Tait equation

Tait equation

The Tait equation is a mathematical formula that describes the relationship between volume, pressure, and temperature in a nonlinear compressible system. Its general form is V(P,T) = V(0,T){1 - C ln[1 + P/B(T)]}, and it is particularly useful for calculating derivative quantities such as isothermal compressibility and thermal expansivity coefficients. The Tait equation is important for tracking pressure waves and accounting for nonlinear compressible effects.From: CRC Handbook of Chemistry and Physics [2016], Numerical simulation of cavitation-bubble expansion and collapse inside a bottle subjected to impact on its topside [2021]

Polymer Properties

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Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016

W. M. Haynes, David R. Lide, Thomas J. Bruno

Numerous theoretical equations of state for polymer liquids have been developed. These, at the minimum, have to provide accurate fitting functions to experimental data. However, for the purpose of this table, the empirical Tait equation along with a polynomial expression for the zero pressure isobar is used. This equation is able to represent the experimental data for the melt state within the limits of experimental errors, i.e., the maximum deviations between measured and calculated specific volumes are about 0.001-0.002 cm3/g. The general form of the Tait equation is: V(P,T) = V(0,T){1 - C ln[1 + P/B(T)]} (1) The Tait equation is particularly useful to calculate derivative quantities, such as the isothermal compressibility and the thermal expansivity coefficients. The isothermal compressibility (P,T) is derived from equation (1) as: (P,T) = -(1/V)(dV/dP) = 1/{[P + B(T)][1/C - ln(1 + P/B(T))]} (8) and the thermal expansivity (P,T) as: (P,T) = (1/V)(dV/dT) = (0,T) - PB1(P,T) (9)

Numerical simulation of cavitation-bubble expansion and collapse inside a bottle subjected to impact on its topside

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Published in Engineering Applications of Computational Fluid Mechanics, 2021

Yue-han Chen, Jie-min Zhan, Yu-tian Li

Both phases are considered compressible, where the ideal gas model is used for the gas and the following Tait equation is used for the liquid: where is the density of water, equal to , is the speed of sound, equal to , at the reference state and the exponent is set to 7.15. The Tait equation accounts for a nonlinear compressible effect, which is a prerequisite for tracking pressure waves.

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Polymer Properties

Numerical simulation of cavitation-bubble expansion and collapse inside a bottle subjected to impact on its topside