Determine the differential area elements on the following...

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CBE 320 September 9, 2013 Transport Phenomena Problem Session II Part A: Differential Areas and Fluxes 1. Determine the differential area elements on the following surfaces. In each case, sketch the coordinate system and the area element. a. on a surface of constant x in rectangular coordinates. b. on a surface of constant z in cylindrical coordinates. c. on a surface of constant r in cylindrical coordinates. d. on a surface of constant θ in cylindrical coordinates. e. on a surface of constant r in spherical coordinates. f. on a surface of constant θ in spherical coordinates. 2. Write integral expressions for the molecular force components (i.e., that caused by τ and perhaps p ) exerted by a flowing fluid on the following solid surfaces. a. the z component of the force exerted on a plane z = 5 (rectangular coordinates; the fluid flows above the plane, with the semi-infinite solid below the plane). b. the z component of the force exerted on the end of a cylinder oriented in the

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