Hydrostatic pressure refers to the pressure exerted by a fluid (gas or liquid) at any point in space within that fluid, assuming that the fluid is incompressible and at rest.

**Pressure** is defined in simplest terms as force per unit area. However, when dealing with pressures exerted by gases and liquids, it is most convenient to approach pressure as a measure of energy per unit volume by means of the definition of **work** (W = F·d). The derivation of pressure as a measure of energy per unit volume from its definition as force per unit area is given in. Since, for gases and liquids, the force acting on a system contributing to pressure does not act on a specific point or particular surface, but rather as a distribution of force, analyzing pressure as a measure of energy per unit volume is more appropriate. For liquids and gases at rest, the pressure of the liquid or gas at any point within the medium is called the **hydrostatic pressure**. At any such point within a medium, the pressure is the same in all directions, as if the pressure was not the same in all directions, the fluid, whether it is a gas or liquid, would not be static. Note that the following discussion and expressions pertain only to incompressible fluids at static equilibrium.

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. It increases in proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above. It can be determined by the following formula:

P = ρgh

**Pascal’s Principle** (or **Pascal’s Law**) applies to static fluids and takes advantage of the height dependency of pressure in static fluids. Pascal’s Principle can be used to exploit pressure of a static liquid as a measure of energy per unit volume to perform work in applications such as** hydraulic presses**. Qualitatively, Pascal’s Principle states that pressure is transmitted undiminished in an enclosed static liquid. Quantitatively, Pascal’s Law is derived from the expression for determining the pressure at a given height (or depth) within a fluid and is defined by Pascal’s Principle:

p_{2} = p_{1 }+ Δρ, Δp = ρgh

where p_{1} is the external applied pressure, ρ is the density of the fluid, Δh is the difference in height of the static liquid, and g is the acceleration due to gravity. Pascal’s Law explicitly determines the pressure difference between two different heights (or depths) within a static liquid. As, by Pascal’s Law, a change in pressure is linearly proportional to a change in height within an incompressible, static liquid of constant density, doubling the height between the two points of reference will double the change of pressure, while halving the height between the two points will half the change in pressure.

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Key Points

• Pressure is the force per unit perpendicular area over which the force is applied, P=F/A.

• Pressure due to the weight of a liquid of constant density is given by P=ρgh where h is the depth of the liquid, ρ is the density of the liquid, and g is the acceleration due to gravity.

• Pascal’s Principle is used to quantitatively relate the pressure at two points in an incompressible, static fluid. It states that pressure is transmitted, undiminished, in a closed static fluid.

• The total pressure at any point within an incompressible, static fluid is equal to the sum of the applied pressure at any point in that fluid and the hydrostatic pressure change due to a difference in height within that fluid.

• Through the application of Pascal’s Principle, a static liquid can be utilized to generate a large output force using a much smaller input force, yielding important devices such as hydraulic presses.

Key Terms

**Pressure**: Defined as a measure of the force applied over a unit area.

**Hydrostatic pressure**: The pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. It increases in proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above.

**Density**: of a substance or object is defined as its mass per unit volume, ρ = m/ V.

**Pascal’s principle**: P = F/A.

**Hydraulic press**: Device that uses a hydraulic cylinder (closed static fluid) to generate a compressive force.

**Pascal’s law:** A principle in fluid mechanics that states that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.