FLUID MECHANICS for CIVIL Engineersredac.eng.usm.my/EAH/EAH221/EAH 221-Aug 10th2009.pdf · FLUID...
Transcript of FLUID MECHANICS for CIVIL Engineersredac.eng.usm.my/EAH/EAH221/EAH 221-Aug 10th2009.pdf · FLUID...
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Dr H Md
AzamathullaLecturer, REDAC, USM
EAH 221 Aug
FLUID MECHANICSfor
CIVIL Engineers
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Flotation
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Flotation•
Buoyancy forces
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Although civil engineers not boat designers, they do have to deal with cases of buoyancy from time to time.
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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)
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BuoyancyNet upward force is called the buoyant force!!!
Easier to lift a rock in water!!
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Displacement of Water
The amount of water displaced is equal to the volume of the rock.
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Archimedes’ Principle•
An immersed body is buoyed up by a force equal to the weight of the fluid it displaces.
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If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float
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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
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Flotation
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A floating object displaces a weight of fluid equal to its own weight.
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Gases
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The primary difference between a liquid and a gas is the distance between the molecules
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In a gas, the molecules are so widely separated, that there is little interaction between the individual molecules
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IDEAL GAS•
Independent of what the molecules are
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Boyle’s Law
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Boyle’s Law
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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
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Double the density, double the number of collisions with the wall and this doubles the pressure
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Boyle’s Law
Density is mass divided by volume.
Halve the volume and you double the density and thus the pressure.
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Boyle’s Law
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At a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant
P1V1 = P2V2
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Buoyancy in a Gas
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An object surrounded by air is buoyed up by a force equal to the weight of the air displace.
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Exactly the same concept as buoyancy in water. Just substitute air for water in the statement
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If the buoyant force is greater than the weight of the object, it will rise in the air
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Buoyancy in a Gas
Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons don’t rise forever!!!