Tait equation

In fluid mechanics, the Tait equation is an equation of state, used to relate liquid density to pressure. The equation was originally published by Peter Guthrie Tait in 1888. It is sometimes written as

\[ \beta_0^{(P)} = \frac{-1}{V_0^{(P)}} \left ( \frac{\partial P}{\partial V} \right )_T = \frac{0.4343C}{V_0^{(P)}(B+P)}\]

or in the integrated form

\[ V_0^{(P)} = V_0^{(1)} - C \log \frac{B+P}{B+1}\]

where

• \( \beta_0^{(P)} \) is the compressibility of water (in units of bar^-1)
• \( V_0 \ \) is the specific volume of water (in units of ml/g)
• \( B \ \) and \( C \ \) are functions of temperature that are independent of pressure