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Fluid Mechanics

Fluid Mechanics. Liquids and gases have the ability to flow They are called fluids. Liquids are incompressible, assume the form of their containers, and have a fixed volume. Gasses are compressible, and assume the shape and volume of their containers. What is a fluid?. Definitions.

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Fluid Mechanics

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  1. Fluid Mechanics

  2. Liquids and gases have the ability to flow They are called fluids. Liquids are incompressible, assume the form of their containers, and have a fixed volume. Gasses are compressible, and assume the shape and volume of their containers. What is a fluid?

  3. Definitions

  4. Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space Density *Sometimes we use “weight density” = weight/volume or mg/V ρw=ρg

  5. Densities of Common Stuff

  6. Specific Gravity • A measure derived by finding the ratio of the density of some material to the ratio of the density of water.

  7. A measure of the amount of force exerted on a surface area, measured in pascals (Pa) which are equivalent to N/m2. Pressure Also: P = ρwh

  8. 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 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) Pressure in a Fluid

  9. 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 Go to a mountaintop and the air pressure is lower Pressure in a Fluid

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

  11. Pressure in a Fluid

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

  13. Buoyancy Net upward force is called the buoyant force!!! Easier to lift a rock in water!!

  14. 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 Archimedes’ Principle

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

  16. Flotation

  17. 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 pressure drops 1/273 for each degree Celsius. Independent of what the molecules are. Gases

  18. 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

  19. Boyle’s Law

  20. Boyle’s Law Density is mass divided by volume. Halve the volume and you double the density and thus the pressure.

  21. At a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant Boyle’s Law

  22. Ideal Gas Law • Pressure = kNT/V • Where k is the Boltzmann’s Constant • K = 1.38 x 10-23 Nm/moleculesºK • Where N is the Number of molecules • Where T is Temperature • Also PV=nRT where n is # of moles and R is the universal gas constant. • .082 L*atmosphere/(mol*K)

  23. 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 Air pressure at sea level is about 105 newtons/meter2 Atmospheric Pressure

  24. Barometers

  25. 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

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

  27. Bernoulli’s Principle

  28. Flow is faster when the pipe is narrower 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 Has to do with the work necessary to compress a gas (PV is energy, more later) Bernoulli’s Principle

  29. When the speed of a fluid increases, internal pressure in the fluid decreases. Bernoulli’s Principle

  30. Bernoulli’s Principle

  31. Bernoulli’s Principle Why the streamlines are compressed is quite complicated and relates to the air boundary layer, friction and turbulence.

  32. Bernoulli’s Principle

  33. Practice: • Page 348-349 of “Wall and Wall” has a useful summary of the concepts covered in the chapter. • You are responsible for answering the “Example Problems” 1-4 on page 350-351. • The answers to these problems are on page 353-356. • I am sure you are all capable of reading the answers… please do the questions first.

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