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Introduction To

Introduction To. Fluids. Fluids. Fluids are substances that can flow. Fluids are liquids and gases, and even some solids. In Physics B, we will limit our discussion of fluids to substances that can easily flow, such as liquids and gases. Density.  = m/V : density (kg/m 3 ) m: mass (kg)

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Introduction To

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  1. Introduction To Fluids

  2. Fluids • Fluids are substances that can flow. • Fluids are liquids and gases, and even some solids. • In Physics B, we will limit our discussion of fluids to substances that can easily flow, such as liquids and gases.

  3. Density •  = m/V • : density (kg/m3) • m: mass (kg) • V: volume (m3) • Units: • kg/m3

  4. Sample Problem • Given that water has a density of 1,000 kg/m3, calculate the mass of a barrel full of water. Assume that the barrel has a diameter of 1.0 m and a height of 1.5 m.

  5. Sample Problem • Given that water has a density of 1,000 kg/m3, calculate the mass of a barrel full of water. Assume that the barrel has a diameter of 1.0 m and a height of 1.5 m.

  6. Sample Problem • Given that water has a density of 1,000 kg/m3, calculate the mass of a barrel full of water. Assume that the barrel has a diameter of 1.0 m and a height of 1.5 m.

  7. Sample Problem • Given that water has a density of 1,000 kg/m3, calculate the mass of a barrel full of water. Assume that the barrel has a diameter of 1.0 m and a height of 1.5 m.

  8. Pressure • P = F/A • P : pressure (Pa) • F: force (N) • A: area (m2) • Pressure unit: Pascal • 1 Pa = N/m2 • Atmospheric pressure is about 101,000 Pa

  9. Sample Problem • Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

  10. Sample Problem • Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

  11. Sample Problem • Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

  12. Sample Problem • Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

  13. Pressure • The force on a surface caused by pressure is always normal to the surface. • The pressure of a fluid is exerted in all directions, and is perpendicular to the surface at every location. balloon

  14. The Pressure of a Liquid • P = gh • P: pressure (Pa) • : density (kg/m3) • g: acceleration constant (9.8 m/s2) • h: height of liquid column (m)

  15. Absolute Pressure • P = Po + gh • p: pressure (Pa) • po: atmospheric pressure (Pa) • gh: liquid pressure (Pa) • Po is atmospheric pressure. • P is commonly referred to as absolute pressure, and includes atmospheric pressure.

  16. Gauge Pressure • Gauge pressure is due to a fluid contained in a container and excludes atmospheric pressure.

  17. Sample Problem • Calculate the pressure at the bottom of a 3 meter (approx 10 feet) deep swimming pool (a) due to the water and (b) due to the water plus the atmosphere.

  18. Sample Problem • Calculate the pressure at the bottom of a 3 meter (approx 10 feet) deep swimming pool (a) due to the water and (b) due to the water plus the atmosphere.

  19. Sample Problem • Calculate the pressure at the bottom of a 3 meter (approx 10 feet) deep swimming pool (a) due to the water and (b) due to the water plus the atmosphere.

  20. Piston Density of Hg 13,400 kg/m2 Sample Problem Area of piston: 8 cm2 Weight of piston: 200 N What is the absolute pressure at point A? 25 cm A

  21. Piston Density of Hg 13,400 kg/m2 Sample Problem Area of piston: 8 cm2 Weight of piston: 200 N What is the absolute pressure at point A? 25 cm A

  22. Piston Density of Hg 13,400 kg/m2 Sample Problem Area of piston: 8 cm2 Weight of piston: 200 N What is the absolute pressure at point A? 25 cm A

  23. Piston Density of Hg 13,400 kg/m2 Sample Problem Area of piston: 8 cm2 Weight of piston: 200 N What is the absolute pressure at point A? 25 cm A

  24. Piston Density of Hg 13,400 kg/m2 Sample Problem Area of piston: 8 cm2 Weight of piston: 200 N What is the absolute pressure at point A? 25 cm A

  25. Floating is a type of equilibrium

  26. Floating is a type of equilibrium • Archimedes’ Principle: a body immersed in a fluid is buoyed up by a force that is equal to the weight of the fluid displaced. • Buoyant Force: the upward force exerted on a submerged or partially submerged body.

  27. Calculating Buoyant Force • Fbuoy = Vg • Fbuoy: the buoyant force exerted on a submerged or partially submerged object. • V: the volume of displaced liquid. • : the density of the displaced liquid. • Buoyant force is enough to float iron ships, automobiles, and brick houses!

  28. Parking in St. Bernard Parish after Hurricane Katrina

  29. Parking in St. Bernard Parish after Hurricane Katrina

  30. Parking in St. Bernard Parish after Hurricane Katrina

  31. “Mobile” Homes in St. Bernard Parish after Hurricane Katrina

  32. “Mobile” Homes in St. Bernard Parish after Hurricane Katrina

  33. Fbuoy = rVg mg Buoyant force on submerged object Note: if Fbuoy < mg, the object will sink deeper!

  34. Fbuoy = rVg mg Buoyant force on submerged object SCUBA divers use a buoyancy control system to maintain neutral buoyancy (equilibrium!)

  35. Fbuoy = rVg mg Buoyant force on floating object If the object floats, we know for a fact Fbuoy = mg!

  36. Sample problem • Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats?

  37. Sample problem • Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats?

  38. Sample problem • Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats?

  39. Sample problem • Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats?

  40. Buoyancy Lab • Using the equipment provided, verify that the density of water is 1,000 kg/m3. • Report (due Tuesday) must include: • Free body diagrams. • All data. • Calculations. air water

  41. Sample problem • You want to transport a man and a horse across a still lake on a wooden raft. The mass of the horse is 700 kg, and the mass of the man is 75.0 kg. What must be the minimum volume of the raft, assuming that the density of the wood is 80% of the density of the water.

  42. Fluid Flow Continuity • Conservation of Mass results in continuity of fluid flow. • The volume per unit time of water flowing in a pipe is constant throughout the pipe.

  43. Fluid Flow Continuity • A1v1 = A2v2 • A1, A2: cross sectional areas at points 1 and 2 • v1, v2: speed of fluid flow at points 1 and 2

  44. Fluid Flow Continuity • V = Avt • V: volume of fluid (m3) • A: cross sectional areas at a point in the pipe (m2) • v: speed of fluid flow at a point in the pipe (m/s) • t: time (s)

  45. Sample problem • A pipe of diameter 6.0 cm has fluid flowing through it at 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 cm?

  46. Sample problem • Suppose the current in a river is moving at 0.20 meters per second where the river is 12 meters deep and 10 meters across. If the depth of the river is reduced to 1.5 meters at an area where the channel narrows to 5.0 meters, how fast will the water be moving through this narrow region?

  47. Sample problem • How much water per second is flowing in the river described in the previous problem?

  48. Bernoulli’s Theorem • The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow. • All other considerations being equal, when fluid moves faster, the pressure drops.

  49. Bernoulli’s Theorem • P +  g h + ½ v2 = Constant • P : pressure (Pa) •  : density of fluid (kg/m3) • g: gravitational acceleration constant (9.8 m/s2) • h: height above lowest point (m) • v: speed of fluid flow at a point in the pipe (m/s)

  50. Sample Problem • Knowing what you know about Bernouilli’s principle, design an airplane wing that you think will keep an airplane aloft. Draw a cross section of the wing.

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