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

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CBE 320September 2, 2009Introductory Transport PhenomenaProblem Session IPart B: Review of Mathematical Topics1.Sketchthe following functions; be sure to label the axes carefully.a.y(x) =tanhbxtanhb,−∞< x <,b= constantb.y(x) =cxebx,−∞< x <,b, c= constantc.y(x) =sinhxx,−∞< x <d.vz(y) =v0yhyh2,0yh,v0, h= constante.vz(r) =v0ln(R/r)ln(1),κRrR,v0, R, κ= constant,0< κ <12.A particle is located atx= 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 atx= 2,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 thevectorv(assume one unit in distance is numerically equal to one cm/sec). Then show the Cartesian components

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