FinalExam compiled

FinalExam compiled - EGM 4313 Spring 2009 Final Exam NAME:_...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
EGM 4313 NAME:_____________________________ Spring 2009 Final Exam Open book/Closed notes/No calculators or computers 2 hour time limit (1) Solve the following heat equation problem: ( 29 ( 29 ( 29 ( 29 2 2 5 , 0, 10, , 20 , ,0 10 5cos 2 u u u x t u t u x x t x x π = = = = + + ÷ . First find the steady-state solution that meets the boundary conditions: ( 29 ( 29 ( 29 ( 29 ( 29 0 10 10 20 10 10 ss ss ss ss u x Ax B du A dx u B u x x = + = = = = = + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 , , 5 , 0, 0, , 0, ,0 5cos 2 ss u x t u x x t x t t x t x x φ φ π = + = = = = ÷ The problem is greatly simplified if you notice that the initial condition on meets the boundary conditions and is in the form that one gets from separation of variables hence you should look for a solution of the form: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 25 25 4 4 25 4 5 5 125 5 , 5cos 0 1, 5cos cos 2 2 4 2 25 5 , 5cos 4 2 5 , 10 5cos 2 t t t x x x x t T t T T t T t T t x T t e x t e T t x u x t x e - - - = = = - ÷ ÷ ÷ = - = = ÷ = + + ÷
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EGM 4313 NAME:_____________________________ Spring 2009 Final Exam (2) Consider the complex potential ( 29 ( 29 ( ) ln 1 ln 1 F z z z = - - + . Find the velocity potential and the streamfunction as functions of x and y . (Hint: First write the velocity potential and streamfunction in terms of 1 1 2 , , , r r θ and 2 as shown in the figure. Then write 1 1 2 , , , r r and 2 in terms of x and y .) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 2 2 2 2 2 1 2 1 2 2 2 2 1 1 2 2 2 2 1 ln ln ln ln ln ln 1 tan ln 1 tan 1 1 ln 1 ln 1 tan tan 1 1 , ln 1 ln 1 , tan tan 1 i w re r i F z r i r i y y x y i x y i x x y y x y x y i x x x y x y x y y x y x φ ψ - - - - - - = = + = + - - = - + + - + + - ÷ ÷ - + = - + - + + + - ÷ ÷ ÷ - + = - + - + + = - ÷ - 1 1 y x ÷ +
Background image of page 2
EGM 4313 NAME:_____________________________ Spring 2009 Final Exam (3) Find the rank of the matrix 1 2 2 3 1 1 3 2 1 2 3 4 2 4 5 7 . Put in row reduced echelon form: 1 2 2 3 1 2 2 3 1 2 2 3 1 1 3 2 0 1 1 1 0 1 1 1 1 2 3 4 0 0 1 1 0 0 1 1 2 4 5 7 0 0 1 1 0 0 0 0 - - - - Hence the rank is 3.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EGM 4313 NAME:_____________________________ Spring 2009 Final Exam (4) The inverse of a Laplace transform is given by ( 29 1 lim 2 c iT st T c iT e f s ds i π + →∞ - where c is chosen so that all the singular points of f(s) lie to the left of the line s = c
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/15/2011 for the course EGM 4313 taught by Professor Mei during the Fall '08 term at University of Florida.

Page1 / 15

FinalExam compiled - EGM 4313 Spring 2009 Final Exam NAME:_...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online