# Bulk Modulus and Fluid Elasticity

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

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The Bulk Modulus Elasticity 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 expressed as

E = - dp / (dV / V) (1)

where

E = bulk modulus elasticity

dp = differential change in pressure on the object

dV = differential change in volume of the object

V = initial volume of the object

The Bulk Modulus Elasticity can be alternatively expressed as

E = dp / (dρ / ρ) (2)

where

dρ = differential change in density of the object

ρ = initial density of the object

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 indicate a relative incompressible fluid.

Bulk Modulus for some common fluids can be found in the table below:

Bulk Modulus - E | 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 | 3.12 | 2.15 |

Water - glycol | 5 | 3.4 |

Water in oil emulsion | 3.3 | 2.3 |

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