-m etc.  Write as 125 Nm not as 125 Nms
3. For numbers less than unity, Write 0 (zero) on the left of the decimal. E.g. 0.37 W
4. For numbers exceeding five digits, leave one blank space every three digits to show thousands or thousandth and millions or millionth as the case may be.  E.g. write 713 290 and 0.625 10

SOME BASIC CONVERSION FACTOR

To convert the following	Into SI units	Multiply by
Inches	Cm	2.54
Feet	m	0.3048
Miles	Km	1.6093
Gallons	m3	4.546 X 10-3
Pints	m3	0.5683 X 10-3
Liters	m3	1.0 X 10-3
Pounds	Kg	0.4536
Pound/sq.inch	kPa	6.895
Gallons/minute	m3/s	75.8 X 10-6
Cuses	m3/s	0.283
Poise	Ns/m2	0.1
Stoke	m2/s	0.1 X 10-3

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Concept of Continuum

Matter exists in molecules. Solids have a great cohesive forece and hence they take any shape. Liquids also have good cohesive force between molecules but not as much as solids. They take the shape of the container. Gases have very less cohesive force between molecles and hence they move randomly in the given volume. In the Macroscopic point of view, the volumes considerd are large compared to the size of the molecules. It is assumed that the volume under consideration will have enough number of molecules present in it, so that the definition of density, mass etc. will not alter eventhough there is movement of molecules in and out.

Let us take a volume comparable to the volume of molecule. Due to the random movement of the molecules, the volume under consideration may have molecules  at an instant and may not have molecules at another instant.  In that case, the definition of density and other properties will not have any meaning.  Hence it is considered that, always, the volume under consideration will have many molecules so that the definition of the properties will have meaning.

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Detailed Explanation of Macroscopic Viewpoint

Matter is composed of atoms. But most of the substances exist in molecular form. In classical thermodynamics where a large number of molecules are considered for thermodynamic properties. For example, if it is said a substance is at 100 DegC then is it assumed that the average temperature of all the molecules is similar. Some of the molecules maybe at higher or lower temperature, but in a Macroscopic point of view the average is taken of the total mass. Same thing holds good for Pressure, volume etc.

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