How to derive P=hdg? by Bikash Shrestha

This formula is used to calculate the pressure exerted by any liquid at certain depth.

Let a vessel with cross sectional area 'A' is filled 

with any liquid of density 'd', volume 'V' and mass

'm' up to the height 'h' as shown in the figure 

alongside. Now ‘h’ is termed as depth of liquid

from the free surface.

According to the definition of Pressure,                                               

       P = F/A

or,   P = mg/A             [ since F = mg ]

or,   P = Vdg/A            [ since m = Vd ]

or    P = Ahdg/A          [ since V = Ah ]

\    P = hdg               where g is the acceleration due to gravity of that place.

This clearly shows that liquid pressure is dependent on h(depth of liquid from the free surface), d( the density of the liquid) and g( the acceleration due to gravity of that place) but independent of volume of liquid, shape and size of the liquid container.

At certain place, the density 'd' of the liquid and acceleration due to gravity 'g' are constant. So, pressure of the liquid only depends on depth 'h' from free surface. Due to this reason a bucket can be filled faster from the tap in ground floor than in other floors as liquid pressure is directly proportional to the depth and the depth of the liquid in the tap of ground floor is maximum.