LearnChemE

#### Hydrostatic Pressure: Screencasts

Derives the hydrostatic pressure equation from the equation for a fluid at rest.

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Derives equations for hydrostatic pressure for compressible fluids.

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##### Important Equations:

Hydrostatic pressure for an incompressible fluid:

$P_1 = P_2 + \gamma_{fl}h = P_2 + \gamma_{fl}(z_2-z_1)$

where $$P_1$$ is the pressure at $$z_1$$, $$P_2$$ is the pressure at $$z_2$$, $$\gamma_{fl}$$ is the specific weight of the fluid, and $$h$$ is the difference in height between $$z_2$$ and $$z_1$$.

For a compressible isothermal ideal gas, the hydrostatic pressure is:

$P_2 = P_1*exp \left(\frac{-g(z_2-z_1)}{RT_0} \right)$

where $$g$$ is the acceleration due to gravity, $$R$$ is the gas constant, and $$T_0$$ is the temperature.

For a compressible non-isothermal ideal gas, an equation for temperature needs to be assumed to derive the equation for hydrostatic pressure.

$T= T_0 – \beta z$

$P_2 = P_1 \left[\frac{T_0 -\beta z_2}{T_0 – \beta z_1} \right] ^{g/R\beta}$

where $$T_0$$ is the temperature when $$z=0$$, and $$\beta$$ is the rate of temperature change with elevation.