Fluid Mechanics with teacher's notes

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$Holt Math Minnesota Test Prep Workbook for Grade 9$

$Math Skills: More Practice$

PRESSURE 9-2 Fluid pressure and temperature Deep-sea explorers wear atmospheric diving suits like the one shown in Figure 9-6 to resist the forces exerted by water in the depths of the ocean. You experience similar forces on your ears when you dive to the bottom of a swimming pool, drive up a mountain, or ride in an airplane. Pressure is force per unit area In the examples above the fluids exert pressure on your eardrums. Pressure is a measure of how much force is applied over a given area. It can be written as follows: PRESSURE F P = ⎯⎯ A pressure = ⎯ force ⎯ area The SI unit of pressure is the pascal (Pa), which is equal to 1 N/m 2 . The pascal is a small unit of pressure. The pressure of the atmosphere at sea level is about 10 5 Pa. This amount of air pressure under normal conditions is the basis for another unit, the atmosphere (atm). When calculating pressure, 10 5 Pa is about the same as 1 atm. The absolute air pressure inside a typical automobile tire is about 3 × 10 5 Pa, or 3 atm. Table 9-2 lists some additional pressures. Table 9-2 Some pressures Location P (Pa) Center of the sun 2 × 10 16 Center of Earth 4 × 10 11 Bottom of the Pacific Ocean 6 × 10 7 Atmosphere at sea level 1.01 × 10 5 Atmosphere at 10 km above sea level 2.8 × 10 4 Best vacuum in a laboratory 1 × 10 −12 Copyright © by Holt, Rinehart and Winston. All rights reserved. 9-2 SECTION OBJECTIVES • Calculate the pressure exerted by a fluid. • Calculate how pressure varies with depth in a fluid. • Describe fluids in terms of temperature. pressure the magnitude of the force on a surface per unit area Figure 9-6 Atmospheric diving suits allow divers to withstand the pressure exerted by the fluid in the ocean at depths of up to 610 m. Fluid Mechanics 325 Section 9-2 Demonstration 5 Defining pressure Purpose Relate pressure and the area on which a force is exerted. Materials flat foam pad, brick or other box-shaped object, demonstration scale Procedure Measure and record the weight of the brick and its dimensions. Place the brick on the pad, large side down. Have students notice the deformation caused on the pad. Ask how much force the brick exerts on the pad (same as the brick’s weight). Over how many square centimeters is this force distributed? (area of contact) Now place the brick on the pad with its smaller face down and raise the same questions. Students will observe a deeper deformation. Discuss how this demonstration relates to the definition of F pressure as P = ⎯⎯. A 325
SECTION 9-2 STOP 326 Misconception Alert Students may confuse the pressure increase in Pascal’s principle with the pressure of the fluid itself. While an increase in pressure is transmitted equally throughout a fluid, the total pressure at different points in the fluid may vary, for example, with depth. Each time you squeeze a tube of toothpaste, you experience Pascal’s principle in action.The pressure you apply by squeezing the sides of the tube is transmitted throughout the toothpaste.The increased pressure near the open mouth of the tube forces the paste out and onto your toothbrush. Figure 9-7 Because the pressure is the same on both sides of the enclosed fluid in a hydraulic lift, a small force on the smaller piston (left) produces a much larger force on the larger piston (right). 326 Chapter 9 Applied pressure is transmitted equally throughout a fluid When you pump a bicycle tire, you apply a force on the pump that in turn exerts a force on the air inside the tire. The air responds by pushing not only against the pump but also against the walls of the tire. As a result, the pressure increases by an equal amount throughout the tire. In general, if the pressure in a fluid is increased at any point in a container (such as at the valve of the tire), the pressure increases at all points inside the container by exactly the same amount. Blaise Pascal (1623–1662) noted this fact in what is now called Pascal’s principle (or Pascal’s law): PASCAL’S PRINCIPLE Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container. A hydraulic lift, such as the one shown in Figure 9-7, makes use of Pascal’s principle. A small force F 1 applied to a small piston of area A 1 causes a pressure increase in a fluid, such as oil. According to Pascal’s law, this increase in pressure, P inc, is transmitted to a larger piston of area A 2 and the fluid exerts a force F 2 on this piston. Applying Pascal’s principle and the definition of pressure gives the following equation: F 1 A 1 F1 F2 Pinc = ⎯⎯ = ⎯⎯ A1 A2 Rearranging this equation to solve for F 2 produces the following: F2 = ⎯ A2 ⎯F1 A1 This second equation shows that the output force, F 2, is larger than the input force, F 1, by a factor equal to the ratio of the areas of the two pistons. F 2 A 2 Copyright © by Holt, Rinehart and Winston. All rights reserved.
Page 1 and 2: Chapter 9 Overview Section 9-1 defi
Page 3 and 4: Section 9-1 Demonstration 1 Volume
Page 5 and 6: SECTION 9-1 The Language of Physics
Page 7 and 8: SECTION 9-1 Demonstration 4 Lifting
Page 9: SECTION 9-1 PRACTICE GUIDE 9A Solvi
Page 13 and 14: SECTION 9-2 Visual Strategy Figure
Page 15 and 16: SECTION 9-2 Classroom Practice The
Page 17 and 18: Section 9-3 Demonstration 7 Fluid f
Page 19 and 20: SECTION 9-3 Misconception STOP Aler
Page 23 and 24: Section 9-4 Demonstration 10 Temper
Page 27 and 28: Chapter 9 Summary Teaching Tip Ask
Page 29 and 30: 9 REVIEW & ASSESS 12. because the p
Page 31 and 32: 9 REVIEW & ASSESS 42. 7.1 m 43. 17
Page 33 and 34: 9 REVIEW & ASSESS 63. 60.9 m/s 2 64
Page 35 and 36: Chapter 9 Laboratory Exercise NOTE
Page 37 and 38: CHAPTER 9 LAB Boyle’s Law Apparat

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