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

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CBE 320 September 3, 2010 Introductory Transport Phenomena Problem Session I Part B: Review of Mathematical Topics Review Appendices A and C in Transport Phenomena before doing this assignment. 1. Sketch the following functions; be sure to label the axes carefully. a. y ( x ) = cosh bx cosh b , −∞ < x < , b = constant b. y ( x ) = e bx , −∞ < x < , b = constant c. y ( x ) = tanh x x , −∞ < x < d. v z ( r ) = v 0 1 r R 2 , 0 r R, v 0 , R = constant e. v z ( r ) = v 0 ln( r/R ) ln κ , κR 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 = 2 , y = 4 , 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 v x and v

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