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hw2asol-dist

# hw2asol-dist - z direction centered at the...

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CBE 320 September 13, 2010 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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Unformatted text preview: z direction, centered at the origin (cylindrical coordinates; the Fuid Fows outside the cylinder of radius R , length L ). c. the z component of the force exerted on the inner wall of a hollow cylinder (oriented in the z direction; cylindrical coordinates; the Fuid Fows inside the cylinder of radius R , length L ). d. the r component of the force exerted on the surface of a cone. In spherical coordinates, the cone may be de±ned as a surface of constant θ (for this problem, assume θ < π/ 2 ). The Fuid Fows external to the cone, which extends to a radius R . ²or this problem, just determine the differential component of the force, not the integral over the surface. 3. Work problem 1.B.1, parts (a) and (b), in BSL. Assume that b > , and ±nd the components of τ and ρ vv in rectangular coordinates. 1 Solutions 1/4 djk 9/13/10 2/4 3/4 4/4 3...
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