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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 Objectives

Identify factors that determine the pressure exerted by a gas

Identify factors that determine the pressure exerted by a static liquid
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)
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: Centripetial Acceleration, Position, Displacement, Velocity, and Acceleration as Vectors, and Graphical Interpretation
 application
 Appears in these related concepts: What is Potential Energy?, Work Done by a Variable Force, and Physics and Other Fields
 energy
 Appears in these related concepts: Energy Transportation, Surface Tension, and Introduction to Work and Energy
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 equilibrium
 Appears in these related concepts: Calculating Equilibrium Concentrations of Polyprotic Acids, Understanding and Finding the Deadweight Loss, and Balance and Determining Equilibrium
 fluid
 Appears in these related concepts: Pumps and the Heart, Surface Tension, and Drag
 force
 Appears in these related concepts: Newton and His Laws, Force, and Force of Muscle Contraction
 gravity
 Appears in these related concepts: Properties of Electric Charges, Defining Graviational Potential Energy, and Key Points: Range, Symmetry, Maximum Height
 mass
 Appears in these related concepts: Mass Spectrometer, Mass, and Pop Art
 medium
 Appears in these related concepts: Waves, Painting, and The Role of the Artist
 relative
 Appears in these related concepts: Relative Deprivation Approach, Relative Velocity, and Addition of Velocities
 static
 Appears in these related concepts: Translational Equilibrium, General ProblemSolving Tricks, and Motion
 work
 Appears in these related concepts: Heat and Work, Free Energy and Work, and Potentials and Charged Conductors
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Cite This Source
Source: Boundless. “Variation of Pressure With Depth.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 02 Sep. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/fluids10/densityandpressure92/variationofpressurewithdepth3388350/