Volume

Written by Jerry Ratzlaff on . Posted in Geometry

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Volume ( \(V\) ) is the space occupied by a mass.  Volume is a extensive variable whose values depend on the quantity of substance under study.  It is expressed in terms of length cubed, a quantity of three dimensional space occupied by gas, liquid, or solid.  Volume is a scalar quantity having direction, some of these include area, density, energy, entropy, length, mass, power, pressure, speed, temperature, and work.

volume formula

\(\large{  V = l  w  h  }\)         

\(\large{  V = \frac { m  }  { \rho  }   }\)         

Where:

\(\large{ V }\) = volume

\(\large{ h }\) = height

\(\large{ l } \) = length

\(\large{ m }\) = mass

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

\(\large{ w }\) = width

Volume Differential

Volume differential ( \(\Delta V\) ) is the difference between an expanded or reduced volume of a liquid.

Volume Differential Formula

\(\large{  \Delta V = V_f -  V_i   }\)         

Where:

\(\large{ \Delta V }\) = volume differential

\(\large{ V_i }\) = initial volume

\(\large{ V_f }\) = final volume

Volumetric Flow Rateflow volumetric

Volumetric flow rate ( \(Q\) or \(V\) ) (also called flow rate) is the amount of fluid that flows in a given time past a specific point.

Volumetric Flow Rate formula

\(\large{  Q = A v  }\)         

\(\large{  Q = \frac {V} {t}   }\)        

\(\large{  Q = k i A   }\)         

Where:

\(\large{ Q }\) = volumetric flow rate

\(\large{ A }\) = cross section area

\(\large{ i }\) = hydraulic gradient

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

\(\large{ t }\) = time

\(\large{ v }\) = flow velocity

\(\large{ V }\) = area volume

Volumetric Thermal Expansion

Volumetric thermal expansion (also known as volume thermal expansion) takes place in gasses and liquids when a change in temperature, volume or type of substance occures.   

Volumetric Thermal Expansion FORMULA

\(\large{  \Delta V  =  \beta   V_o  \Delta T  }\)         

\(\large{  \frac { \Delta V}  { V_o }  =  \beta   \Delta T   }\) 

Where:

\(\large{ \Delta V }\) = volume differential

\(\large{ \beta }\)   (Greek symbol beta) = volumetric thermal expansion coefficient

\(\large{ \Delta T }\) = temperature differential

\(\large{ V_o }\) = origional volume of object

volumetric Thermal Expansion Coefficient

Volumetric thermal expansion coefficient ( \(\beta\) ) (also known as coefficient of volumetric thermal expansion) is the ratio of the change in size of a material to its change in temperature.

Volumetric Thermal Expansion Coefficient FORMULA

\(\large{  \beta  =  \frac { 1 }{ V }  \frac {\Delta A } {\Delta T}   }\)         

Where:

\(\large{ \beta }\)   (Greek symbol beta) = volumetric thermal expansion coefficient

\(\large{ \Delta A }\) = area differential

\(\large{ \Delta T }\) = temperature differential

\(\large{ V }\) = volume of the object

Reduced Specific Volume

Reduced specific volume ( \(\upsilon_r\) ) (pseudo-reduced specific volume) of a fluid is ratio of the specific volume of a substance's critical pressure and temperature.

Reduced Specific Volume formula

\(\large{  \upsilon_r = \frac {\upsilon p_c}{R^*T_c}   }\)         

Where:

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

\(\large{ p_c }\) = critical pressure

\(\large{ R^* }\) = universal gas constant

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

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

Specific Volume

Specific volume ( \(\upsilon\) ) is the volume in a unit of mass.  Specific volume is a intensive variable whose physical quantity value does not depend on the amount of the substance for which it is measured.  Specific volume is the reciprocal of density, a substance with a higher density will have a lower specific volume.

Specific Volume formula

\(\large{  \upsilon = \frac{V}{m}   }\)         

\(\large{  \upsilon = \frac{1}{\rho}   }\)         

Where:

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

\(\large{ m }\) = mass

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

\(\large{ V }\) = volume

Solve for:

\(\large{  \rho = \frac{1}{\upsilon}   }\)

 

Tags: Equations for Volume