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Solid & Fluid Dynamics

Solid & Fluid Dynamics . Physics. Solids & Fluids Contents. Overview of the four physical states of Matter Solids, liquids, and gases Solid Mechanics Deformation of Solids Fluid Mechanics Density & Pressure Buoyant Forces: Archimedes’ Principle Fluids in Motion Bernoulli Equation

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Solid & Fluid Dynamics

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  1. Solid & Fluid Dynamics Physics

  2. Solids & Fluids Contents Overview of the four physical states of Matter • Solids, liquids, and gases Solid Mechanics • Deformation of Solids Fluid Mechanics • Density & Pressure • Buoyant Forces: Archimedes’ Principle • Fluids in Motion • Bernoulli Equation • Application of Fluid Dynamics

  3. Intermolecular Forces hold molecules together • Instantaneous Dipoles that are created by constantly moving electrons.

  4. Comparisons of the Three States of Matter

  5. Three States of MatterShape • Gases have no shape because of little attractive forces and independent movement. Liquids take the shape of their container but do not expand readily because of attractive forces. Solid molecules have definite shape and are held in fixed position.

  6. Section 4 Changes of State States of Matter Density • Density is mass per unit volume and indicates the closeness of particles in a sample of matter. • Gas Liquid Solid Low High High

  7. Three States of MatterParticle Energy • Differences in attractive forces slow down particle movement. • Gases- high kinetic energy because of low attraction between particles. • Liquids- moderate kinetic energy and attraction • Solids- low kinetic energy and high attractive forces.

  8. Factors that effect a GAS • The quantity of a gas, n, in moles • The temperature of a gas, T, in Kelvin (Celsius degrees + 273) • The pressure of a gas, P, in pascals • The volume of a gas, V, in cubic meters

  9. Gas Law #1 – Boyles’ Law(complete TREE MAP) “The pressure of a gas is inverse related to the volume” • Moles and Temperature are constant

  10. Gas Law #2 – Charles’ Law “The volume of a gas is directly related to the temperature” • Pressure and Moles are constant

  11. Gas Law #3 – Gay-Lussac’s Law “The pressure of a gas is directly related to the temperature” • Moles and Volume are constant

  12. Gas Law #4 – Avogadro’s Law “The volume of a gas is directly related to the # of moles of a gas” • Pressure and Temperature are constant

  13. Gas Law #5 – The Combined Gas Law You basically take Boyle’s Charles’ and Gay-Lussac’s Law and combine them together. • Moles are constant

  14. Solids & Fluids Contents Solid Mechanics • Deformation of Solids • Stress, strain, and • Young’s Modulus: Elasticity of Length • Shear modulus: Elasticity of Shape • Bulk Modulus: Volume Elasticity

  15. Atomic Arrangement of a solid • Crystalline Solid • Very structured atomic arrangement. • Ex: sodium chloride (salt) • Amorphous Solid • Randomly arranged atoms • Ex: glass

  16. Solids: vibrating atoms Temperature is related to the average kinetic energy of the particles in a substance. Vibration is slight, essentially fixed Atomic attraction is electrical Solids are elastic KE = mv2 2

  17. Deformation of a Solid • Solids are elastic • Application of a external force can… • Deform a solid • Break a solid • Removal of external force • Solid returns to original shape • Unless you surpass the elastic limit. • Video

  18. Stress & Strain Demo Stress & strain are the terms used to discuss the elastic properties of a solid. Stress (σ)- is the force per unit area causing deformation Strain (s)- is a measure of the amount of the deformation Hooke’s Law: K = springness Δx = displacement Elastic modulus Y: proportionality constant. It is analogous to the spring constant k. Y is the stiffness of a material. It is determined experimentally A material having a large is very stiff, therefore difficult to deform.

  19. Elastic Modulus • Elastic modulus “Y” is like the spring constant. • stiffness of a material. • Large elastic modulus = very stiff • Small elastic modulus = not stiff • Three types of stress related to this expression • Tensile “Y” - pulling apart, force is perpendicular to cross-section • Shear “S”- pushing apart, force is parallel to cross-section • Bulk “-B”- squeezing force

  20. Elastic Modulus Values

  21. Overview

  22. Stress & Strain Elastic Modulus Y is determine in the lab and is unique to the material.

  23. Tensile Stress: Young’s Modulus Elasticity of length • A- is cross-sectional area • F- force perpendicular to cross-section • Y- young’s modulus • Lo- original length’ • ΔL – change in length • Units:

  24. Tensile Stress: Young’s Modulus Elasticity of length • Strain • Consider the metal bar. When an external force is applied perpendicular cross-sectional area the atomic bonds of the metal, by their nature, resist the distortion (“stretching”). • The bar is said to experience tensile stress.(pulling) • Strain is the ratio of change in length and original length.

  25. Tensile Strength Breaking Point

  26. Pause for a Cause A vertical steel beam in a building supports a load of 6.0 X 104 N. A) If the length of the beam is 4.0 m and its cross-sectional area is 8.0 X 10-3 m2, find the distance the beam is compressed along its length. B) Find the maximum load that the beam can support. F = 6.0 X 104 N A = 8.0 X 10-3 m2 Lo = 4.0 m Y = 20 X 1010 Pa ΔL =?

  27. Pause for a Cause A vertical steel beam in a building supports a load of 6.0 X 104 N. A) If the length of the beam is 4.0 m and its cross-sectional area is 8.0 X 10-3 m2, find the distance the beam is compressed along its length. B) Find the maximum load that the beam can support. Look up Tensile Strength limit from chart for steel F = 6.0 X 104 N A = 8.0 X 10-3 m2 Lo = 4.0 m Y = 20 X 1010 Pa ΔL =?

  28. Pause for a Cause • Determine the elongation of the metal rod if it is under a tension of 5.8 X 103 N. F = 5.8 X 103 N A = π r2 LoCu = 2.6 m LoAl = 1.3 m Ycu = 11 X 1010 Pa YAl = 7.0 X 1010 Pa ΔL =?

  29. Shear Modulus: rigidness Elasticity of shape • A- is cross-sectional area • F- force parallel to cross-section • S- Shear modulus • h- height of object • Δx – distance displaced • Units:

  30. Shear Modulus: rigidness Elasticity of shape • When a force is applied parallel to one its faces while the other is held fixed. • Ex: A rectangular block under shear stress would become a parallelogram. • Force must be parallel to the cross-sectional area. • Ex: book

  31. Shear Modulus: Pause for a Cause A 125 kg linebacker of makes a flying tackle at vi = 4.00m/s on a stationary quarterback of mass 85 kg. The linebackers helmet makes solid contact with the quarterbacks femur. a) What is the speed vf of the two athletes immediately after contact? Assume this is a Perfectly inelastic collision from the point of impact. b) If the collision last for 0.100 s, estimate the average force exerted on the quarterbacks femur. c) If the cross-sectional area of the quarterback’s femur is 5.0 x 10-4 m2, calculate the shear stress exerted on the bone in the collision.

  32. Shear Modulus: Practice A 125 kg linebacker of makes a flying tackle at vi = 4.00m/s on a stationary quarterback of mass 85 kg. The linebackers helmet makes solid contact with the quarterbacks femur. a) What is the speed vf of the two athletes immediately after contact? Assume this is a Perfectly inelastic collision from the point of impact.

  33. Shear Modulus: Practice A 125 kg linebacker of makes a flying tackle at vi = 4.00m/s on a stationary quarterback of mass 85 kg. The linebackers helmet makes solid contact with the quarterbacks femur. b) If the collision last for 0.100 s, estimate the average force exerted on the quarterbacks femur.

  34. Shear Modulus: Practice A 125 kg linebacker of makes a flying tackle at vi = 4.00m/s on a stationary quarterback of mass 85 kg. The linebackers helmet makes solid contact with the quarterbacks femur. c) If the cross-sectional area of the quarterback’s femur is 5.0 x 10-4 m2, calculate the shear stress exerted on the bone in the collision. The average shear stress of an athletes femur is 7x107 Pa, so his did not leg break?

  35. Bulk Modulus: compressibility Elasticity of volume • ΔP- volume stress • F/A • B- Bulk modulus, always - • V- original volume • ΔV- change in volume • Units:

  36. Bulk Modulus: compressibility Elasticity of volume • This is a deformation due to uniform squeezing. • All the external forces are perpendicular to every surface and are evenly distributed. • Ex: Deep sea diving • An object under this stress will experience a deformation of volume.

  37. Bulk Modulus: Pause for a Cause A solid lead sphere of volume 0.50 m3, dropped in the ocean, sinks to a depth of 2.0 x 103 m (1 mile), where the pressure increases by 2.0 x 107 Pa. Lead has a bulk modulus of 4.2 x 1010 Pa. What change is the change in volume of the lead sphere?

  38. Fluid Mechanics - Hydrostatics

  39. Fluids Contents Fluid Mechanics • Density & Pressure • Pressure with Depth • Pressure Measurements • Buoyant Forces: Archimedes’ Principle • Fluids in Motion

  40. Density: Quick Quiz Suppose you have one cubic meter of gold, two cubic meters of silver, and six cubic meters of aluminum. Rank each of them by mass, from smallest to largest.

  41. Density The 3 primary states have a distinct density, which is defined as mass per unit of volume. Density is represented by the Greek letter, “RHO”, r Specific gravity- is the ratio of an objects density to the density of water at 4˚ C (1.0 X 103 kg/m3)

  42. Common Densities

  43. Pause for a Cause A water bed is 2.0 m on each side an 30.0 cm deep. (a) Find its weight if the density of water is 1000 kg/m3. (b) Find the pressure the that the water bed exerts on the floor. Assume that the entire lower surface of the bed makes contact with the floor. 1.2 m3 1200 kg 11760 N 2940 N/m2

  44. Why fluids are useful in physics? Typically, liquids are considered to be incompressible. That is once you place a liquid in a sealed container you can DO WORK on the FLUID as if it were an object. The PRESSURE you apply is transmitted throughout the liquid and over the entire length of the fluid itself.

  45. What is a Fluid? By definition, a fluid is any material that is unable to withstand a static shear stress. Unlike an elastic solid which responds to a shear stress with a recoverable deformation, a fluid responds with an irrecoverable flow. The only stress a fluid can exert is compression on a submerged object. What kind of stress is that? The stress experienced on a submerged object is always perpendicular to all surfaces.

  46. Hydrostatic Pressure Video1 Video2 Suppose a Fluid (such as a liquid) is at REST, we call this HYDROSTATIC PRESSURE Two important points • A fluid will exert a pressure in all directions • A fluid will exert a pressure perpendicular to any surface it compacts The only stress a fluid can exert on a submerged object is compression. Notice that the arrows on TOP of the objects are smaller than at the BOTTOM. This is because pressure is greatly affected by the DEPTH of the object. Since the bottom of each object is deeper than the top the pressure is greater at the bottom.

  47. Pressure One of most important applications of a fluid is it's pressure- defined as a Force per unit Area Atmospheric pressure: Is defined as the amount of pressure exert on an object due to the weight of the air from the object to outer space. The boiling point of liquids is dependant on the atmospheric pressure. English PSI: pound/inch2

  48. Pressure One of most important applications of a fluid is it's pressure- defined as a Force per unit Area Blood Pressure: is the measure of how much pressure one heart beat exerts on the walls of your vascular system How is it measured? English PSI: pound/inch2

  49. Pressure: Example If you tried to support your total weight (F=mg), on a bed of one nail. Your weight would be divided by the tiny area of the tip of the nail.

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