Fluid Pressure Equations (College Board AP® Physics 1: Algebra-Based)

Gauge pressure equation

Incompressible fluids

• When a pressure is exerted on an incompressible fluid:

  • its total volume remains constant

  • its density remains constant

Gauge pressure

• When an object is submerged under a given height of fluid, it experiences pressure form the weight of the column of fluid above it

• This is called the gauge pressure and is described by the equation:

• Where:

  • = gauge pressure, measured in

  • = density, measured in

  • = height of the fluid column above the point experiencing pressure, measured in

• For a given fluid, this formula depends only on height, so all points the same depth from a fluid's surface experience the same pressure

  • Note that this is independent of the shape of the container

• As shown in the diagram below, if three containers of different shapes hold the same height of fluid:

  • All points at a certain depth experience the same pressure, even in differently shaped containers

• The pressure experienced by a object's surface is independent of the mass of the object

  • A cardboard box and a solid steel cube will both experience the same pressure under water, provided they are at the same depth

Pressure in containers of different shapes

Absolute pressure equation

• For an object submerged in a fluid, the pressure it experiences also depends on the fluid's surroundings

• If the fluid experiences a pressure from its surroundings, then the pressure on the submerged object also experiences this pressure

  • This is a consequence of the fluid being incompressible - any pressure it experiences at its surface is transferred to the object

  • e.g. an object submerged in water experiences a pressure due to the weight of the water plus pressure due to the weight of the atmosphere

• This total pressure from fluid and surroundings is called absolute pressure

absolute pressure = reference pressure + gauge pressure

• With this external 'reference' pressure, the equation for absolute pressure experienced by an object becomes:

• Where:

  • = total (or absolute) pressure experienced by the object, measured in

  • = reference pressure, measured in

  • = density, measured in

  • = height of the fluid column above the object experiencing pressure, measured in

• The most common scenario is a liquid in Earth's atmosphere, making the reference pressure equal to atmospheric pressure:

• Where:

  • = pressure of the atmosphere at sea level, measured in