hw1bsol-dist - Solutions CBE 320 Introductory Transport...

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CBE 320 September 2, 2009 Introductory Transport Phenomena Problem Session I Part B: Review of Mathematical Topics 1. Sketch the following functions; be sure to label the axes carefully. a. y ( x )= tanh bx tanh b , −∞ <x< ,b = constant b. y ( x cxe bx , −∞ , c = constant c. y ( x sinh x x , −∞ d. v z ( y v 0 ± y h ² y h ³ 2 ´ , 0 y h, v 0 ,h = constant e. v z ( r v 0 ln( R/r ) ln(1 ) R r R, v 0 ,R,κ = constant , 0 <κ< 1 2. A particle is located at x =4, y =2, z = 1 in Cartesian (rectangular) coordinates. a. What are the cylindrical coordinates of the particle ( r, θ, z )? b. What are the spherical coordinates of the particle ( r, θ, φ )? 3. A particle, located at x y =1, z = 0, is moving in a Northeasterly direction with speed 8 cm/sec (“North” = direction of the + y -axis; “East” = direction of the + x -axis). By means of a carefully labelled sketch, show the vector v (assume one unit in distance is numerically equal to one cm/sec). Then show the Cartesian components
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This note was uploaded on 05/06/2010 for the course CBE 320 taught by Professor Staff during the Fall '08 term at University of Wisconsin.

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hw1bsol-dist - Solutions CBE 320 Introductory Transport...

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