CBSE Class 9 Physics Fluid Mechanics Notes Set 06

Pressure in a Liquid

The pressure at a depth h in a liquid of density \( \rho \) is \( P = h\rho g \). It increases with depth and acts equally in all directions at a given depth.
Pascal's law: a pressure applied to an enclosed liquid is transmitted equally to every part of the liquid. A hydraulic press uses this: a small force \( F_1 \) on a small piston of area \( A_1 \) gives a large force \( F_2 = F_1 A_2/A_1 \) on a large piston of area \( A_2 \).

Buoyancy and Archimedes' Principle

A body in a fluid feels an upward force called the buoyant force or upthrust. Archimedes' principle states that the upthrust equals the weight of the fluid displaced by the immersed part of the body: \( F_b = V\rho g \).
A body floats if its average density is less than that of the liquid, and sinks if it is greater. A floating body displaces its own weight of liquid, so the fraction submerged equals the ratio of the body's density to the liquid's density.
Floating ice displaces water equal to its own weight, so when it melts the water level does not change.

Density and Relative Density

Density is mass per unit volume, in kg/m³ (SI) or g/cm³. Relative density is the density of a substance divided by the density of water, and it has no unit. Relative density = weight in air / loss of weight in water.

Equation of Continuity

For an incompressible fluid flowing steadily through a tube, \( A_1 v_1 = A_2 v_2 \). The fluid speeds up where the tube is narrow. This expresses the conservation of mass in flow.