Tait's equation

The Tait equation is the classic equation of state for water . It gives a relationship between pressure and density for media that are difficult to compress :

{\ displaystyle p-p_ {0} = B \ left (\ left ({\ frac {\ rho} {\ rho _ {0}}} \ right) ^ {m} -1 \ right)}

where is the initial density and the density is in the compressed state. The constants occurring and their numerical values for water are ${\ displaystyle \ rho _ {0}}$ ${\ displaystyle \ rho}$

{\ displaystyle B = {\ frac {\ rho _ {0} c_ {0} ^ {2}} {m}} = {\ frac {K _ {\ mathrm {w}}} {m}} \ approx 0 { ,} 3214 \; {\ rm {GPa}}}

{\ displaystyle m = {\ frac {c_ {p}} {c_ {v}}} \ approx 7}

where represents the speed of sound at the outlet pressure and the compression modulus . The constant is the adiabatic exponent . With other numerical values for and , the equation can also be applied to other liquids. ${\ displaystyle c_ {0}}$ ${\ displaystyle K _ {\ mathrm {w}}}$ ${\ displaystyle m}$ ${\ displaystyle m}$ ${\ displaystyle B}$

The equation is named after Peter Guthrie Tait , who set it up when evaluating the temperature measurement results in the deep sea during the Challenger expedition .

The Taitsche equation is sometimes to be found under the (false) name Tatesche equation .

Individual evidence

↑ Anika Stein: Simulation of rotordynamic problems with the Smoothed Particle Hydrodynamics method . Kassel University Press, ISBN 3-7376-0220-4 , pp. 31 ( limited preview in Google Book search).

[1] Anika Stein: Simulation of rotordynamic problems with the Smoothed Particle Hydrodynamics method . Kassel University Press, ISBN 3-7376-0220-4 , pp. 31 ( limited preview in Google Book search).