test 2 solutions

# test 2 solutions - MMAE 350 D Rempfer Computational...

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MMAE 350 Computational Mechanics Page 1 of 2 D . Rempfer 2nd Mid - Term Exam - Solutions November 13th, 2006 N A M E O F S T U D E N T Please return this sheet together with your solution. If you have any loose sheets, don't forget to write your name on every sheet that you want considered as part of your solution! 1. (20 points) In an experiment involving the flow between two parallel plates which are a distance of Ay = H apart, one of which is at rest, while the other one is moving at some velocity, a student measures the velocity as a function of the normalized distance q = y / H from the lower plate. Here is what he finds: It is known that the velocity law for this kind of flow is of the form The matrix F of function values such t h a t fij = fj+1(xi), is given by and the corresponding coefficient matrix C = F~ . F is The right - hand side of the system, r = F~ q is After these preparations, the coefficients ui of our regression function follow from the solution of C . u = r, which becomes a. What is the best (in a least-squares sense) estimate for the velocity of the upper plate? Thus, the velocity of the upper plate can be estimated by

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