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)
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) .
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 )
|ISO 32 mineral oil||2.6||1.8|
|Petrol||1.55 - 2.16||1.07 - 1.49|
|SAE 30 Oil||2.2||1.5|
|Water (10 o C)||3.12||2.09|
|Water - glycol||5||3.4|
|Water in oil emulsion||3.3||2.3|
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 .
- 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 sea-level 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.
( o C)
|Bulk Modulus |
(10 9 Pa)
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