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Fluid Mechanics

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Published in: Mechanical | Physics
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Notes On Buoyancy & Flotation.

Navin S / Hyderabad

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Qualification: B.Tech/B.E. (Bit Sindri , Sindri - 2011)

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  1. BUOYANCY & FLOTATION Buoyancy Buoyancy is also known as buoyant force. It is the force exerted on an object that is wholly or partly immersed in a fluid. Concept of Buoyancy: When a body is immersed in a fluid, an upward force is exerted by fluid on the body which is equal to weight of fluid displaced by body. This acts as upward. Archimedes' Principle: It states, when a body is immersed completely or partially in a fluid, it is lifted up by a force equal to weight of fluid displaced by the body. h 1 1 Cylinder-fluid systern Buoyant force = Weight of fluid displaced by body Buoyant force on cylinder -Weight of fluid displaced by cylinder Value of immersed part of solid or -B Volume of fluid displaced Volume of cylinder immersed inside the water Principle of Flotation: According to this principle, if weight of body is equal to buoyant force then, body will float. FE mg CIT2X The factors that affect buoyancy are: the density of the fluid, the volume of the fluid displaced, and the local acceleration due to gravity. The buoyant force is not affected by the mass of the immersed object or the density of the immersed object.
  2. BUOYANCY & FLOTATION Center of Buoyancy: The point at which force of buoyancy acts is called center of buoyancy. It lies on center of gravity of volume of fluid displaced or center of gravity of the part of the body which is inside the water. Point B is the center of buoyancy. x 72 Centre Of buoyancy diagrary) Buoyancy on a submerged body: The Archimedes principle states that the buoyant force on a submerged body is equal to the weight of liquid displaced by the body, and acts vertically upward through the centroid of the displaced volume. Thus the net weight of the submerged body, (the net vertical downward force experienced by it) is reduced from its actual weight by an amount that equals the buoyant force. Buoyancy on a partially immersed body: According to Archimedes principle, the buoyant force of a partially immersed body is equal to the weight of the displaced liquid. Therefore the buoyant force depends upon the density of the fluid and the submerged volume of the body. For a floating body in static equilibrium and in the absence of any other external force, the buoyant force must balance the weight of the body. Metacentre of a Floating Body: If a body which is floating in liquid is given small angular displacement, it starts oscillating about some point M. This point is called metacentre.
  3. BUOYANCY & FLOTATION Body floating in liquid The equilibrium of a submerged body in a liquid requires that the weight of the body acting through its centre of gravity should be colinear with equal hydrostatic lift acting through the centre of buoyancy. Let us suppose that a body is given a small angular displacement and then released. Then it will be said to be in distance MG is calledmetacentric height (it is the distance between gravity centre and metacentre) Gravity centre and metacentre Stability of Submerged Body: It is classified into the three groups. Stable Equilibrium: When centre of buoyancy lies above the centre of gravity, submerged body is stable. •G Stable equilibrium
  4. BUOYANCY & FLOTATION B lies below G, then body is in unstable equilibrium. Unstable equilibrium Neutral Equilibrium: When B and G coincide then, body is in neutral equilibrium. Neutral equilibrium Stability of Floating Bodies: When the body undergoes an angular displacement about a horizontal axis, the shape of the immersed volume changes and so the centre of buoyancy moves relative to the body. Stale Equilibrium: When a body is given a small angular displacement by external means and if body comes to its original position due to internal forces then, it is called stable equilibrium. Stable position It occurs, when metacentre lies above centre of gravity.
  5. BUOYANCY & FLOTATION Unstable Equilibrium: In the above case, if body does not come in its original position and moves further away then, it is known as unstable equilibrium. M lies below centre of gravity. Unstable position Neutral equilibrium: When a body is given a small angular displacement and it sets on new position then, body is called in neutral equilibrium. In this, M and G coincide. Neutral position 1 Relation between B,G and M is GM Here, I = Least moment of inertia of plane of body at water surface G = Centre of gravity B = Centre of buoyancy M = Metacentre
  6. BUOYANCY & FLOTATION x x x — min(l I ) I x Front view bcP 12 Top view V is volume submerged inside the water can be given as V bdx Where b,d and x are the length, width and depth of the section or body. Subrnerged part of body BG is distance between centre of gravity and centre of buoyancy. (In other words, BG=distance between centre of gravity of whole body and centre of gravity of submerged part of body) When we find out GM then, we can determine the status of body as GM > 0 (stable equilibrium), GM < 0 (unstable equilibrium), GM = 0 (neutral equilibrium)

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