Computational Fluid Dynamics Outline Example | Topics and Well Written Essays - 1250 words

Computational Fluid Dynamics - Outline Example In the design of pipe systems it is necessary to take into account with Water Hammer effect and consequently, it is important that these Water Hammer effects be calculated with the appropriate accuracy. Application of Newton’s second law of motion to the case of unsteady flow of a compressible liquid in an elastic pipe leads ultimately to the momentum equation in pipes. The following equation expresses the law of conservation of momentum in 1D-dimension. where is the diameter of the circular pipe and is the friction factor of the pipe. The value of is a function of the Reynolds number and the roughness of the pipe and is given below. Also is the pressure of the liquid in the pipe, is the liquid velocity in the x-direction coinciding with the pipe length, is the fluid density and is the time. We notice that the convective term is negligible compared with other terms. Where is the speed of sound in the pipe as a function of the local density, the compressibility of the liquid (bulk modulus) which is defined as , the elasticity of the wall, the diameter of the pipe , the thickness of the wall and the lame coefficient of the material of the pipe. The equation (1) and (2) are a simultaneous pair of partial differential equations which relate the two dependent variable and , as function of and . All methods of analysis of Water Hammer have theses equations, or simplified forms of them, as their starting points and it is important to note the assumption and approximations which have been used in their derivation. These are as follow: The pair of partial differential equation 1 and 2 are of hyperbolic type and, consequently, linear combinations of them can be found which reduce to ordinary differential equations along two intersecting families of curves in the -plane. The Equations which specify the two families of curves and the ordinary differential

Curriculum Alignment for 3rd Grade Research Paper

Curriculum Alignment for 3rd Grade - Research Paper Example It is a recognized element that the standards in place demand that a learner gains knowledge so as to address the immediate need of passing tests and SAT’s. This should not be the case in the modern educational setting. Knowledge must be gained for the learner to have the capability of addressing any issues they come across in life. This application should be quick and even in the face of difficult challenges; learners might apply this knowledge to advance onto the next stages (Falk, 2012). This paper will examine one subject area, and some recommendations that may assist learners cope with the present situations. Subject and grade that need assistance It is crucial to nurture the minds of learners at a tender age. This is where the mind is eager to learn and receive new ideologies. In 3rd grade, it is highly vital for educators to instil a number of methods of educating learners. At this stage, it is particularly easy for the learners mind to be distracted. During learning se ssions, teachers may find it difficult to capture the learner’s attention throughout the whole session. It would be considered a waste of treasured period if the pupil got into class, and only benefitted from the first few minutes of the lesson. Teachers need to understand that having long periods is detrimental to the minds of young learners. It does not make sense to the learner to have long periods of which they do the same thing, and do not grasp any new concept (Elmore & Green, 2006). In mathematics, for example, some of the learners find it problematic to handle new concepts. Instead of teachers taking the time to teach these new concepts and later explain them, they are keener on finishing one concept while heading to another. This is one of the core reasons why learners end up hating mathematics as a subject. Effective mathematics should provide the learner with an instructional program that is balanced. In this approach, the learner acquires basic computational exper tise. They also grasp the basic concepts they are provided with, and become adept at solving mathematical problems (Kagan & Kauerz, 2012). Some improved/advocated for standards in mathematics are underway and are of significance to this stage in learning. How teachers and all stakeholders will provide for curriculum alignment Teachers and guardians in the school should participate fully in the learner’s intellectual growth. This provides a cushion for the child to fall onto whenever a problem arises during the course of their studies. To improve the relationship between the parent, teacher, and learner, it is crucial for the parties to sit down and advice each other. They can advise each other on all possible things that go on in each other’s lives. This is because they must help each other understand how to relate with one another. Learners at this stage tend to relate to their elders by acting out, or lashing out at them. This is one way for the created forums to rea ch out to them, and teach them ways of how to communicate (Kagan & Kauerz, 2012). The taught curriculum in this class should go hand in hand with the school calendar. This is to prevent the pushing of course content into the next academic year. Usually when this happens, the learner is at a disadvantage. They do not acquire the needed knowledge at the time they are supposed to, which makes them stagnate at the previous level (Mooney & Mausbach, 2008). They, therefore, lack the