### Specific Gravity - Industrial Instrumentation

# Specific Gravity or Relative Density

## Definition:

**Specific gravity**or

**Relative Density**of a substance is the ration of the density of that substance to the density of a reference substance. We can calculate the specific gravity of liquid and gas assuming the reference substance as

**water**and

**air**respectively.

## 1. Specific gravity of Liquid

Specific gravity of liquid is defined as the ratio of
density of the liquid at a standard or any temperature to the density of water
at some standard reference temperature at atmospheric pressure. We take water
as reference as the specific gravity of water [

**(S.G)**] is 1._{water}**Mathematically,**

**Specific Gravity of liquid = (S.G)**

_{liquid}**= (density of liquid at any temperature) / (Density of water at some standard temperature)**

For scientific purpose the distilled water is taken as
reference.

Standard reference temperature = 4°C

Atmospheric pressure = 760 mm of Hg

As per

**American Petroleum Institute (API),**Standard reference temperature = 15.6°C or 60°F
As per

**International standard Organization (ISO),**standard reference temperature = 15°C or 59°F## 2. Specific Gravity of Gas

The specific gravity of gas can be defined in either of two
ways.

(i)

**Real Specific Gravity:**The ratio of the**density of the gas**(**ρ**) to the_{gas}**density of air**(**ρ**) at a particular temperature and pressure is called the Real Specific Gravity._{air}
Mathematically,

**(S.G)**

_{gas}= (**ρ**

_{gas }/ ρ_{air})_{T,P}

_{}
(ii)

**Ideal Specific Gravity:**Ratio of the**molecular weight of the gas**(**W**) to the_{gas}**molecular weight of air**(**W**), is called the Ideal Specific Gravity._{air}
Mathematically,

**(S.G)**

_{gas}= (W_{gas}/ W_{air})

**◘ At normal atmosphere, temperature and pressure, the real specific gravity [(RSG)**

_{gas}] and the Ideal Specific Gravity [(ISG)_{gas}] of Gas are same, except- Steam, Carbon di oxide and some gases.**PROOF:**

**Ideal Gas Law = PV=nRT**

P= pressure

V= volume

n= number of moles

R= Gas constant=8.314

T= temperature

**For Real Gas = PV=nZRT**

Z is defined as the ratio of the volume of the gas to the
volume occupied by the same number of moles of ideal gas, at particular temperature
and pressure.

Z = (Volume of real gas) / (Volume of same no. of moles of
ideal gas)

Z is called the Compressibility factor.

**PV=nZRT**

**PV = [m/M**

_{w}] ZRT**m/V = (PM**

_{W})/(ZRT)**ρ = (PM**

_{W})/(ZRT)**ρ**

_{gas }= [P (M_{W})_{gas}]/ (Z_{gas}RT)…………….(I)**ρ**

_{air }= [P (M_{W})_{air}]/ (Z_{air}RT)……………….(II)

**Now,**

**(RSG)**

_{gas }=**ρ**

_{gas }/ ρ_{air}

_{}**Putting the values of (I) and (II) in this equation,**

**(RSG)**

_{gas}= [(M_{W})_{gas}/(M_{W})_{air}] * [ Z_{air}/Z_{gas}]**(RSG)**

_{gas}= (ISG)_{gas }* [Z_{air}/Z_{gas}]……………….(III)

**At normal atmosphere, temperature and pressure,**

**Z**

_{air}= Z_{gas}

_{}**From equation (III),**

**(RSG)**

_{gas}= (ISG)_{gas}**Hence proved.**

**Read Also,**

**Reynolds Number of Fluid : http://www.theincredibletruths.com/2018/10/reynolds-number-reynolds-number-is.html**

**Thermocouples : http://www.theincredibletruths.com/2018/08/thermocouple-types-construction-details.html**

**RTD wiring and color codes : http://www.theincredibletruths.com/2018/08/rtd-wiring-color-code.html**

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