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Fluid Mechanics: Hydrostatic Pressure

When dealing with static pressure it can be assumed that the pressure will be same around a specific point or element of interest. This is due to Pascal's Law "The pressure at a point in a fluid at rest, or in motion, is independent of direction as long as there are no shearing stress present." Refer to the equation below.

Fluid Element Force Relation Equation (1)

Fluid Element

Hydrostatic Pressure

Hydrostatic pressure has a relation to the depth of fluid. This is also known as fluid head. The relationship between height and pressure of a fluid can be seen in equations 2-4.

Pressure on a fluid element on the x direction (2)

Pressure on a fluid element on the y direction (3)

Pressure on a fluid element on the z direction (4)

Notice from equations 2-4 the x and y plane has no influence on hydrostatic pressure. Instead the entire influence is due to the height of the fluid. This means the container's cross-sectional area has no influence on hydro static pressure.

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