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

Computational Fluid Dynamics - Outline ExampleIn the design of pipe systems it is necessary to take into tarradiddle with Water Hammer effect and consequently, it is important that these Water Hammer effects be calculated with the appropriate accuracy.Application of Newtons second faithfulness 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 undermentioned 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 bourne is negligible compared with other terms.Where is the speed of sound in the pipe as a functio n of the local density, the compressibility of the liquid (bulk modulus) which is defined as , the snatch 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 cardinal 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 tincture the assumption and approximations which have been used in their derivation. These are as followThe pair of partial differential equation 1 and 2 are of increased type and, consequently, linear combinations of them can be found which reduce to middling differential equations along two intersecting families of curves in the -plane. The Equations which specify the two families of curves and the ordinary differential