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.

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Chapter 15 Fluids and Elasticity

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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

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

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

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

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

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

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

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

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