Faculty of EngineeringFaculty of Engineering

Fluid MechanicsFluid Mechanics

Dr. Eng. Hasan HamoudaDr. Eng. Hasan Hamouda

From Buoyancy principle, we can see whether an object floats or sinks. It isbased on not only its weight, but also the amount of water it displaces.That is why a very heavy ocean liner can float. It displaces a large amount of water.

Buoyancy: Archimedes’ PrincipleBuoyancy: Archimedes’ Principle

Flotation and sedimentationFlotation and sedimentation

What is the effect of buoyancy on theapparent weight of an object?A. Buoyancy is the ability of a fluid to exert an upward force on an object placed in it.Buoyancy results in the apparent loss ofweight of an object in a fluid.

I. Buoyant Force

Buoyancy: Archimedes’ PrincipleBuoyancy: Archimedes’ Principle

Flotation and sedimentationFlotation and sedimentation

II. Archimedes Principle

A. Archimedes principle: the buoyant force on an object is equal to the weight of the fluiddisplaced by the object.1.A submerged object pushes aside, or displaces, a volume of fluid equal to its own volume.2. A floating object displaces a volume equal to the volume of the part of the object that is submerged.

Every object in a fluid experiences buoyancyEvery object in a fluid experiences buoyancy.. 1. Water pressure increases with depth.1. Water pressure increases with depth. 2. Forces pushing up on the bottom of the object 2. Forces pushing up on the bottom of the object

are greater than the forces from pressure are greater than the forces from pressure pushing down on the top.pushing down on the top.

3. This upward force, which acts in the opposite3. This upward force, which acts in the opposite direction of gravity, is called the direction of gravity, is called the buoyant force.buoyant force.

Two forces act on every object in a fluidTwo forces act on every object in a fluid weight and the buoyant force.weight and the buoyant force. 1. The force of gravity, equal to the objects 1. The force of gravity, equal to the objects

weight, acts downward on the object.weight, acts downward on the object. 2. The buoyant force, equal to the weight 2. The buoyant force, equal to the weight

of the volume of displaced fluid, acts of the volume of displaced fluid, acts upward on the object.upward on the object.

Buoyancy: Buoyancy: Archimedes’ PrincipleArchimedes’ Principle

Archimedes (287-212 BC)

Archimedes’ Principle states that the buoyant force has a magnitude equal to the weight of the fluid displaced by the body and is directed vertically upward.

•Buoyant force is a force that results from a floating or submerged body in a fluid.•The force results from different pressures on the top and bottom of the object•The pressure forces acting from below are greater than those on top

Now, treat an arbitrary submerged object as a planar surface:

Arbitrary Shape

V

Forces on the Fluid

Buoyancy and Flotation: Buoyancy and Flotation: Archimedes’ PrincipleArchimedes’ Principle

Balancing the Forces of the F.B.D. in the vertical Direction:

VAhhW 12

W is the weight of the shaded areaF1 and F2 are the forces on the plane surfacesFB is the buoyant force the body exerts on the fluid

Then, substituting:

Simplifying,

The force of the fluid on the body is opposite, or vertically upward and is known as the Buoyant Force.

The force is equal to the weight of the fluid it displaces.

g

Suspended objectSuspended object

1. An object that has the same density as the 1. An object that has the same density as the fluid it is submerged in will be suspended (it will fluid it is submerged in will be suspended (it will float at any level) in the fluid.float at any level) in the fluid.

a. The buoyant force acting on the suspended a. The buoyant force acting on the suspended object exactly equals the object s weight.object exactly equals the object s weight.

b. Submarines and some fish are able to b. Submarines and some fish are able to suspend themselves in water partly by suspend themselves in water partly by adjusting their density.adjusting their density.

Sinking1. When a ship weight becomes greaterthan the buoyant force acting on it, the shipwill sink.2. As a sinking ship takes on water, the shipdisplaces less water, and the buoyant force decreases

Floating1. A solid piece of steel sinks in water. A heavy steel ship floats because of the shape of its hull.2. The hull is shaped so that it displaces alarge volume of water, creating a large buoyant force.

Buoyancy and Flotation: Buoyancy and Flotation: Archimedes’ PrincipleArchimedes’ Principle

We find that the buoyant force acts through the centroid of the displaced volume.

The location is known as the center of buoyancyThe location is known as the center of buoyancy.

Buoyancy and Flotation: Buoyancy and Flotation: Archimedes’ PrincipleArchimedes’ Principle

We can apply the same principles to floating objects:

If the fluid acting on the upper surfaces has very small specific weight (air), the centroid is simply that of the displaced volume, and the buoyant force is as before.

Example 1Example 1

h0.75

1.25

G

B

A wooden block of width 1.25 m, depth 0.75And length 3.0 m is floating in water. Specific weightOf wood is 6.4kN/m3 find:

Position of center of buoyancy

m

h

h

KNW

gVW

FW

dis

B

244.02

0.489buoyancy ofCenter

489.0

)3*25.1*(*81.9*10001018

184.6*0.3*25.1*75.03

.

Example 2Example 2

MercuryWater BB FFW

Buoyancy and Stability: Floating ObjectBuoyancy and Stability: Floating Object

Slightly more complicated as the location of the center buoyancy can change:

In Water

h

bdhV

bdI

12

section crossr rectangulaFor 3

Example 1Example 1

mBGBMGM

mV

IBM

mOBOGBG

OG

mB

h

h

gVW

FW

dis

B

019.005.0069.0

069.015.03.0

12/15.0

05.015.02.0

2.0

15.02

0.3O

3.0

)1*50.0*(*81.9*100010472.1

3

3

.

Example 2Example 2