Mechanics of Fluids and the
Rayleigh-Bénard Problem 1 Introduction
The motion of fluids in certain systems continues to be a relevant to physicists. From the coiling of dribbling fluids to the convection current of a slice of fluid heated from below, patterns forming in natural systems are still unsolved. The best that can be done is to make models of the systems and use approximations.
In this paper I will give an overview of the Rayleigh-Bénard problem as well as describe the derivation of a four-mode lorenz model and a linear stability analysis of the hydrodynamic equations to find the critical Rayleigh number responsible for predicting convection in a system.
2 Basic Fluid Dynamics
2.1 What is a fluid?
A fluid is a substance that will deform (flow) when a shear stress is applied. This is in contrast to a solid, which will compress rather than continuously deform under such a stress. Fluids are a subset of the phases of matter and include liquids (incompressible fluids), and gases (compressible fluids).
Shown in Figure 2.1.1 is of a slice of fluid between two plates undergoing a shear stress. The bottom plate is stationary, while the top one is allowed to move. The fluid adjacent to the top plate will be pulled along at about the same speed as the plate, but the layer of fluid below that resists the motion just a bit and moves slower, same with the layer below that all the way to the layer next to the bottom plate. Figure 2.1.1
2.2
3. Convection the transfer of heat through currents of gases or liquids. (occurs passively as warmer air at the surface of the body rises away from the body and is replaced by cooler air – process is aided by wind or fans)
However, there are some other factors that affect the fall rate of the marble, including; size and the shape of the marble. Therefore, the marble undergoes drag force and the effect of gravity, which all accounts for hydrodynamic forces. Hydrodynamic forces are the forces which slow the snow as it moves through liquids. In this experiment, turbulent flow can affect the snow’s timing to reach the base of the breaker in water as the flow of the fluid is
Turbulent flow is the flow of fluids in a chaotic way due to property changes. The Reynolds number is higher than that of laminar flow making it able to freely move. They create a rotational high energy movement. Eddies are a good example of turbulent flow off of jet streams. They create that vortex circular motion and are high energy to start and will
Surface Tension: The measure of how difficult it is to stretch or break the surface of a liquid.
Immigration issues are not issues only encountered here in the United States, but are also issues faced throughout the world. There have been numerous of debates on the issues of immigration in the United States. The most controversial was the passing of a new bill in Arizona. Governor Jan Brewer passed into Arizona legislature the SB1070, which became very controversial because of the demands that this law was enforcing. This controversial bill gives any Arizona law enforcement personnel full authority to stop any people who they think have reasonable suspicion of living in the United States illegally. It also gives
The second order upwind discretization model was used in this problem. The truncated error due to selected terms in the Taylor series expansion is reduced and a more accurate solution is implied. Fewer grid points are necessary to give the same level of accuracy.
4. The flow velocity increases as the flow gets closer to the barrier wall and reduces as it moves away from the wall. This is because as the flow rate is constant (Conservation of mass) while the area of the flow cross section decreases when it gets closer to the barrier wall, the flow velocity increases. This is best understood by referring to the continuity equation,
I will share my newfound knowledge through this paper and I will discuss my finding with my peers and other people who enjoy chemistry. We have been discussing both water displacement and density in class; I assume the relevancy of this lab was to help people who learn better kinesthetically a chance to learn the material in a way they learn best.
[2] Kinnas, Dynamic Viscosity of Air as a Function of Time, http://www.ce.utexas.edu/prof/kinnas/319lab/Book/CH1/PROPS/GIFS/dynair.gif Accessed on 15/04/2013
Liquid: having a consistency like that of water or oil, flowing freely but of a constant volume.
Despite unnecessary changes to plot and some flawed character portrayals, Nicholas Hytner’s 1996 film adaptation of Arthur Miller’s 1953 play, The Crucible, is overall a viable adaptation of Miller’s original work. Many of the directorial changes made by Hytner in creating this screenplay are successful in further emphasising Miller’s central ideas. The characterisation of Abigail Williams is captured appropriately in the film displaying her overall manipulative nature by drawing extensively on the original text, thus exploring Miller’s idea of the use of hysteria and rumour in order to seek personal vengeance. Hytner’s depiction of Salem is well represented and the use of space, both outdoor and indoor, helps to visually depict Miller’s
The lid-driven cavity flow is most probably one of the most studied fluid problems in the
In the introduction, Deber review statements made by Weber expounding social institutions. Weber mentions in the nineteenth century that religion and economy played an big-time role in how the society functioned. Deber was describing how economy and religion do not play the same role as they did in the nineteenth century. Deber uses the illustration of same sex marriage and attests that heterosexual marriage has changed social institution over the centuries. In the late twentieth and early twenty-first century that same sex marriage, single parents, and re-marriage is the institutional shift. In the excerpt, The Protestant Ethic and the Spirit of Capitalism, Weber describes how religion and the economy function in a society. Religion changed
The purpose of this module is to investigate hydrostatic forces on a plane surface under partial and full submersion.
This experiment is conducted in order to study a condensed system (solid-liquid) at constant temperature (atmospheric temperature). It should be noted that the atmospheric pressure is unlikely to be the equilibrium pressure for the system. However, equilibria in condensed systems are not very sensitive to pressure.