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# Fluids Pressure Upthrust and Flotation Concepts

## Introduction

The pressure exerted by a liquid on the base of the container depends on the vertical height of the liquid over it not on the area of cross-section. As one goes deeper in the swimming pool, the pressure on the ear drum is found to increase.

## Transmission of Pressure in Liquids

The transmission of power is made use of in hydraulic machines where a small force applied at one point is made to exert a much larger force at some other point. This principle is made use of in the working of a hydraulic press and hydraulic brakes.

## Atmospheric Pressure

The atmosphere is the layer of air around the earth. It extends up to 1000 km above the surface of the earth and has a total weight of 4.5 1018 kg (i.e., five million billion tons).

## Different Types of Barometers

A barometer is a device for measuring the atmospheric pressure.

## Pressure in a Liquid

It is a simple pressure gauge and it measures differences in pressure exerted at the two ends of the apparatus. It is called manometer. The mouth of a thistle funnel is tightly covered with a thin plastic sheet.

## Buoyancy

A cork is pushed down into water kept in a glass. We find that as soon as it is released, the cork rises on its own and comes to the surface.

## Upthrust in Fluids

Any liquid or gas produces upthrust. For example, the upthrust of air keeps a hot air balloon up.

## Archimede's Principle

The underlying fact on which the principle is based was discovered by Archimedes in about 300 B.C. The story goes that the King of Sicily suspected that the goldsmith has mixed some silver in his crown and cheated him. Without destroying the crown he wanted to know the truth. Archimedes was asked to find out whether this was so, without destroying the crown.

## Relative Density (or Specific gravity)

Relative density (RD) of a substance is defined as the ratio of the density of the substance to density of water at 4oC.

## R.D and Archimede's Principle

A solid weighs 50 gf in air and 44 gf when completely immersed in water. Calculate (i) R.D of the solid (ii) upthrust (iii) density of the solid in cgs and SI units.

## Floating Bodies

Usually, all bodies less than that of water float, bodies which are denser than water sink. You might have noticed that a piece of steel sinks, but a ship made of steel floats. This is because of the design of the ship. The steel body of the ship encloses large quantity of air. Thus, the average density of the ship is less than that of water and the ship floats in water.

## Submarine

The submarine is another application of 'Archimedes Principle'. On surface, the submarine floats, with its conning tower and most of the deck, being clear of the water.

## Hydrometer

Hydrometer is an instrument used for determining the density of a liquid. It usually consists of a glass float with a long thin stem which is graduated. The glass float is a large hollow bulb which increases the buoyancy so that the hydrometer floats. The narrow stem increases the sensitivity of the hydrometer. The bottom of the hydrometer is made heavier by loading it with lead shots so that it floats vertically.

## Summary

Pressure at a point in a liquid depends upon the depth and on the density of the liquid.

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