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Fluid Mechanics Liquids and gases have the ability to flow Liquids and gases have the ability to flow They are called fluids They are called fluids There are a variety of LAWS that fluids obey There are a variety of LAWS that fluids obey Need some definitions Need some definitions

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Density Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space

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Pressure A measure of the amount of force exerted on a surface area A measure of the amount of force exerted on a surface area

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Pressure Which shoes create the most pressure?

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Pressure in a Fluid The pressure is just the weight of all the fluid above you The pressure is just the weight of all the fluid above you Atmospheric pressure is just the weight of all the air above on area on the surface of the earth Atmospheric pressure is just the weight of all the air above on area on the surface of the earth In a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water) In a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water)

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Pressure in a Fluid So, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE you So, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE you The deeper you go, the more weight above you and the more pressure The deeper you go, the more weight above you and the more pressure Go to a mountaintop and the air pressure is lower Go to a mountaintop and the air pressure is lower

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Pressure in a Fluid Pressure acts perpendicular to the surface and increases at greater depth.

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Pressure in a Fluid

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Pascals Principle Pascals Principle Pascals Principle pressure applied to a fluid is transmitted unchanged throughout the fluid pressure applied to a fluid is transmitted unchanged throughout the fluid

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

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A. Archimedes Principle Bouyant Force Bouyant Force upward force exerted by a fluid on an immersed object upward force exerted by a fluid on an immersed object bouyant force > weight bouyant force > weight bouyant force = weight bouyant force = weight bouyant force < weight bouyant force < weight balloon rises balloon sinks balloon floats

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

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Flotation

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Gases The primary difference between a liquid and a gas is the distance between the molecules 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 In a gas, the molecules are so widely separated, that there is little interaction between the individual molecules IDEAL GAS IDEAL GAS Independent of what the molecules are Independent of what the molecules are

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Boyles Law

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Pressure depends on density of the gas 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 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 Double the density, double the number of collisions with the wall and this doubles the pressure

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Boyles Law Density is mass divided by volume. Halve the volume and you double the density and thus the pressure.

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

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Atmospheric Pressure Just the weight of the air above you Just the weight of the air above you Unlike water, the density of the air decreases with altitude since air is compressible and liquids are only very slightly compressible Unlike water, the density of the air decreases with altitude since air is compressible and liquids are only very slightly compressible Air pressure at sea level is about 10 5 newtons/meter 2 Air pressure at sea level is about 10 5 newtons/meter 2

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Measuring Pressure Barometer Atmospheric Pressure Manometer Contained Pressure

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Effect on Boiling Point When atmospheric pressure increases, the boiling point of a liquid increases. When atmospheric pressure increases, the boiling point of a liquid increases. When atmospheric pressure decreases, the boiling point of a liquid decreases. When atmospheric pressure decreases, the boiling point of a liquid decreases. EX: high altitude cooking, boiling cold water EX: high altitude cooking, boiling cold water

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Buoyancy in a Gas An object surrounded by air is buoyed up by a force equal to the weight of the air displaced. An object surrounded by air is buoyed up by a force equal to the weight of the air displaced. Exactly the same concept as buoyancy in water. Just substitute air for water in the statement 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 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 dont rise forever!!!

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High Altitude Balloon

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Bernoullis Principle

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Flow is faster when the pipe is narrower Flow is faster when the pipe is narrower Put your thumb over the end of a garden hose Put your thumb over the end of a garden hose Energy conservation requires that the pressure be lower in a gas that is moving faster Energy conservation requires that the pressure be lower in a gas that is moving faster

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Bernoullis Principle When the speed of a fluid increases, internal pressure in the fluid decreases. When the speed of a fluid increases, internal pressure in the fluid decreases.

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Bernoullis Principle

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