Download Presentation
## Chapter 15 Fluids and Elasticity

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Chapter 15 Fluids and Elasticity**Chapter Goal: To understand macroscopic systems that flow or deform. Slide 15-2**Chapter 15 Preview**Slide 15-3**Chapter 15 Preview**Slide 15-4**Chapter 15 Preview**Slide 15-5**Chapter 15 Preview**Slide 15-6**Chapter 15 Preview**Slide 15-7**Chapter 15 Preview**Slide 15-8**Gases**• A gas is a system in which each molecule moves through space as a free particle until, on occasion, it collides with another molecule or with the wall of the container. • Gases are fluids; they flow, and exert pressure. • Gases are compressible; the volume of a gas is easily increased or decreased. Slide 15-19**Liquids**• Liquids are fluids; they flow, and exert pressure. • Liquids are incompressible; the volume of a liquid is not easily increased or decreased. Slide 15-20**Volume**• An important parameter of a macroscopic system is its volume V. • The S.I. unit of volume is m3. • Some unit conversions: 1 m3 = 1000 L 1L = 1000 cm3 1m3 =106 cm3 Slide 15-21**Density**The ratio of an object’s or material’s mass to its volume is called the mass density, or sometimes simply “the density.” The SI units of mass density are kg/m3. Slide 15-22**QuickCheck 15.1**A piece of glass is broken into two pieces of different size. How do their densities compare? 1 > 3 > 2. 1 = 3 = 2. 1 < 3 < 2. Slide 15-23**QuickCheck 15.1**A piece of glass is broken into two pieces of different size. How do their densities compare? 1 > 3 > 2. 1 = 3 = 2. 1 < 3 < 2. Density characterizes the substance itself, not particular pieces of the substance. Slide 15-24**Densities of Various Fluids**Slide 15-25**Example 15.1 Weighing the Air**Slide 15-26**Pressure**• What is “pressure”? • Consider a container of water with 3 small holes drilled in it. • Pressure pushes the water sideways, out of the holes. • In this liquid, it seems the pressure is larger at greater depths. Slide 15-27**Pressure**• A fluid in a container presses with an outward force against the walls of that container. • The pressure is defined as the ratio of the force to the area on which the force is exerted. The SI units of pressure are N/m2, also defined as the pascal, where 1 pascal= 1 Pa = 1 N/m2. Slide 15-28**Learning About Pressure**FACTS about PRESSURE Slide 15-29**Pressure**There are two contributions to the pressure in a container of fluid: A gravitational contribution, due to gravity pulling down on the liquid or gas. A thermal contribution, due to the collisions of freely moving gas molecules within the walls, which depends on gas temperature. Slide 15-31**Atmospheric Pressure**The global average sea-level pressure is 101,300 Pa. Consequently we define the standard atmosphere as Slide 15-32**Pressure**• If you hold out your arm, which has a surface area of about 200 cm3, the atmospheric pressure on the top of your arm is 2000 N, or about 450 pounds. • How can you even lift your arm? • The reason is that a fluid exerts pressure forces in all directions. • The air underneath your arm exerts an upward force of the same magnitude, so the net force is close to zero. Slide 15-33**Example 15.2 A Suction Cup**Slide 15-34**Example 15.2 A Suction Cup**Slide 15-35**Example 15.2 A Suction Cup**Slide 15-36**Example 15.2 A Suction Cup**Slide 15-37**net= 0**Pressure in Liquids • The shaded cylinder of liquid in the figure, like the rest of the liquid, is in static equilibrium with . • Balancing the forces in the free-body diagram: • The volume of the cylinder is V = Ad and its mass is m = Ad. • Solving for pressure: Slide 15-38**Example 15.3 The Pressure on a Submarine**Slide 15-39**Liquids in Hydrostatic Equilibrium**• No! • A connected liquid in hydrostatic equilibrium rises to the same height in all open regions of the container. Slide 15-40**QuickCheck 15.2**What can you say about the pressures at points 1 and 2? p1 > p2. p1 = p2. p1 < p2. Slide 15-41**QuickCheck 15.2**What can you say about the pressures at points 1 and 2? p1 > p2. p1 = p2. p1 < p2. Hydrostatic pressure is the same at all points on a horizontal line through a connected fluid. Slide 15-42**Liquids in Hydrostatic Equilibrium**• No! • The pressure is the same at all points on a horizontal line through a connected liquid in hydrostatic equilibrium. Slide 15-43**QuickCheck 15.3**An iceberg floats in a shallow sea. What can you say about the pressures at points 1 and 2? p1 > p2. p1 = p2. p1 < p2. Slide 15-44**QuickCheck 15.3**An iceberg floats in a shallow sea. What can you say about the pressures at points 1 and 2? p1 > p2. p1 = p2. p1 < p2. Hydrostatic pressure is the same at all points on a horizontal line through a connected fluid. Slide 15-45**Example 15.4 Pressure in a Closed Tube**Slide 15-46**Example 15.4 Pressure in a Closed Tube**Slide 15-47**Example 15.4 Pressure in a Closed Tube**Slide 15-48**Example 15.4 Pressure in a Closed Tube**Slide 15-49**QuickCheck 15.4**What can you say about the pressures at points 1, 2, and 3? p1 = p2 = p3. p1 = p2 > p3. p3 > p1 = p2. p3 > p1 > p2. p1 = p3 > p2. Slide 15-50**QuickCheck 15.4**What can you say about the pressures at points 1, 2, and 3? p1 = p2 = p3. p1 = p2 > p3. p3 > p1 = p2. p3 > p1 > p2. p1 = p3 > p2. Hydrostatic pressure is the same at all points on a horizontal line through a connected fluid. Slide 15-51**Gauge Pressure**where 1 atm = 101.3 kPa. Many pressure gauges, such as tire gauges and the gauges on air tanks, measure not the actual or absolute pressure p but what is called gauge pressure pg. A tire-pressure gauge reads the gauge pressure pg, not the absolute pressure p. Slide 15-52**Example 15.5 An Underwater Pressure Gauge**Slide 15-54**Barometers**• Figure (a) shows a glass tube, sealed at the bottom and filled with liquid. • We seal the top end, invert the tube, place it in an open container of the same liquid, and remove the seal. • This device, shown in figure (b), is a barometer. • We measure the height h of the liquid in the tube. • Since p1 = p2: Slide 15-57**Pressure Units**Slide 15-58**The Hydraulic Lift**• Consider a hydraulic lift, such as the one that lifts your car at the repair shop. • The system is in static equilibrium if: Force-multiplying factor If h is small, negligible Slide 15-60**The Hydraulic Lift**• Suppose we need to lift the car higher. • If piston 1 is pushed down a distance d1, the car is lifted higher by a distance d2: Work is done on the liquid by the small force; work is done by the liquid when it lifts the heavy weight. What about PE grav of the liquid!!! Slide 15-61**Example 15.7 Lifting a Car**Slide 15-62**Example 15.7 Lifting a Car**Slide 15-63**Buoyancy**• Consider a cylinder submerged in a liquid. • The pressure in the liquid increases with depth. • Both cylinder ends have equal area, so Fup > Fdown. • The pressure in the liquid exerts a net upward force on the cylinder: • Fnet = Fup – Fdown. • This is the buoyant force. Slide 15-64**Buoyancy**The buoyant force on an object is the same as the buoyant force on the fluid it displaces. Slide 15-65**Buoyancy**• When an object (or portion of an object) is immersed in a fluid, it displaces fluid. • The displaced fluid’s volume equals the volume of the portion of the object that is immersed in the fluid. • Suppose the fluid has density f and the object displaces volume Vfof fluid. • Archimedes’ principle in equation form is: Slide 15-66