Density

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

density 9Density, abbreviated as \(\rho\) (Greek symbol rho) or DENS, also called volumetric mass density or specific mass, more precisely volumetric mass density (mass density), is the ratio of the amount of matter in an object compared to its volume.  A small, heavy object, such as a rock or a lump of lead, is denser than a larger object of the same mass, such as a piece of cork or foam.

Density is a scalar quantity having direction, some of these include area, energy, entropy, length, mass, power, pressure, speed, temperature, volume, and work.

Depending on its density determines whether or not oil will sink or float on water.  Density can also be expressed as specific gravity, which is the ratio of the density of the substance as compared to a reference material at a standard set of conditions.

 

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Density types

  • Area Density  -  Mass over a one-dimensional area.
  • Bulk Density  -  The ratio total weight of soil to the total volume of soil.
  • Charge Density  -  The electric charge per volume.
  • Current Density  -  The ratio of electric current to area.
  • Densitometry  -  Measuring the optical density of photographic paper, photographic film and x-ray film.
  • Energy Density  -  Potential energy per unit volume or mass.
  • Force Density  -  Force per unit volume.
  • Linear Density  -  Mass over a one-dimensional line.
  • Number Density  -  The number of particles per unit volume, area, or length.
  • Optical Density  -  The absorbance of a material.
  • Particle Density  -  Density of the particles that make up a particulate solid or a powder.
  • Steam Density  -  Has a higher density than water vapor, the higher the pressure the higher the steam density.
  • Vapour Density  -  A relative density used for gases.

 

Density formula

 

\(\large{ \rho = \frac{m}{V} }\) 

Where:

 Units English Metric
\(\large{ \rho }\)   (Greek symbol rho) = density \(\large{\frac{lbm}{ft^3}}\) \(\large{\frac{kg}{m^3}}\)
\(\large{ m }\) = mass \(\large{lbm}\) \(\large{kg}\)
\(\large{ V }\) = volume \(\large{ft^3}\) \(\large{m^3}\)

 

Related formulas

\(\large{ \rho = \frac{ \rho_r }{ 1 \;+\; \alpha_c \; T_c }   }\)  (volumetric mass density of a material varies with the pressure and temperature) 
\(\large{ \rho =  \frac {Ca \; B}  { v^2  }    }\) (Cauchy Number)
\(\large{ \rho =  \frac { 2\; \left (p \;-\;p_v \right)}  {Ca\; U^2}  }\) (Cavitation Number)
\(\large{ \rho = \frac{\Delta p}{Eu  \;  U^2}  }\) (Euler Number)
\(\large{ \rho = \frac {p }{R \; T} }\) (Ideal Gas Law)
\(\large{ \rho = \frac{2 \; L}{ C_l \; v^2 \; A} }\) (Lift Force)
\(\large{ \rho = \frac{p_b \;-\; p_t }{g\; h} }\) (Pascal's Law)
\(\large{ \rho =  \frac {Pe \; k}{ v \; C \; l_c }   }\) (Peclet Number)
\(\large{ \rho = \frac{ Re \; \mu }{ l_c \; v }  }\)  (Reynolds Number
\(\large{ \rho = \frac{ \left(SG_s \;+\; S \; e\right) \; \rho_w  }{ 1 \;+\; e }  }\) (density of soil)
\(\large{ \rho_d = \frac{ SG_s \; \rho_w  }{ 1 \;+\; e }  }\) (dry density of soil)
\(\large{ \rho_{sat} = \frac{ \left(SG_s \;+\; e \right)  \; \rho_w  }{ 1 \;+\; e }  }\) (saturated density of soil)
\(\large{ \rho ' = \frac{ \left(SG_s \;-\; 1 \right) \; \rho_w  }{ 1 \;+\; e }  }\) (buoyant density of soil)
\(\large{ \rho_s = SG \; \rho_w  }\) (Specific Gravity)
\(\large{ \rho_w = \frac { \rho_s } { SG  }  }\) (Specific Gravity)
\(\large{  \rho = \frac{1}{\upsilon}   }\) (Specific Volume)
\(\large{ \rho_m = \rho_p  \; \frac { 18\; \eta \;  v } { g \;  d^2 }   }\) (Stokes' Law)
\(\large{ \rho_p =   \frac { 18\; \eta \;  v } { g \;  d^2 }  + \rho_m     }\) (Stokes' Law)
\(\large{ \rho = \frac{ k  }{ \alpha \; Q }   }\)  (Thermal Diffusivity)
\(\large{ \rho = \frac{ We \; \sigma  }{ v^2 \;  l_c   }   }\) (Weber Number)

Where:

\(\large{ \rho }\)   (Greek symbol rho) = density

\(\large{ T_a }\) = absolute temperature of gas

\(\large{ A }\) = area

\(\large{ B }\) = bulk modulus elasticity

\(\large{ \rho ' }\)   (Greek symbol rho) = buoyant density of soil

\(\large{ Ca  }\) = Cauchy number

\(\large{ Ca }\) = Cavitation number

\(\large{ l_c }\) = characteristic length or diameter of fluid flow

\(\large{ U }\) = characteristic velocity

\(\large{ S }\) = degree of saturation

\(\large{ \rho_r }\)  (Greek symbol rho) = density of reference material

\(\large{ \rho_m }\)  (Greek symbol rho) = density of medium

\(\large{ \rho_p }\)  (Greek symbol rho) = density of particle

\(\large{ \rho_s }\)  (Greek symbol rho) = density of sample

\(\large{ \rho_w }\)  (Greek symbol rho) = density of water

\(\large{ d }\) = diameter

\(\large{ \rho_d }\)   (Greek symbol rho) = dry density of soil

\(\large{ \mu }\)  (Greek symbol mu)  = dynamic viscosity

\(\large{ Eu }\) = Euler number

\(\large{ g }\) = gravitational acceleration

\(\large{ C }\) = heat capacity

\(\large{ h }\) = height of liquid column

\(\large{ C_l }\) = lift coefficient

\(\large{ L }\) = lift force

\(\large{ Pe  }\) = Peclet number

\(\large{ p }\) = pressure

\(\large{ \Delta p }\) =  pressure differential

\(\large{ p_b }\) = pressure at bottom of column

\(\large{ p_t }\) = pressure at top of column

\(\large{ Re }\) = Reynolds number

\(\large{ \rho_{sat} }\)   (Greek symbol rho) = saturated density of soil

\(\large{ R }\) = specific gas constant

\(\large{ SG }\) = specific gravity

\(\large{ SG_s }\) = specific gravity of soil

\(\large{ Q }\) = specific heat capacity

\(\large{ \sigma }\)  (Greek symbol sigma) = surface tension

\(\large{ \upsilon }\)   (Greek symbol upsilon) = specific volume

\(\large{ T }\) = temperature

\(\large{ T_c }\) = temperature change

\(\large{ k }\) = thermal conductivity

\(\large{ \alpha }\)  (Greek symbol alpha) = thermal diffusivity

\(\large{ \alpha_c }\)  (Greek symbol alpha) = thermal expansion coefficient

\(\large{ p_v }\) = vapor pressure

\(\large{ v }\) = velocity

\(\large{ \eta }\) = viscosity of medium

\(\large{ e }\) = void ratio

\(\large{ w }\) = water content

\(\large{ We }\) = Weber number

\(\large{ W_s } \) = weight of soil

 

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