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Chapter 9 Solids and Fluids

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Solids Has definite volume Has definite volume Has definite shape Has definite shape Molecules are held in specific locations Molecules are held in specific locations by electrical forces by electrical forces vibrate about equilibrium positions vibrate about equilibrium positions Can be modeled as springs connecting molecules Can be modeled as springs connecting molecules

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Liquid Has a definite volume Has a definite volume No definite shape No definite shape Exist at a higher temperature than solids Exist at a higher temperature than solids The molecules “wander” through the liquid in a random fashion The molecules “wander” through the liquid in a random fashion The intermolecular forces are not strong enough to keep the molecules in a fixed position The intermolecular forces are not strong enough to keep the molecules in a fixed position

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Gas Has no definite volume Has no definite volume Has no definite shape Has no definite shape Molecules are in constant random motion Molecules are in constant random motion The molecules exert only weak forces on each other The molecules exert only weak forces on each other Average distance between molecules is large compared to the size of the molecules Average distance between molecules is large compared to the size of the molecules

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Deformation of Solids All objects are deformable All objects are deformable It is possible to change the shape or size (or both) of an object through the application of external forces It is possible to change the shape or size (or both) of an object through the application of external forces when the forces are removed, the object tends to its original shape when the forces are removed, the object tends to its original shape elastic behavior elastic behavior

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Elastic Properties Stress is related to the force causing the deformation Stress is related to the force causing the deformation Strain is a measure of the degree of deformation Strain is a measure of the degree of deformation The elastic modulus is the constant of proportionality between stress and strain The elastic modulus is the constant of proportionality between stress and strain

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Young’s Modulus Young’s modulus applies to a stress of either tension or compression Young’s modulus applies to a stress of either tension or compression It is possible to exceed the elastic limit of the material It is possible to exceed the elastic limit of the material No longer directly proportional No longer directly proportional Ordinarily does not return to its original length Ordinarily does not return to its original length If stress continues, the object may break If stress continues, the object may break

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Young’s Modulus: Elasticity in Length Tensile stress is the ratio of the external force to the cross- sectional area Tensile stress is the ratio of the external force to the cross- sectional area The elastic modulus is called Young’s modulus The elastic modulus is called Young’s modulus

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Fig. P9.12, p. 295 Slide 65

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Shear Modulus A material having a large shear modulus is difficult to bend A material having a large shear modulus is difficult to bend

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Bulk Modulus Volume stress, ΔP, is the ratio of the force to the surface area Volume stress, ΔP, is the ratio of the force to the surface area This is also the Pressure This is also the Pressure The volume strain is equal to the ratio of the change in volume to the original volume The volume strain is equal to the ratio of the change in volume to the original volume

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Density The density of a substance of uniform composition is defined as its mass per unit volume: The density of a substance of uniform composition is defined as its mass per unit volume: Units are kg/m 3 (SI) or g/cm 3 (cgs) Units are kg/m 3 (SI) or g/cm 3 (cgs) 1 g/cm 3 = 1000 kg/m 3 1 g/cm 3 = 1000 kg/m 3

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Pressure The force exerted by a fluid on a submerged object at any point if perpendicular to the surface of the object The force exerted by a fluid on a submerged object at any point if perpendicular to the surface of the object

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Measuring Pressure The spring is calibrated by a known force The spring is calibrated by a known force The force the fluid exerts on the piston is then measured The force the fluid exerts on the piston is then measured

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Pressure and Depth Examine the darker region, assumed to be a fluid Examine the darker region, assumed to be a fluid It has a cross- sectional area A It has a cross- sectional area A Extends to a depth h below the surface Extends to a depth h below the surface Three external forces act on the region Three external forces act on the region

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Pressure and Depth equation P o is normal atmospheric pressure P o is normal atmospheric pressure 1.013 x 10 5 Pa = 14.7 lb/in 2 1.013 x 10 5 Pa = 14.7 lb/in 2 The pressure does not depend upon the shape of the container The pressure does not depend upon the shape of the container

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Pascal’s Principle A change in pressure applied to an enclosed fluid is transmitted undimished to every point of the fluid and to the walls of the container. A change in pressure applied to an enclosed fluid is transmitted undimished to every point of the fluid and to the walls of the container. The hydraulic press is an important application of Pascal’s Principle The hydraulic press is an important application of Pascal’s Principle Also used in hydraulic brakes, forklifts, car lifts, etc. Also used in hydraulic brakes, forklifts, car lifts, etc.

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Pressure Measurements: Manometer One end of the U- shaped tube is open to the atmosphere One end of the U- shaped tube is open to the atmosphere The other end is connected to the pressure to be measured The other end is connected to the pressure to be measured Pressure at B is P o +ρgh Pressure at B is P o +ρgh

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Pressure Measurements: Barometer Invented by Torricelli Invented by Torricelli A long closed tube is filled with mercury and inverted in a dish of mercury A long closed tube is filled with mercury and inverted in a dish of mercury Measures atmospheric pressure as ρgh Measures atmospheric pressure as ρgh One atmosphere (1 atm) = One atmosphere (1 atm) = 76.0 cm of mercury 76.0 cm of mercury 1.013 x 10 5 Pa 1.013 x 10 5 Pa 14.7 lb/in 2 14.7 lb/in 2

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Buoyant Force The magnitude of the buoyant force always equals the weight of the displaced fluid The magnitude of the buoyant force always equals the weight of the displaced fluid The buoyant force is the same for a totally submerged object of any size, shape, or density The buoyant force is the same for a totally submerged object of any size, shape, or density

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Archimedes’ Principle: Floating Object The object is in static equilibrium The object is in static equilibrium The upward buoyant force is balanced by the downward force of gravity The upward buoyant force is balanced by the downward force of gravity Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level

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Fig. P9.26, p. 297 Slide 70

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Characteristics of an Ideal Fluid The fluid is nonviscous The fluid is nonviscous There is no internal friction between adjacent layers There is no internal friction between adjacent layers The fluid is incompressible The fluid is incompressible Its density is constant Its density is constant The fluid is steady The fluid is steady Its velocity, density and pressure do not change in time Its velocity, density and pressure do not change in time The fluid moves without turbulence The fluid moves without turbulence No eddy currents are present No eddy currents are present

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Equation of Continuity A 1 v 1 = A 2 v 2 A 1 v 1 = A 2 v 2 The product of the cross-sectional area of a pipe and the fluid speed is a constant The product of the cross-sectional area of a pipe and the fluid speed is a constant Speed is high where the pipe is narrow and speed is low where the pipe has a large diameter Speed is high where the pipe is narrow and speed is low where the pipe has a large diameter Av is called the flow rate Av is called the flow rate

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Bernoulli’s Equation Relates pressure to fluid speed and elevation Relates pressure to fluid speed and elevation Bernoulli’s equation is a consequence of Conservation of Energy applied to an ideal fluid Bernoulli’s equation is a consequence of Conservation of Energy applied to an ideal fluid Assumes the fluid is incompressible and nonviscous, and flows in a nonturbulent, steady-state manner Assumes the fluid is incompressible and nonviscous, and flows in a nonturbulent, steady-state manner

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Applications of Bernoulli’s Principle: Venturi Meter Shows fluid flowing through a horizontal constricted pipe Shows fluid flowing through a horizontal constricted pipe Speed changes as diameter changes Speed changes as diameter changes Can be used to measure the speed of the fluid flow Can be used to measure the speed of the fluid flow Swiftly moving fluids exert less pressure than do slowly moving fluids Swiftly moving fluids exert less pressure than do slowly moving fluids

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Fig. P9.45, p. 298 Slide 75

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