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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 (SG) • A measure derived by finding the ratio of the density of some material to the ratio of the density of water. Weight Density of water = 62.4 lb/ft3

  7. A measure of the amount of force exerted on a surface area, measured in pounds/in2. 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. Hydraulic Lift Pressure is the same everywhere.From Kuphaldt’s book Liii.pdf

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

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

  15. 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

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

  17. Flotation

  18. 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

  19. The Gas Laws Charles’s and Gay-Lussac’s law,(or simply Charles’s Law) states that the volume of a gas maintained at constant pressure is directly proportional to the absolute temperature of the gas. at constant pressure

  20. The Volume of a gas is directly proportional to the Temperature (Kelvin) at constant pressure and # moles. Charles’s Law

  21. 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

  22. Boyle’s Law

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

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

  25. IDEAL GAS LAW An Ideal Gas or perfect gas is a hypothetical gas con-sisting of identical particles with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container. Real gases act like ideal gases at low pres-sures and high temperatures. Real Gases do not exhibit these exact properties, although the approximation is often good enough to describe real gases. The properties of real gases are influenced by compressibility and other thermodynamic effects.

  26. 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)

  27. IDEAL GAS LAW PV = nRT Where: P = Pressure (psia) V = Volume (FT3) n = Number of Moles of Gas (1 mole = 6.02 x 1023 molecules) R = Gas Constant (10.73 FT3 PSIA / lb-mole oR) T = Temperature (oR)

  28. REAL GASES • Compressibility Factor (Z) - The term "compressibility" is used to describe the deviance in the thermodynamic properties of a real gas from those expected from an ideal gas. • Real Gas Behavior can be calculated as: PV = nZRT

  29. STANDARD CONDITIONS • P = 14.7 PSIA • T = 520 deg R (60 deg F) • Behavior of gases in a process can be equally compared by using standard conditions – This is due to the nature of gases.

  30. ACTUAL CONDITIONS • Standard conditions can be converted to Actual Conditions using the Ideal Gas Law.

  31. Dalton’s Law of Partial Pressures Dalton’s Law of Partial Pressures indicates that • pressure depends on the total number of gas particles, not on the types of particles • the total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases PT = P1 + P2 + P3 + .....

  32. Dalton’s Law of Partial Pressures (continued)

  33. Total Pressure • For example, at STP, one mole of a pure gas in a volume of 22.4 L will exert the same pressure as one mole of a gas mixture in 22.4 L. V = 22.4 L Gas mixtures 1.0 mole N2 0.4 mole O2 0.6 mole He 1.0 mole 0.5 mole O2 0.3 mole He 0.2 mole Ar 1.0 mole 1.0 atm 1.0 atm 1.0 atm

  34. Guide to Solving for Partial Pressure

  35. Generic Heating/Cooling Curve • Freezing is the phase change as a substance changes from a liquid to a solid. • Melting is the phase change as a substance changes from a solid to a liquid. • Condensation is the phase change as a substance changes from a gas to a liquid. • Vaporization is the phase change as a substance changes from a liquid to a gas.

  36. Phase Diagram Definitions • Sublimation is the phase change as a substance changes from a solid to a gas without passing through the intermediate state of a liquid. • Deposition is the phase change as a substance changes from a gas to a solid without passing through the intermediate state of a liquid. • TRIPLE POINT - The temperature and pressure at which the solid, liquid, and gas phases exist simultaneously. • CRITICAL POINT - The temperature above which a substance will always be a gas regardless of the pressure. • Freezing Point - The temperature at which the solid and liquid phases of a substance are in equilibrium at atmospheric pressure. • Boiling Point - The temperature at which the vapor pressure of a liquid is equal to the pressure on the liquid. • Normal (Standard) Boiling Point - The temperature at which the vapor pressure of a liquid is equal to standard pressure (1.00 atm = 760 mmHg = 760 torr = 101.325 kPa)

  37. 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

  38. Barometers

  39. 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

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

  41. Bernoulli’s Principle

  42. 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

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

  44. Bernoulli’s Principle

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

  46. Bernoulli’s Principle

  47. THE END

  48. Relative Density • Relative Density or Specific Gravity - the ratio of the density of a material to the density of water • Substances with a specific gravity of less than 1 are lighter than water so they float • Substances with a specific gravity of greater than 1 are heavier than water so they sink • Knowing the specific gravity is important for planning spill cleanup and fire-fighting procedures

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