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Engineering and Construction
Pages 4 (1004 words)
NORTHUMBRIA UNIVERSITY School of Computing, Engineering & Information Sciences EN0201: Energy Conversion Systems Assignment 1of 1 Assignment weighting: 15% of total unit (Total marks = 50) Learning outcome You are expected to show the understanding of 1. the mathematical principles of model and prototype testing for the solution and analysis of engineering problems.
(a) Determine the non-dimensional expressions and . [8 marks] Solution: There are 6 variables involved in the problem: velocity , density , viscosity , surface tension , diameter is and acceleration . Choose the three 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 design 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 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 linear system: For For For The solutions for is given as: Giving as And a similar procedure is followed for the other groups. ...
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