Relative Equilibrium of Liquids

Relative equilibrium of liquid is a condition where the whole mass of liquid including the vessel in which the liquid is contained, is moving at uniform accelerated motion with respect to the earth, but every particle of liquid have no relative motion between each other. There are two cases of relative equilibrium that will be discussed in this section: linear translation and rotation. Note that if a mass of liquid is moving with constant speed, the conditions are the same as static liquid in the previous sections.
 

Formulas
For details of the following formulas see the translation and rotation pages.
 

Horizontal Motion
$\tan \theta = \dfrac{a}{g}$
 

Inclined Motion
$\tan \theta = \dfrac{a_h}{g \pm a_v}$
 

Vertical Motion
$p = \gamma h \left(1 \pm \dfrac{a}{g}\right)$
 

Rotation
$\tan \theta = \dfrac{\omega^2x}{g}$   and   $y = \dfrac{\omega^2x^2}{2g}$
 

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