# Density

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Density, 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.

To calculate the weight density see weight.

## Density formulas

 $$\large{ \rho = \frac{m}{V} }$$ $$\large{ \rho = \frac {k} { \alpha \; Q} }$$ $$\large{ \rho = \frac{ \rho_r }{ 1 \;+\; \alpha_c \; T_c } }$$ (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) $$\large{ \rho_s = SG \; \rho_w }$$ (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) $$\large{ \rho = \frac{ We \; \sigma }{ v^2 \; l_c } }$$ (Weber number)

### Where:

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

$$\large{ T_a }$$ = absolute temperature of gas

$$\large{ A }$$ = area

$$\large{ B }$$ = bulk modulus elasticity

$$\large{ Ca }$$ = Cauchy number

$$\large{ Ca }$$ = Cavitation number

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

$$\large{ U }$$ = characteristic velocity

$$\large{ \rho_r }$$  (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

$$\large{ \mu }$$  (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

$$\large{ m }$$ = mass

$$\large{ Pe }$$ = 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

$$\large{ R }$$ = specific gas constant

$$\large{ SG }$$ = specific gravity

$$\large{ Q }$$ = 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

$$\large{ V }$$ = volume

$$\large{ We }$$ = Weber number