EAH 221 Aug

FLUID MECHANICS for CIVIL Engineers

Dr H Md Azamathulla Lecturer, REDAC, USM Flotation Flotation

• • 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 corporations 3. Towing large steel dock/lock gates by sea or river (Assuming that structure can float, of course) Buoyancy

Net upward 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 of the fluid it displaces. • If the buoyant force on an object y is greater than the force of gravity p1 acting on the object, the object will float • The apparent weight of an object cylinder L in a liquid is gravitational force (weight) minus the buoyant force p2 The force acting downwards is due From figure Vertical forces acting on an immersed to on the top i.e p1 A=ρgyA cylinder of horizontal c/s area A with its axis vertical

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

p2 A= ρg(y+L)A So, total upthrust =FB= ρg(y+L)A- ρgyA= ρgLA This leads to Archimedes’ principle that upthrust Where LA is volume of cylinder on 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

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 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!!!