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Fluid Mechanics

Fluid Mechanics. 1. Hydrostatic pressure The concept of pressure as it applies to fluids: a) Apply the relationship between pressure, force, and area. b) Apply the principle that a fluid exerts pressure in all directions.

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Fluid Mechanics

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  1. Fluid Mechanics 1. Hydrostatic pressure The concept of pressure as it applies to fluids: a) Apply the relationship between pressure, force, and area. b) Apply the principle that a fluid exerts pressure in all directions. c) Apply the principle that a fluid at rest exerts pressure perpendicular to any surface that it contacts. d) Determine locations of equal pressure in a fluid. e) Determine the values of absolute and gauge pressure for a particular situation. f) Apply the relationship between pressure and depth in a liquid, P = Dgh .

  2. What is a fluid? • fluid – a substance that can change shape and flow (when forces are applied to it); both gases and liquids are fluids. • density – the ratio of mass to volume • You should already know this part:When two states interact, such as 2 liquids or a solid and a liquid: the more dense material sinks, the less dense material floats

  3. How can we give fluids a shape? • Put it in a container! • A fluid exerts pressure in all directions.

  4. Fluids • The features of fluids include: • Density • Pressure • Forces • Area over which the force acts • Buoyancy • An upward force we’ll clarify later • Fluids can either be still or moving

  5. Because fluids can easily change shape, forces applied to fluids create more complex effects than forces applied to solids. • Forces applied to fluids create pressure. pressure is a ratio of force per unit area • However, pressure acts in all directions, not just the direction of the applied force. Pressure is caused by forces acting on and within fluids.

  6. Units of Pressure • The metric unit of pressure is the N/m2, named the pascal (Pa). • The English unit of pressure is pounds per square inch (psi). One pascal is much smaller than one psi

  7. Pressure from the weight of a fluid • Gravity is one cause of pressure because fluids have weight. • The pressure increases the deeper you go beneath the surface of a fluid because the weight of fluid above you increases with depth. • The rate at which pressure increases depends on the density of the fluid. Heavy fluids (water) create more pressure than light fluids (air) at the same depth.

  8. Pressure in a Liquid • The pressure at the same depth is the same everywhere in any liquid that is not moving. It does not matter what the shape of the container is. The formula below gives the pressure in a fluid that is not moving.

  9. Hydrostatic Pressure • Think of water as stacked molecules that flow and slide around each other. • Depending on where you are in the stack of molecules, you’ll experience a different amount of hydrostatic pressure

  10. Hydrostatic Pressure • Hydrostatic pressure is the pressure exerted on an object by a column of fluid. • So in summary, the pressure at a given depth in a static fluid is a result of: the weight of the liquid acting on a unit area at a depth + any pressure acting on the surface of the liquid

  11. Hydrostatic Pressure • Did we say a column of stacked liquid or stacked fluid? • So althought we say liquid, we’re talking about water • Can this same thing apply to air? What kind of pressure is this? Atmospheric pressure

  12. Hydrostatic Pressure • Hydrostatic pressure = atmospheric pressure + (density)(accel. due to gravity)(height) • Ph = Pa + ρgh • Normal atmospheric pressure: 1.01x105 Pa • A pascal is equivalent to a newton per square meter (N/m2)

  13. Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure. • Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure. Negative signs are usually omitted. To distinguish a negative pressure, the value may be appended with the word "vacuum" or the gauge may be labeled a "vacuum gauge." • Differential pressure is the difference in pressure between two points. • The zero reference in use is usually implied by context, and these words are added only when clarification is needed. Tire pressure and blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressures must be absolute. • For most working fluids where a fluid exists in a closed system, gauge pressure measurement prevails. Pressure instruments connected to the system will indicate pressures relative to the current atmospheric pressure. The situation changes when extreme vacuum pressures are measured; absolute pressures are typically used instead.

  14. Pressure = important concept • The motion of fluids depends on pressure and density in a similar way as the motion of solids depends on force and mass. • In agreement with Newton’s third law (action- reaction), pressure exerts forces on all surfaces that come in contact with a fluid.

  15. Pascal’s Principle • The change in pressure on one part of a confined fluid is equal to the change in pressure on any other part of the confined fluid. • A small force applied over a small area will result in a large force exerted over a large area. • Example: Hydraulic Lifts

  16. Pascal’s Principle

  17. Pascal’s Principle

  18. http://dsc.discovery.com/tv-shows/mythbusters/videos/explosive-decompression-minimyth.htmhttp://dsc.discovery.com/tv-shows/mythbusters/videos/explosive-decompression-minimyth.htm • http://www.youtube.com/watch?v=vaho7JSVS1I&safety_mode=true&persist_safety_mode=1&noredirect=1

  19. Buoyancy • An upward force exerted by a fluid, that opposes the weight of an immersed object

  20. Archimedes’ Principle • Any fluid applies a buoyant force to an object that is partially or completely immersed in it; the magnitude of the buoyant force equals the weight of the fluid that the object displaces: • Forcebuoyant= Weightdisplaced fluid • Fb = ρVg • Density & volume are those of the displaced fluid • If the object is only partially submerged, the volume used is only that of the submerged portion ρ= Mass / Volume Mass = ρ*Volume Weight = Mass * 9.8

  21. http://phet.colorado.edu/en/simulation/buoyancy

  22. What is the size of the buoyant force that acts on a floating ball that normally weighs 5.0 N?

  23. What is the apparent weight of a rock submerged in water if the rock weighs 54 N in air and has a volume of 2.3x10-3 m3?

  24. During an ecology experiment, an aquarium half filled with water is placed on a scale. The scale reads 195 N. A rock weighing 8 N is added to the aquarium. If the rock sinks to the bottom of the aquarium, what will the scale read?

  25. The rock in the above question is removed from the aquarium, and the amount of water is adjusted until the scale again reads 195 N. A fish weighing 2 N is added to the aquarium. What is the scale reading with the fish in the aquarium?

  26. A metal object is suspended from a spring scale. The scale reads 920 N when the object is suspended in air, and 750 N when the object is completely submerged in water (ρ = 1000 kg/m3). What is the volume AND density of the metal object?

  27. A 5450 m3 blimp circles Fenway Park during the World Series, suspended in Earth’s 1.21 kg/m3 atmosphere. The density of the helium in the blimp is 0.178 kg/m3. • What is the buoyant force that suspends the blimp in the air? • How much weight, in addition to the helium, can the blimp carry and still continue to maintain a constant altitude?

  28. A 1.9 kg piece of wood from a sunken pirate ship has a volume of 2.16 x 10-3 m3. Will this piece of wood float to the surface of the water or remain submerged with the ship?

  29. What is the maximum weight that a balloon filled with 1.00 m3 of helium can lift in air? Assume that the density of air is 1.20 kg/m3 and that the helium is 0.177 kg/m3. (Neglect the mass of the balloon this time.)

  30. Pages 339-340 32, 34, 36, 38, 39, 42, 43, 48

  31. http://phet.colorado.edu/en/simulation/buoyancy

  32. Fluid Flow Continuity (pg 322) • Have you ever used your thumb to control the water flowing from the end of a hose? • If so, you have seen that the water velocity increases when your thumb reduces the cross-sectional area of the hose opening. This kind of fluid behavior is described by the equation of continuity. • If a fluid enters one end of a pipe at a certain rate, then fluid must also leave at the same rate (assuming no places between entry and exit to add or remove fluid) • The mass of fluid per second that flows through a tube is called the mass flow rate.

  33. Fluid Flow Continuity (pg 322) mass flow rate = (fluid density)(cross-sectional area of the tube)(fluid speed) mass flow rate = ρ A v The Equation of Continuity says that the mass flow rate has the same value at every position along a tube that has a single entry and single exit for fluid flow. For two positions along such a tube: ρ1A1v1= ρ2A2v2 SI Unit: kg/s

  34. Bernoulli’s Principle • As the speed of a fluid (liquid or gas) increases the pressure of the fluid decreases. • The shape of an airplane wing causes the air to move faster over the top of the wing, thus lifting the wing up.

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