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4.3.5.3: Liquid Under Varying Gravity

  • Page ID
    675
  • For comparison reason consider the deepest location in the ocean which is about 11,000 [m]. If the liquid "equation of state'' (61) is used with the hydrostatic fluid equation results in

    \[ \dfrac{\partial P}{\partial r} = -
    {\rho_0} \text{ e}^{\dfrac{P- {P_0}}{ B_T}}
    \dfrac{G}{r^2}
    \label{static:eq:liquidGhydro}
    \]
    which the solution of equation (118) is

    \[ \text{e}^{\dfrac{P_0-P}{B_T}}
    =Constant -\dfrac{B_T\,g\;\rho_0}{r}
    \label{static:eq:liquidGhroS}
    \]

    Since this author is not aware to which practical situation this solution should be applied, it is left for the reader to apply according to problem, if applicable.

    Contributors and Attributions

    • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.