Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3/3/13 PHYS 220 General Physics I A large fish is perfectly motionless about two feet below the surface of a lake. Which of these best describes the free body diagram for the fish? mg A. Spring Semester 2013 Assigned Reading: Ch 10, sections 4-7 mg mg B. C. mg D. mg E. Lecture 16 Buoyancy A short time later, the fish swims away. The space that used to be occupied by the fish is now filled with water, which is also at rest. Does this volume of water have the same free body diagram as the fish? Are the forces exerted by the water on the fish any different from the forces exerted on the water that took the place of the fish? Would the forces exerted by the water be any different if the actual fish were replaced by a heavy marble statue that was exactly the same size and shape as the fish? Archimedes's Principle: When an object is immersed in a fluid, the fluid exerts an upward force on the object that is equal to the weight of the fluid displaced by the object Buoyant force arises because of the differences in the pressures on the top and the bottom of the object (which arise because of the weight of the fluid). 1 3/3/13 A heavy mass is slowly lowered into a beaker of water until it is completely submerged, but it does not touch bottom. How does the weight of the scale under the beaker change? Archimedes’ Principle A. Unchanged, as long as the mass does not touch bottom. B. Increases by the actual weight of the mass. C. Something else…. Buoyant Force A floating object experiences a buoyant force due only to the submerged portion of the object If an object with an area A and height h is submerged in a liquid of density ρliq, the buoyant force of the liquid, Fliq, on the object is…. Fbuoyant = m f g = Vsubmerged rg F liq = + P bot A− P top A The maximum buoyant force is experienced by a fully submerged object. P bot= P top + ρ liq g h F liq= (P top+ ρ liq gh) A− P top A mg Fbuoyant = m f g F liq= ρliq g h A= ρ liq gV = mliq g …equal to the weight of the fluid displaced by the object. Vr f g V: Total volume of the object 2 3/3/13 “Light” versus Regular Coke Why does one sink but the other one doesn’t? (Does this have anything to do with the calorie content of Diet Coke vs regular Coke?) Why do some objects float and others sink? Fbuoyancy Fgravity Fbuoyancy Fbuoyancy Fgravity Fgravity Fgravity > Fbuoyancy Bernoulli Cans Fluid Dynamics 3 3/3/13 Li* on a Plane Wing Assume fluids are “Ideal” Assump8ons: Density is constant Fluid velocity is independent of 8me (not of posi8on) No fric8on (no viscosity) No complex flow paIerns (no turbulence) Equation of Continuity Work-‐Energy and Fluids Principle of con8nuity: The amount of fluid that flows through a pipe must be conserved. The rate at which a volume of fluid flows into a sec8on of pipe must be the same as the rate at which the same volume leaves the pipe Vin = Vout vL AL = vR AR 4 3/3/13 Bernoulli's Equa8on Venturi Tubes 1 2 1 2 P 1+ ρ v 1+ ρ g h1= P 2+ ρ v 2+ ρ g h2 2 2 Change in energy due to work done at point 1 Kine8c energy at point 1 Kine8c Poten8al energy at energy at point 1 Change in point 2 energy due to work done at point 2 Poten8al energy at point 1 This predicts that pressure is connected to changes in velocity, and to changes in the height of the fluid. (Follows from conservation of energy.) Real Fluids Fric8on between the fluid and the wall of the container or object it is flowing around – viscous forces. Forces depend on the speed of the fluid and the type of fluid. Viscosity of the fluid (air) led to the drag forces (Stokes's Law) discussed in Chapter 3 Surface Tension Arises from interac8ons of fluid molecules with themselves and with a surface. η 5 3/3/13 Capillary Pressure Explains how plants (and paper towels) work. For a pressure difference of 1 atm (the atmospheric pressure), water can be “pumped” a height of 10m. Some trees grow significantly taller than 10m. 6