Thus P₀=rgh.

Where             r=density of the mercury.

The atmospheric pressure is often given as the length of mercury column in a barometer. Thus, a pressure of 76cm of mercury means,

b) Manometer:

Manometer is a simple device to measure the pressure in a closed vessel containing a gas. It consists of a U-shape tube having some liquid. One end of the tube is open to the atmosphere and the other end is connected to the vessel as shown in figure (4).

                          Fig (4)

The pressure of the gas is equal to the pressure at A

= Pressure at B

= Pressure at C + hrg

= P₀ + hrg

Where P₀ is the atmospheric pressure h = BC is the difference in levels of the liquid in the two arms and r is the density of the liquid.

ARCHIMEDES PRINCIPLE:

When the body is partially or fully dipped into a fluid, the fluid exerts forces on the body. At any small portion of the surface of the body, the force by the fluid is perpendicular to the surface and is equal to the pressure at that point multiplied by the area as shown in figure (5).

The resultant of all these contact forces is called the forces of buoyancy or buoyant force.

Archimedes principle states that when a body is partially or fully dipped into a fluid at rest, the fluid exerts an upward force of buoyancy equal to the weight of the displaced fluid.

Numerical:

1)      A 700g solid cube having an edge of length 10cm floats in water. How much volume of the cube is outside the water? Density of water = 1000 kg/m³.

Solution:

The weight of the cube is balanced by the buoyant force. The buoyant force is equal to the weight of the water displaced. If a volume V of the cube is inside the water, the weight of the displaced water = Vrg, Where r is the density of water,

Thus Vrg = (0.7kg) g.

Or,

The total volume of the cube = (10cm) ³ = 1000cm³.

The volume outside the water is 1000-700 = 300 cm³.