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.

(Eq 1) $δF_s=-\left(\frac{δP}{δx}i+\frac{δP}{δy}j+\frac{δP}{δz}k\right)δ_xδ_yδ_z$

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.

(Eq 2)   $\frac{δP}{δx}=0$

(Eq 3)   $\frac{δP}{δy}=0$

(Eq 4)   $\frac{δP}{δz}=γ$

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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