Homework Solutions - 1B - Solution CBE 320 Introductory...

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CBE 320September 2, 2011Introductory 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=2,y= 3,z= 6in 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 vectorv=vxδx+vyδy+vzδzhas Cartesian componentsvx= 1,vy= 2, andvz= 3.a.What are the components ofvin cylindrical coordinates (vr, vθ, vz)?b.What are the components ofvin spherical coordinates (vr, vθ, vφ)?4.The flow of a fluid past a wedge is described by the potential

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