Faculty of Engineering Fluid Mechanics Dr. Eng. Hasan Hamouda

Buoyancy: Archimedes’ Principle Flotation and sedimentation From Buoyancy principle, we can see whether an object floats or sinks. It is based 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.

I. Buoyant Force What is the effect of buoyancy on the apparent 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 of weight of an object in a fluid.

Buoyancy: Archimedes’ Principle Flotation and sedimentation

II. Archimedes Principle A. Archimedes principle: the buoyant force on an object is equal to the weight of the fluid displaced by the object. 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 buoyancy. 1. Water pressure increases with depth. 2. Forces pushing up on the bottom of the object are greater than the forces from pressure pushing down on the top. 3. This upward force, which acts in the opposite direction of gravity, is called the buoyant force.

Two forces act on every object in a fluid weight and the buoyant force. 1. The force of gravity, equal to the objects weight, acts downward on the object. 2. The buoyant force, equal to the weight of the volume of displaced fluid, acts upward on the object.

Buoyancy: Archimedes’ Principle 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. Archimedes (287-212 BC) 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: Forces on the Fluid Arbitrary Shape V

Buoyancy and Flotation: Archimedes’ Principle Balancing the Forces of the F.B.D. in the vertical Direction: Then, substituting: W is the weight of the shaded area F1 and F2 are the forces on the plane surfaces FB is the buoyant force the body exerts on the fluid 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.

Suspended object 1. An object that has the same density as the fluid it is submerged in will be suspended (it will float at any level) in the fluid. a. The buoyant force acting on the suspended object exactly equals the object s weight. b. Submarines and some fish are able to suspend themselves in water partly by adjusting their density.

Sinking Floating 1. When a ship weight becomes greater than the buoyant force acting on it, the ship will sink. 2. As a sinking ship takes on water, the ship displaces less water, and the buoyant force decreases Floating 1. 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 a large volume of water, creating a large buoyant force.

Buoyancy and Flotation: Archimedes’ Principle We find that the buoyant force acts through the centroid of the displaced volume. The location is known as the center of buoyancy.

Buoyancy and Flotation: Archimedes’ 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 1 A wooden block of width 1.25 m, depth 0.75 And length 3.0 m is floating in water. Specific weight Of wood is 6.4kN/m3 find: Position of center of buoyancy h 0.75 1.25 G B

Example 2

Buoyancy and Stability: Floating Object Slightly more complicated as the location of the center buoyancy can change:

In Water

h

Example 1

Example 2