HYDROSTATICS THIS PROJECT IS DONE BY: VIJAY ANAND (X STD) UNDER THE GUIDANCE OF : MR.K.V. RAJESH (PHYSICS)

INTRODUCTION 1. LAW OF FLOATATION 2. STABILITY OF A FLOATING BODIES 3. STABILITY AND METACENTRE OF A SHIP 4. EXPERIMENTAL DETERMINATION OF THE METACENTRIC HEIGHT OF A SHIP. 5. PLIMSOLL LINE 6. HYDROMETER

LAW OF FLOATATION STABILITY OF FLOATING BODIES: The weight of the floating is equal to the weight of the liquid displaced by it. The centre of gravity of the floating body and the centre of gravity of the liquid displaced are in the same vertical line. STABILITY OF FLOATING BODIES: The equilibrium of a freely floating body is said to be Stable , if on being slightly displaced, the body returns To the original equilibrium position. Consider a floating body in equilibrium.G is the centre of gravity of the floating body and B is The center of buoyancy . The line BG is vertical .

When the floating body is slightly displaced C is the new center Of buoyancy. The vertical line through C meets the original Vertical line BG at M.M is called the Hydrostatics. ` Metacenter’ of the floating body. GM is called the metacentric height. The weight Of the body W acts vertically downwards Through G. The up thrust of value W acts Vertically upwards through C.If the metacenter Is above G, the couple due to the forces at G and C is the anticlock wise and brings the floating body Back to its original position. Hence in this case the Equilibrium is stable. But if M lies below G, the couple due to the forces at G. And C is clock-wise and the couple tends to turn the body away from the equilibrium position. Hence this equilibrium is unstable .

body to be in stable equilibrium , the Metacenter must be always above the center of gravity of the body. Note: In the case of a sphere floating in a Liquid , a tilt one way or other does not change The shape of the displaced liquid. Hence M Coincides with G all the time . Therefore , it is said to be in neutral equilibrium and it continues to float in all positions.

EXPERIMENTAL DETERMINATION OF THE METACENTRIC HEIGHT OF A SHIP. The weight of the ship W is determined By the displaced method. Two identical Boats are attached one on each side of The ship. In A and B represent the boats At a distance l apart on the deck. Filling A and B alternately with water is Equivalent to moving a known weight W from A and B across the deck. Filling The boat B with the same mass of water As in A , turns the ship through an angle ⍬. The tilt ⍬ is determined by means Of a plumb line suspended in the ship.

PLIMSOLL LINE In 1876, Samuel Plimsoll took up the matter and Suggested that compulsory load lines called plimsoll Lines be introduced. These lines were drawn on the side of every ship for safe loading. The line for tropical fresh water (lowest density) is at the top and That for the north Atlantic seas is at the bottom (highest density being very cold). A ship will be loaded till it sinks to the appropriate line. Then whatever its destination it will Float at the safe level.

HYDROMETER A hydrometer is an instrument which works on the Principle that when a body floats in any liquid the weight of the floating body is equal to the weight of the liquid displaced. A hydrometer is used to find the specific gravity of a liquid. There are two type of hydrometers, (1) The variable immersion hydrometer and (2) The constant immersion hydrometer.

VARIABLE IMMERSION HYDROMETER In the variable immersion hydrometer, the weight of the hydrometer is kept constant but the depth of immersion varies depending on the density of the liquid in which it is floated. CONSTANT IMMERSION HYDROMETER In the constant immersion hydrometer, the depth of the hydrometer is kept constant where as the weight of the hydrometer is changed to make it float to the same depth.

COMMON HYDROMETER A common hydrometer consists of a uniform glass stem which ends in a broader glass tube. Below this is bulb containing mercury or lead shots to make it float vertically. The hydrometer sinks to different depths in different liquids And deeper immersion occurs in Lighter liquids. There are two sets of hydrometers having different ranges of specific gravities. One for liquids Lighter then water and the other for Liquids heavier then water.