Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Bulk Modulus and Fluid Elasticity

Introduction to - and definition of - Bulk Modulus Elasticity commonly used to characterize the compressibility of fluids.

Sponsored Links

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.

Bulk Modulus Elasticity

The Bulk Modulus Elasticity can be calculated as

K = - dp / (dV / V0

   = - (p1 - p0) / ((V1 - V0) / V0)                       (1)

where

K = Bulk Modulus of Elasticity (Pa, N/m2)

dp = differential change in pressure on the object (Pa, N/m2)

dV = differential change in volume of the object (m3)

V0 = initial volume of the object  (m3)

p0 = initial pressure (Pa, N/m2)

p1 = final pressure (Pa, N/m2)

V1 = final volume (m3)

The Bulk Modulus Elasticity can alternatively be expressed as

K = dp / (dρ / ρ0

   = (p1 - p0) / ((ρ1 - ρ0) / ρ0)                              (2)

where

dρ = differential change in density of the object   (kg/m3)

ρ0 = initial density of the object  (kg/m3)

ρ1 = final density of the object (kg/m3)

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/m2 (Pa)
  • The imperial (BG) unit is lbf/in2 (psi)
  • 1 lbf/in2 (psi) = 6.894 103 N/m2 (Pa)

A large Bulk Modulus indicates a relative incompressible fluid.

Bulk Modulus for some common fluids:

FluidBulk Modulus
- K -
Imperial Units - BG
  (105 psi, lbf/in2)
SI Units
  (109 Pa, N/m2)
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 oC) 3.12 2.09
Water - glycol 5 3.4
Water in oil emulsion 3.3 2.3
  • 1 GPa = 109 Pa (N/m2)

Stainless steel with Bulk Modulus 163 109 Pa is aprox. 80 times harder to compress than water with Bulk Modulus 2.15 109 Pa.

Example - Density of Seawater in the Mariana Trench

- the deepest known point in the Earth's oceans - 10994 m.

Mariana Trench

The hydrostatic pressure in the Mariana Trench can be calculated as

p1 = (1022 kg/m3) (9.81 m/s2) (10994 m)

    = 110 106 Pa  (110 MPa)

The initial pressure at sea-level is 105 Pa and the density of seawater at sea level is 1022 kg/m3.

The density of seawater in the deep can be calculated by modifying (2) to

ρ1 = ((p1 - p0) ρ0  + K ρ0) / K

    = (((110 106 Pa) - (1 105 Pa)) (1022 kg/m3) + (2.34 109 Pa) (1022 kg/m3)) / (2.34 109 Pa)

    = 1070 kg/m3

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
(oC)
Bulk Modulus
(109 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
Sponsored Links

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

    Material properties of gases, fluids and solids - densities, specific heats, viscosities and more.

Related Documents

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

Citation

This page can be cited as

  • The Engineering ToolBox (2004). Bulk Modulus and Fluid Elasticity. [online] Available at: https://www.engineeringtoolbox.com/bulk-modulus-elasticity-d_585.html [Accessed Day Month Year].

Modify the access date according your visit.

close

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter

















































9.19.12

Sponsored Links
.