Bulk Modulus and Fluid Elasticities
Introduction to  and definition of  Bulk Modulus Elasticity commonly used to characterize the compressibility of fluids.
The Bulk Modulus Elasticity  or Volume Modulus  is a material property characterizing the compressibility of a fluid  how easy a unit volume of a fluid can be changed when changing the pressure working upon it.
The Bulk Modulus Elasticity can be calculated as
K =  dp / (dV / V _{0 } )
=  ( p _{ 1 }  p _{0 } ) / ((V _{ 1 }  V _{0 } ) / V _{0 } ) (1)
where
K = Bulk Modulus of Elasticity (Pa, N/m^{2})
dp = differential change in pressure on the object (Pa, N/m^{2})
dV = differential change in volume of the object (m ^{ 3 } )
V _{0 } = initial volume of the object (m ^{ 3 } )
p _{0 } = initial pressure ( Pa, N/m^{2})
p _{ 1 } = final pressure ( Pa, N/m^{2})
V _{ 1 } = final volume ( m ^{ 3 } )
The Bulk Modulus Elasticity can alternatively be expressed as
K = dp / (dρ / ρ _{0 } )
= ( p _{ 1 }  p _{0 } ) / (( ρ _{ 1 }  ρ _{0 } ) / ρ _{0 } ) (2)
where
dρ = differential change in density of the object (kg/m ^{ 3 } )
ρ _{0 } = initial density of the object (kg/m ^{ 3 } )
ρ _{ 1 } = final density of the object ( kg/m ^{ 3 } ) <
An increase in the pressure will decrease the volume (1). A decrease in the volume will increase the density (2) .
 The SI unit of the bulk modulus elasticity is N/m^{2}(Pa)
 The imperial (BG) unit is lb _{ f } /in^{2}(psi)
 1 lb _{ f } /in^{2}(psi) = 6.894 10 ^{ 3 } N/m^{2}(Pa)
A large Bulk Modulus indicates a relative incompressible fluid.
Bulk Modulus for some common fluids:
Fluid  Bulk Modulus  K   

Imperial Units  BG ( 10 ^{ 5 } psi, lb _{ f } /in^{2})  SI Units ( 10 ^{ 9 } Pa, N/m^{2})  
Acetone  1.34  0.92 
Benzene  1.5  1.05 
Carbon Tetrachloride  1.91  1.32 
Ethyl Alcohol  1.54  1.06 
Gasoline  1.9  1.3 
Glycerin  6.31  4.35 
ISO 32 mineral oil  2.6  1.8 
Kerosene  1.9  1.3 
Mercury  41.4  28.5 
Paraffin Oil  2.41  1.66 
Petrol  1.55  2.16  1.07  1.49 
Phosphate ester  4.4  3 
SAE 30 Oil  2.2  1.5 
Seawater  3.39  2.34 
Sulfuric Acid  4.3  3.0 
Water (10 ^{o}C)  3.12  2.09 
Water  glycol  5  3.4 
Water in oil emulsion  3.3  2.3 
 1 GPa = 10 ^{ 9 } Pa (N/m^{2})
Stainless steel with Bulk Modulus 163 10 ^{ 9 } Pa is aprox. 80 times harder to compress than water with Bulk Modulus 2.15 10 ^{ 9 } Pa .
Example  Density of Seawater in the Mariana Trench
 the deepest known point in the Earth's oceans  10994 m .
The hydrostatic pressure in the Mariana Trench can be calculated as
p _{ 1 } = (1022 kg/m ^{ 3 } ) (9.81 m/s^{2}) (10994 m)
= 110 10 ^{ 6 } Pa (110 MPa)
The initial pressure at sealevel is 10 ^{ 5 } Pa and the density of seawater at sea level is 1022 kg/m ^{ 3 } .
The density of seawater in the deep can be calculated by modifying (2) to
ρ _{ 1 } = ( ( p _{ 1 }  p _{0 } ) ρ _{0 } + K ρ _{0 } ) / K
= (((110 10 ^{ 6 } Pa)  (1 10 ^{ 5 } Pa)) (1022 kg/m ^{ 3 } ) + (2.34 10 ^{ 9 } Pa) (1022 kg/m ^{ 3 } )) / ( 2.34 10 ^{ 9 } Pa )
= 1070 kg/m ^{ 3 }
Note!  since the density of the seawater varies with dept the pressure calculation could be done more accurate by calculating in dept intervals.
Bulk Modulus of Water vs. Temperature
Temperature ( ^{o}C)  Bulk Modulus (10 ^{ 9 } Pa) 

0.01  1.96 
10  2.09 
20  2.18 
30  2.23 
40  2.26 
50  2.26 
60  2.25 
70  2.21 
80  2.17 
90  2.11 
100  2.04 
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