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Chapter 9 Solids and Fluids

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

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.

9.1 Solids and Elastic Moduli Stress is defined as the force per unit area:

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.

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:

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.

9.1 Solids and Elastic Moduli

Shear modulus:

9.1 Solids and Elastic Moduli Bulk modulus (the only one relevant for fluids—why?)

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.

9.2 Fluids: Pressure and Pascal’s Principle Unit of pressure: the Pascal (Pa) Density is defined as mass per unit volume:

9.2 Fluids: Pressure and Pascal’s Principle

The pressure in a fluid increases with depth, due to the weight of fluid above it.

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.

9.2 Fluids: Pressure and Pascal’s Principle Hydraulic lifts and shock absorbers take advantage of Pascal’s principle.

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.

9.2 Fluids: Pressure and Pascal’s Principle There are a number of methods used to measure pressure.

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.

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

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.

9.3 Buoyancy and Archimedes’ Principle The buoyant force on an object that is completely submerged:

9.3 Buoyancy and Archimedes’ Principle It is the average density that matters; a boat made of steel can float because its interior is mostly air. An object’s density may be changed; submarines fill tanks with water to submerge, and with air to rise.

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9.3 Buoyancy and Archimedes’ Principle Specific gravity is the ratio of an object’s density to that of water at 4°C.

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.

9.4 Fluid Dynamics and Bernoulli’s Equation Irrotational flow means that a fluid element (a small volume of the fluid) has no net angular velocity. This condition eliminates the possibility of whirlpools and eddy currents. (The flow is nonturbulent.) In the previous figure, the paddle wheel does not turn, showing that the flow at that point is irrotational.

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.

9.4 Fluid Dynamics and Bernoulli’s Equation Equation of continuity:

9.4 Fluid Dynamics and Bernoulli’s Equation If the density is constant,

9.4 Fluid Dynamics and Bernoulli’s Equation Bernoulli’s equation is a consequence of the conservation of energy.

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.

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.

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.

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

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

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.

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:

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.

Review of Chapter 9 Equation of continuity: Flow rate equation: Bernoulli’s law:

Review of Chapter 9 Surface tension is due to intermolecular forces. Viscosity is a fluid’s internal resistance to flow. Poiseuille’s law: