Dr H Md

AzamathullaLecturer, REDAC, USM

EAH 221 Aug

FLUID MECHANICSfor

CIVIL Engineers

Flotation

Flotation•

Buoyancy forces

•

Although civil engineers not boat designers, they do have to deal with cases of buoyancy from time to time.

•

Some typical examples are: 1.

Buried gas pipelines in waterlogged ground

2.

Exploration rigs used by oil or gas corporations3.

Towing large steel dock/lock gates by sea or river (Assuming that structure can float, of course)

BuoyancyNet upward force is called the buoyant force!!!

Easier to lift a rock in water!!

Displacement of Water

The amount of water displaced is equal to the volume of the rock.

Archimedes’ Principle•

An immersed body is buoyed up by a force equal to the weight of the fluid it displaces.

•

If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float

•

The apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force

p2

y

L

p1

From figure Vertical forces acting on an immersed cylinder of horizontal c/s

area A with its axis vertical

The force acting downwards is due to pressure on the top i.e

p1

A=ρgyA

The force acting upwards is due to pressure on bottom surface, and is given by p2

A= ρg(y+L)ASo, total upthrust

=FB

= ρg(y+L)A-

ρgyA= ρgLA

Where LA is volume of cylinderThis leads to Archimedes’

principle that upthruston a body is equal to the weight of fluid displaced The upthrust

acts through the centre of buoyancy B, which is the CG of displaced fluid

cylinder

Flotation

•

A floating object displaces a weight of fluid equal to its own weight.

Gases

•

The primary difference between a liquid and a gas is the distance between the molecules

•

In a gas, the molecules are so widely separated, that there is little interaction between the individual molecules

•

IDEAL GAS•

Independent of what the molecules are

Boyle’s Law

Boyle’s Law

•

Pressure depends on density of the gas•

Pressure is just the force per unit area exerted by the molecules as they collide with the walls of the container

•

Double the density, double the number of collisions with the wall and this doubles the pressure

Boyle’s Law

Density is mass divided by volume.

Halve the volume and you double the density and thus the pressure.

Boyle’s Law

•

At a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant

P1V1 = P2V2

Buoyancy in a Gas

•

An object surrounded by air is buoyed up by a force equal to the weight of the air displace.

•

Exactly the same concept as buoyancy in water. Just substitute air for water in the statement

•

If the buoyant force is greater than the weight of the object, it will rise in the air

Buoyancy in a Gas

Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons don’t rise forever!!!