Lecture Outline Chapter 9 College Physics, 7 th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.

Units of Chapter 9 Solids and Elastic Moduli Fluids: Pressure and Pascal’s Principle Buoyancy and Archimedes’ Principle Fluid Dynamics and Bernoulli’s Equation Surface Tension, Viscosity, and Poiseuille’s Law © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli All solids are elastic to some degree, due to the spring-like structure of the intermolecular bonds holding them together. © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli Stress is defined as the force per unit area: © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli The stress results in a change in the shape of the solid, called the strain: The strain is related to the stress; how much strain a particular stress causes depends on the material. © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli Changes in length, shape, and volume are described by Young’s modulus, the shear modulus, and the bulk modulus, respectively. Young’s modulus: © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli Stress is proportional to strain until the strain gets too large. Then a material becomes permanently deformed, and finally breaks. © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli Shear modulus: © 2010 Pearson Education, Inc.

9.1 Solids and Elastic Moduli Bulk modulus (the only one relevant for fluids—why?) © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle Pressure is defined as the force per unit area: If the force is at an angle to the surface, the more general form (blue box) is used. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle Unit of pressure: the Pascal (Pa) Density is defined as mass per unit volume: © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle The pressure in a fluid increases with depth, due to the weight of fluid above it. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle Pascal’s principle: Pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid and to the walls of the container. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle Hydraulic lifts and shock absorbers take advantage of Pascal’s principle. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle Since the pressure is constant, a small force acting over a small area can become a large force acting over a large area. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle There are a number of methods used to measure pressure. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle Absolute pressure is the total force per unit area. We often measure the gauge pressure, which is the excess over atmospheric pressure. Atmospheric pressure historically was measured using a mercury barometer. © 2010 Pearson Education, Inc.

9.2 Fluids: Pressure and Pascal’s Principle The pressure corresponding to 1 mm of mercury is called the torr (in honor of Torricelli). © 2010 Pearson Education, Inc.

9.3 Buoyancy and Archimedes’ Principle A body immersed wholly or partially in a fluid experiences a buoyant force equal in magnitude to the weight of the volume of fluid that is displaced: An object’s density will tell you whether it will sink or float in a particular fluid. © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation In an ideal fluid, flow is steady, irrotational, nonviscous, and incompressible. Steady flow means that all the particles of a fluid have the same velocity as they pass a given point. Steady flow can be described by streamlines. © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation Nonviscous flow means that viscosity is negligible. Viscosity produces drag, and retards fluid flow. Incompressible flow means that the fluid’s density is constant. This is generally true for liquids, but not for gases. © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation Equation of continuity: © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation If the density is constant, © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation Bernoulli’s equation is a consequence of the conservation of energy. © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation One consequence of Bernoulli’s equation, that the pressure is lower where the speed is higher, can be counterintuitive. © 2010 Pearson Education, Inc.

9.4 Fluid Dynamics and Bernoulli’s Equation The flow rate from a tank with a hole is given by Bernoulli’s equation; the pressure at open areas is atmospheric pressure. © 2010 Pearson Education, Inc.

9.5 Surface Tension, Viscosity, and Poiseuille’s Law Surface tension is due to the forces that molecules in a liquid exert on each other. There is a net inward force at the surface. © 2010 Pearson Education, Inc.

9.5 Surface Tension, Viscosity, and Poiseuille’s Law All real fluids have some viscosity, which causes drag. © 2010 Pearson Education, Inc.

9.5 Surface Tension, Viscosity, and Poiseuille’s Law The higher a fluid’s viscosity, the more it resists flow. © 2010 Pearson Education, Inc.

9.5 Surface Tension, Viscosity, and Poiseuille’s Law Poiseuille’s law describes viscous flow in a tube or pipe of length L and radius r. © 2010 Pearson Education, Inc.

Review of Chapter 9 Stress is a measure of the force causing a deformation; strain is a measure of the deformation itself. Elastic modulus is the ratio of stress to strain. Pressure is defined as force per unit area. Pressure varies with depth in a fluid: © 2010 Pearson Education, Inc.

Review of Chapter 9 Pressure in an enclosed fluid is transmitted unchanged to every part of the fluid. The buoyant force is equal to the weight of displaced fluid. An object will float if its average density is less than that of the fluid; if it is greater, the object will sink. © 2010 Pearson Education, Inc.

Review of Chapter 9 Equation of continuity: Flow rate equation: Bernoulli’s law: © 2010 Pearson Education, Inc.

Review of Chapter 9 Surface tension is due to intermolecular forces. Viscosity is a fluid’s internal resistance to flow. Poiseuille’s law: © 2010 Pearson Education, Inc.

36. A cylinder has a diameter of 15 cm. The water level in the cylinder is maintained at a constant height of 0.45 m. If the diameter of the spout pipe is 0.50 cm, how high is h, the vertical stream of water? (Assume the water to be an ideal fluid.)

© 2010 Pearson Education, Inc. 14. Two metal plates are held together by two steel rivets, each of diameter 0.20 cm and length 1.0 cm. How much force must be applied parallel to the plates to shear off both rivets?

© 2010 Pearson Education, Inc.