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Variation of Pressure With Depth
Pressure within static fluids depends on the properties of the fluid, the acceleration due to gravity, and the depth within the fluid.
Learning Objective

Identify factors that determine the pressure exerted by static liquids and gases
Key Points
 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 within a liquid depends only on the density of the liquid, the acceleration due to gravity, and the depth within the liquid. The pressure exerted by such a static liquid increases linearly with increasing depth.
 Pressure within a gas depends on the temperature of the gas, the mass of a single molecule of the gas, the acceleration due to gravity, and the height (or depth) within the gas.
Terms

incompressible
Unable to be compressed or condensed.

static equilibrium
the physical state in which all components of a system are at rest and the net force is equal to zero throughout the system
Full Text
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.
Energy per Unit Volume
This equation is the derivation of pressure as a measure of energy per unit volume from its definition as force per unit area.
The pressure exerted by a static liquid depends only on the depth, density of the liquid, and the acceleration due to gravity. gives the expression for pressure as a function of depth within an incompressible, static liquid as well as the derivation of this equation from the definition of pressure as a measure of energy per unit volume (ρ is the density of the gas, g is the acceleration due to gravity, and h is the depth within the liquid). For any given liquid with constant density throughout, pressure increases with increasing depth. For example, a person under water at a depth of h_{1} will experience half the pressure as a person under water at a depth of h_{2} = 2h_{1}. For many liquids, the density can be assumed to be nearly constant throughout the volume of the liquid and, for virtually all practical applications, so can the acceleration due to gravity (g = 9.81 m/s^{2}). As a result, pressure within a liquid is therefore a function of depth only, with the pressure increasing at a linear rate with respect to increasing depth. In practical applications involving calculation of pressure as a function of depth, an important distinction must be made as to whether the absolute or relative pressure within a liquid is desired. Equation 2 by itself gives the pressure exerted by a liquid relative to atmospheric pressure, yet if the absolute pressure is desired, the atmospheric pressure must then be added to the pressure exerted by the liquid alone.
Pressure as Energy per Unit Volume
This equation gives the expression for pressure as a function of depth within an incompressible, static liquid as well as the derivation of this equation from the definition of pressure as a measure of energy per unit volume (ρ is the density of the gas, g is the acceleration due to gravity, and h is the depth within the liquid).
When analyzing pressure within gases, a slightly different approach must be taken as, by the nature of gases, the force contributing to pressure arises from the average number of gas molecules occupying a certain point within the gas per unit time. Thus the force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids and the barometric equation given in must be utilized to determine the pressure exerted by the gas at a certain depth (or height) within the gas (p_{0} is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas). Equation 3 assumes that the gas is incompressible and that the pressure is hydrostatic.
Pressure within a gas
The force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids and the barometric equation given in this figure must be utilized to determine the pressure exerted by the gas at a certain depth (or height) within the gas (p0 is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas)
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Key Term Reference
 Pressure
 Appears in these related concepts: SI Units of Pressure, Physics and Engineering: Fluid Pressure and Force, and Surface Tension and Capillary Action
 acceleration
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Scientific Applications of Quadratic Functions, and Centripetial Acceleration
 application
 Appears in these related concepts: Introduction to Elementary operations and Gaussian Elimination, Physics and Other Fields, and XRay Imaging and CT Scans
 energy
 Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction to Work and Energy
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 equilibrium
 Appears in these related concepts: Homogeneous versus Heterogeneous Solution Equilibria, Diffusion, and Second Condition
 fluid
 Appears in these related concepts: Pumps and the Heart, Drag, and B.11 Chapter 11
 force
 Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
 gravity
 Appears in these related concepts: Defining Graviational Potential Energy, Key Points: Range, Symmetry, Maximum Height, and Properties of Electric Charges
 mass
 Appears in these related concepts: Mass Spectrometer, Pop Art, and Mass
 medium
 Appears in these related concepts: Waves, The Role of the Artist, and Refraction Through Lenses
 relative
 Appears in these related concepts: Relative Deprivation Approach, Addition of Velocities, and Relative Velocity
 static
 Appears in these related concepts: Friction: Static, Time and Motion, and Alternative Views
 work
 Appears in these related concepts: Heat and Work, Free Energy and Work, and The First Law of Thermodynamics
Sources
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Cite This Source
Source: Boundless. “Variation of Pressure With Depth.” Boundless Physics. Boundless, 08 Aug. 2016. Retrieved 27 Oct. 2016 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/fluids10/densityandpressure92/variationofpressurewithdepth3388350/