class4lecturenotes

class4lecturenotes - Class 4, Wednesday, January 13, 2010...

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Class 4, Wednesday, January 13, 2010 Reading: 15.4 One more example, left over from last class: Example 1. Build your boat from a slab of steel. How can that ever work? Everybody knows that a slab of steel will sink, because its density is nearly 8 times larger than that of water. So, how can we make it float? How can we make it "more buoyant"? Given that it has to float on water. the only possible way to increase the slab's buoyancy would be to somehow lower "its density". One can't. however. make steel less dense. One can build on the steel slab an air-tight container with very thin walls, so that the mass of this "boat" would be practically the mass of the slab, m. In doing so, we create a compound object (slab+air container), which has a smaller average density than water. All we need, is to have enough air to offset the high density of steel. We want to build the boat as high as to barely float. How tall do we need to buDd our container? J - , I
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Fluid Dynamics So far we talked about fluids in static equilibrium, i.e. situations in which the fluids do not move. We are now making the transition to moving fluids. In the most general framework, moving fluids are treated within the discipline of "fluid Dynamics". Solutions to various circumstances in this domain can most often only be found by using a computer code that solves for a system of coupled differential equations. These equations describe mass, momentum and energy conservation of the fluid in question, and the system is closed by a so-called "equation of state" that links the pressure, density and temperature in the fluid. While there is a range of fascinating applications involving fluids in motion, we will restrict ourselves to a simple model, which provides us with a framework for studying some simpler effects that tie strongly into our everyday life. This is the so-called ideal- fluid-model. Next class we will look at a few more complicated examples. An ideal fluid fulfills the following conditions: 1. It is incompressible, Le. the density is constant throughout the fluid. This is an excellent assumption for liquids, but not always appropriate for gasses. That is, whenever a gas flows with a speed that is much smaller than the speed
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class4lecturenotes - Class 4, Wednesday, January 13, 2010...

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