Fluid MechanicsBuoyancy & Floatation

Prepared By: Guided By:Shuaib Kohee (151100106079)Wahedullah Ehsas (151100106080)Ehsanullah Aydin (151100106078)

Prof. Mamta PatelProf. Metal MistryProf. Nafisha Shaikh

Content:Buoyant ForceBuoyancy and center of buoyancy Archimedes PrincipleMet centre and Meta-centric height Equilibrium of floating and submerged

bodiesMeta-centric height elevation- theoretical

and experimental method

Buoyant ForceWhen a body is

immersed in a fluid, there is tendency of fluid to exert force on the submerged body. This upward force is same as weight of fluid displaced by the body is known as force of buoyancy or BOYANCY.

Center of BuoyancyIt’s the point body, where the force of

buoyancy acts. It’s always the center of gravity of displaced liquid.

Upward force of buoyancy=Weight of body

FB=m.g (N)

Archimedes PrincipleWhen a body is immersed wholly or partially

in a fluid it is lifted up by a force equal to the weight of fluid displaced by the body.

Consider density of immersed body is ρDownward gravitational force (W)Upward force of liquid (Buoyancy FB) FB= m.g FB= ρ.g(l.b.h)

Meta-Centre When a body is floating in liquid, is a given

a small angular displacement, it starts oscillating about a point, that point is meta-centre.

Meta-centric Height It’s a distance between the centre of gravity

(G) of floating body and the meta-centre (M). The distance GM is called meta-centric height.

Equilibrium of Submerged BodiesThe stability of submerged body is

determined by the location of G and M.There are also three types of equilibrium of

submerged body as follow:Stable Equilibrium Unstable Equilibrium Neutral Equilibrium

(a) Stable condition: G is below BFor totally immersed body the G and B is

fixed, the stability of submerged body can be determined by the locations of G and B.

Let a balloon completely submerged in air.Where W is weight of the balloonFB is the buoyancy force For equilibrium FB=W

(b)Unstable Condition:G is Above B If the balloon is given smaller angular

displacement ѳIn clockwise direction, then W and FB produce

a coupleacting in same direction of displacement

(clockwise) sothat body does not returns to its original

position and body is said to be in unstable equilibrium.

(c) Neutral Equilibrium:G and B are at same point

If the balloon is given small angular displacement in any direction. There is no any couple produce, since W and FB is acting at a same point and body is said to be in neutral equilibrium

Equilibrium of floating bodiesThe stability of floating body is determined by

the location of G and M.There are also three types of equilibrium of

floating body as follow:Stable Equilibrium Unstable Equilibrium Neutral Equilibrium

(a) Stable Equilibrium:When M is above G W=FBIf the floating body is small angular

displacement (ѳ) in clockwise direction, then the centre of buoyancy shifts from B to B1, the buoyant force FB through B1 and W produces a couple acting in a anticlockwise direction, hence floating body returns in its original position. So floating body said to be in stable equilibrium

(b) Unstable Equilibrium:W= FBM is Below GIf the floating body is given small angular

displacement (ѳ) in clockwise direction, then FB and W produce a couple acting in clockwise direction, hence overturning the floating body.

(c)Neutral Equilibrium:W=FBM and G are at same points If the floating body is given small angular

displacement in any direction, there is no any couples produce due to W and FB, since W and FB are acting at same point and floating body said to be in neutral equilibrium.

Determination Of The Meta-Centric Height (Experimental Method)The meta-centric height of a floating vessel

can be determined if the angle of tilt Ѳ caused by moving a load P placed over the centre of the floating body.

Where :W = total weight of floating body(weight of

body + weight of load P) G = C.G. of floating body B = Centre of buoyancy of the body

GM= (Px)/(wѲ)

References:A textbook of Fluid Mechanics and Hydraulic

Machines (Dr. R.K. Bansal)www.Wikipedia.com

Thank You