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CAIE A-Level Physics 4.3.3 Derivation of Liquid Pressure

Practise deriving delta p = rho g delta h from pressure, density and weight definitions, stating assumptions and checking dimensions and depth dependence.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • derive Δp = ρgΔh from pressure as force per area, density as mass per volume and weight as mg
  • state the assumptions in the hydrostatic derivation, including uniform density and a static fluid column
  • check the dimensions and physical meaning of Δp = ρgΔh, including how pressure changes with depth

4.3.3—Derive, from the definitions of pressure and density, the equation question 1

[Maximum number: 3]

A beaker in air contains a liquid. The base of the beaker is in contact with the liquid and has area A, as shown in Fig. 4.1.

Fig. 4.1

Fig. 4.1

The liquid has density ρ\rho and fills the beaker to a depth h.

By using the definitions of pressure and density, show that

p=ρghp=\rho g h

where p is the pressure due to the liquid that is exerted on the base of the beaker and g is the acceleration of free fall.

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