Variation of Pressure with Depth in a Fluid

Consider two points 1 and 2 lie in the ends of fluid prism having a cross-sectional area dA and length L. The difference in elevation between these two points is h as shown in Figure 02 below. The fluid is at rest and its surface is free. The prism is therefore in equilibrium and all forces acting on it sums up to zero.
 

000-variations-in-pressure.gif

 

Note: FFS stands for Free Fluid Surface which refers to fluid surface subject to zero gauge pressure.
 

Principles of Hydrostatic Pressures

Unit Pressure
Unit pressure or simply called pressure is the amount of force exerted by a fluid distributed uniformly over a unit area.
 

$p = \dfrac{Force, \, F}{Area, \, A}$

 

If the unit pressure is not uniform over the unit area, it can be expressed as the sum of differential pressure.
 

$\displaystyle p = \int \dfrac{dF}{dA}$

 

001-blaise-pascal.jpg
Blaise Pascal (1623 – 1662)

 

Since fluid at rest cannot resist shearing stress, pressure is always at right angle to the area where it is acting. It is also worthy to note that the total hydrostatic force F = pA, which can be found by cross multiplication.
 

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