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 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 
Related Topics

Fluid Mechanics
The study of fluids  liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time. 
Material Properties
Properties of gases, fluids and solids. Densities, specific heats, viscosities and more.
Related Documents

Cauchy Number
Introduction to the Cauchy Number. 
Heavy Water  Thermophysical Properties
Thermodynamic properties of heavy water (D2O) like density, melting temperature, boiling temperature, latent heat of fusion, latent heat of evaporation, critical temperature and more. 
Liquids  Densities vs. Pressure and Temperature Change
Densities and specific volume of liquids vs. pressure and temperature change. 
Mach Number
An introduction to the Mach Number. 
Metals and Alloys  Bulk Modulus Elasticity
The Bulk Modulus  resistance to uniform compression  for some common metals and alloys. 
Minerals  Densities
Densities of minerals. 
Modulus of Rigidity
Shear Modulus (Modulus of Rigidity) is the elasticity coefficient for shearing or torsion force. 
Speed of Sound  Equations
Calculate the speed of sound (the sonic velocity) in gases, fluids or solids. 
Water Hammer
Rapidly closing or openingĀ valves  or starting stopping pumps  may cause pressure transients in pipelines known as surge or water hammers.