Question

derive an expression for the pressure exerted by a liquid column on the bottom of the vessel.

Answer 1

Consider an imaginary cuboid of area of cross-section a of liquid with upper and lower cap passing through A and B respectively in order to evaluate the pressure difference between points A and B.

Volume of the imaginary cylinder is, V = ah

Mass of liquid of imaginary cylinder, m = ρah

Let, P1 and P2 be the pressure on the upper and lower face of cylinder.

Forces acting on the imaginary cylinder are:

(i) Weight, mg = ρahg in vertically downward direction.

(ii) Downward thrust of F1 =P1a on upper cap.

(iii) Upward thrust of F2 = P2a on lower face.

As the imaginary cylinder in the liquid is in equilibrium, therefore the net force on the cylinder is zero.


i
.
e
.
,

F
1

+

mg

=

F
2


P
1
a

+

ρahg

=

P
2
a

⇒



P
2

−

P
1

=

ρgh
ieF1mgF2
P1aρahgP2a
P2P1ρgh

Thus, the pressure difference between two points separated vertically by height h in the presence of gravity is ρgh.