ï»¿ Obtain an expression for the pressure exerted by liquid column. from Physics Mechanical Properties of Fluids Class 11 Manipur Board

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Obtain an expression for the pressure exerted by liquid column.

Consider a liquid of density ρ in a vessel as shown in figure.

To find: Pressure difference between two points A and B separated by vertical height h.

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.

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

Note: In the absence of gravity this pressure difference becomes zero.

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What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. The study of fluids at rest or objects placed at rest in fluids is hydrostatics.
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Do intermolecular or inter-atomic forces follow inverse square law?

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What is fluid?

Any material that can flow is a fluid. Liquids and gases are examples of fluid.

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Why solids have definite shape while liquids do not have definite shape?

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