Consider the flow of a fluid down a long cylindrical tube (of radius a). ignore any viscous effects and assume "plug flow" (velocity is in the z direction with speed v, independent of r or z). the fluid carries with it some molecules of con- centration c(z). the number of these molecules moving down the tube in the z direction per unit time per unit area is j.(z) = vc. the molecules can diffuse radi- ally out through the wall of the tube. the concentration of molecules outside the tube is zero, so the number of molecules moving in the r direction out through the tube wall per unit time per unit area is ja(z) = kc. a) analyze a section of the tube between z ånd z+az. use conservation of the number of molecules to determine a differential equation describing the steady- state concentration distribution, c(z). b) assume that at z = 0, c = co. derive an expression for c(z).