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
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.
Liquid: having a consistency like that of water or oil, flowing freely but of a constant volume.
Slime is a non-newtonian fluid. A non-newtonian fluid does not have a constant viscosity. Viscosity is a liquid's ability to flow and is most often measured by square meters per Second. As temperatures decrease viscosity decreases, as temperatures increase viscosity increases. A non-Newtonian fluids viscosity depends on the amount of force applied to it.
Surface Tension: The measure of how difficult it is to stretch or break the surface of a liquid.
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
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
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)
Assuming no viscous forces present an inviscid model has been used for the calculations. Also from the equation of the Reynolds number Re=ρvl/μ due to Re being really big rearranging and assuming v and l to be constant the viscous force μ =ρvl/Re becomes negligible.
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.
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,
The volume is definite if the temperature and pressure are constant. When a solid is heated above its melting point, it becomes liquid, given that the pressure is higher than the triple point of the substance. Intermolecular (or interatomic or interionic) forces are still important, but the molecules have enough energy to move relative to each other and the structure is mobile. This means that the shape of a liquid is not definite but is determined by its container. The volume is usually greater than that of the corresponding solid, the most well known exception being water, H2O. The highest temperature at which a given liquid can exist is its critical temperature.[5]
Which of the following properties of a fluid is responsible for offering resistance to shear ?
-The Reynolds number of this experiment was then calculated using equation (4) where c is the length of the aerofoil chord and is the dynamic viscosity of air.
The purpose of this module is to investigate hydrostatic forces on a plane surface under partial and full submersion.
The lid-driven cavity flow is most probably one of the most studied fluid problems in the