Fluid Mechanics: Hydrostatic Pressure

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Hydrostatic Pressure

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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.

(2)

(3)

(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.

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.

(5)

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.

(6)

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.

(7)

(8)

(9)

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.