Energy Conversion System Assignment Example | Topics and Well Written Essays - 1000 words

Energy Conversion System - Assignment Example(a) Determine the non-dimensional expressions and . 8 marks reply There are 6 variables involved in the problem velocity , density , viscosity , surface tension , diameter is and acceleration . Choose the terce recurring variables velocity , density and diameter . From Buckingham pi theorem we have non-dimensional groups. The choice of velocity , density and diameter as the repeating variables satisfies They are measurable, good name parameters and in combination, contain all the dimension and . We form the three groups according to the 2nd theorem. As the groups are all dimensionless, there must have dimensions such(prenominal) as , we can use the principle of dimensional homogeneity to equate the dimensions for each group. For the first group, In terms of dimensions, we have that Thus, we have the following bilinear system For For For The solutions for is disposed(p) as Giving as And a similar procedure is followed for the separat e groups. Thus, we have the following linear system For For For The solutions for is wedded as Giving as Finally the group Thus, we have the following linear system For For For The solutions for is given as Giving as Thus the problem whitethorn be described by the following function of three non-dimensional groups, We take into account that any dimensionless group may be raised to any agent and it is still a valid group. Furthermore, the reciprocal of any dimensionless group is valid, too. We concluded that Finally the non-dimensional expressions and are Pay attention that the group obeys manipulation rules of equivalence. Remember that amphetamine Density Viscosity Surface tension Distance Acceleration (b) Comment on the physical significance of the non-dimensional numbers formed. 6 marks Solution The non-dimensional expressions found for and were The non-dimensional number given by is the so-called Reynolds number The Reynolds number is a non-dimensional number that give s a measure of the ratio of inertia force to gluey force. This parameter correlates the viscous mien of all Newtonian fluids. In fluid dynamic engineer should do estimate of the Reynolds number range of the flow under study. Very low indicates viscous creeping motion, where inertia effects are negligible. Moderate implies a smoothly varying laminar flow. High probably spells turbulent flow, which is slowly varying in the time-mean but has superimposed strong random high-frequency fluctuations. The non-dimensional number given by is the so-called Weber number It is a non-dimensional number useful for analyzing fluid flows where there is an interface between two different fluids. The Weber number is the ratio between the inertial force and the surface tension force. Since the Weber number represents an list of the inertial force to the surface tension force acting on a fluid element, it can be useful analyzing thin films flows and the formation of droplets and bubbles. straits 2 ( a) Two vessels are connected by a pipe in which there is a valve. One vessel of contains nitrogen at and , and the other of contains helium at and . The valve is opened and the two gases are allowed to mix. Assuming the system is well insulated, calculate (i) the final temperature of the mixture 8 marks Solution The amount of energy given off by the warmer gas equals the amount