Fluid Mechanics: Hydrostatic Pressure

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Hydrostatic Pressure

Length: 12 Minutes 31 Seconds

Static 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.

(1)

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.

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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.

Hydrostatic Pressure of an Incompressibile Fluid

A fluid can be considered incompressible if it takes a large amount of pressure to compress the fluid. Liquids can be considered incompressible fluids. To determine the hydrostatic pressure of an incompressible fluid refer to equation 5.

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Hydrostatic Pressure of a Compressibile Fluid

A compressible fluid easily changes its density and volume under different pressures. To calculate the hydrostatic pressure of a compressible fluid the ideal gas law would be used.

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Hydrostatic Force on a Plane

When calculating hydrostatic force on a plane you have to realize that the pressure along the plane can change based on its relationship to the fluids depth. To calculate the resultant force equation 7 would be used. Also, to find the location of the resultant force on the plane equations 8-9 would be used.

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Hydrostatic Force on a Curved Surface

There are also some cases where the hydrostatic force on a curved surface is of interest. To calculate the hydrostatic force on a curved surface refer to the equations below.

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(11)

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F1 in equation 12 represents the force above the curve.