ASPhysicsCIERevision Notes4. Forces, Density & Pressure4.2 Forces: Density & Pressure4.2.3 Derivation of ∆p = ρg∆h

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Derivation of ∆p = ρg∆h (CIE AS Physics)

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Derivation of ∆p = ρg∆h

  • Hydrostatic pressure is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity
  • The derivation for this equation is shown below:

Derivation for hydrostatic pressure (1), downloadable AS & A Level Physics revision notes

Derivation for hydrostatic pressure (2), downloadable AS & A Level Physics revision notes

Hydrostatic pressure derivation

Examiner Tip

You will be expected to remember all the steps for this derivation for an exam question. If any equations which look unfamiliar, have a look at the notes for “Density” and “Pressure”.

Using the Equation for Hydrostatic Pressure

  • Hydrostatic pressure is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity
  • This is when an object is immersed in a liquid, the liquid will exert a pressure, squeezing the object
  • The size of this pressure depends upon the density (ρ) of the liquid, the depth (h) of the object and the gravitational field strength (g):

Hydrostatic pressure equation, downloadable AS & A Level Physics revision notes

  • When asked about the total pressure remember to also add the atmospheric pressure

Total pressure = Hydrostatic pressure + Atmospheric pressure

  • Atmospheric pressure (also known as barometric pressure) is 101 325 Pa

Worked example

Atmospheric pressure at sea level has a value of 100 kPa. The density of sea water is 1020 kg m-3.At what depth in the sea would the total pressure be 250 kPa?A. 20 m               B. 9.5 m               C. 18 m          D. 15 m

Examiner Tip

These pressures can vary widely and depend on metric prefixes such as kPa or MPa. When you’re doing calculations make sure all the pressures are in the same units (otherwise you may be out by a factor of 1000!). To be on the safe side, you can convert them all to Pascals.

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    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.