2.3.2: Fluid-static equation
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Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. It embraces the study of the conditions under which fluids are at rest in stable equilibrium.
Figure 2.16: Differential cylinder of air. Adapted from Franchini et al. [3].
If we assume the air at rest as in Hypothesis (2.1), we can formulate the equilibrium of a differential cylindrical element where only gravitational volume forces and pressure surface forces act (see Figure 2.16):
\[pdS - (p + dp) dS = \rho g d Sdh, \nonumber \]
which gives rise to the equation of the fluid statics:
\[\dfrac{d p}{dh} = -\rho g. \nonumber \]