How to Prove Pressure (P) = hdg? - Pressure Proof

Liquid pressure is the pressure exerted by the liquid per unit area of the surface. Liquid pressure is defined by one important formula i.e. p = hdg. 

In this formula, 'p' stands for 'liquid pressure', 'h' stands for the height or depth of the liquid, 'd' stands for the density of the liquid and 'g' stands for acceleration due to gravity.

Prove: P = hdg 

Consider a liquid of density(d) is kept in a container with the base area (A) and the height (depth) of the liquid is (h) as shown in the figure.



We know that,

Pressure (P) = Force (F) /Area(A) [ General formula of Pressure ]

= (m × g) / A [ Force = mass(m) * acceleration due to gravity(g) ]

= (d × v × g) / A [ mass(m) = density(d) * volume(v) from the formula: d=m/v ]

= (d × A × h × g) / A [ volume(v) = Base area (A) * height(h) ]

= d × h × g [ Area on the numerator and denominator get canceled out ]

= hdg [ Rewriting the above expression ]

Therefore, P = hdg   #proved


From the above formula P = hdg, we can conclude the following things:

Factors affecting liquid pressure:

  1. Depth of liquid (h)
  2. Density of liquid (d)
  3. Acceleration due to gravity (g)

We hope that you loved this proof of Pressure (P) = hdg. We would like to ask you to read this note: Pressure - Unit 2 Notes for Class 10 with Solved Numericals.

The pressure is one of the important chapters from Physics for Class 10. In class 10, we mostly focus on liquid pressure and hydraulic than other types of pressure. So, this proof of P = hdg is the most important for class 10 board preparation for every batch that would be appearing in the class 10 finals examination.

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