hw2b - b. the z component of the force exerted on the end...

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CBE 320 September 9, 2009 Transport Phenomena Problem Session II Part B: Viscosity, Differential Areas and Fluxes 1. Work problem 1A.6 in BSL. 2. 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. 3. 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).
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Unformatted text preview: b. the z component of the force exerted on the end of a cylinder oriented in the z direction, centered at the origin (cylindrical coordinates; the fluid flows 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 fluid flows 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 defined as a surface of constant θ (for this problem, assume θ < π/ 2 ). The fluid flows external to the cone, which extends to a radius R . For this problem, just determine the differential component of the force, not the integral over the surface. 1...
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This note was uploaded on 05/06/2010 for the course CBE 320 taught by Professor Staff during the Fall '08 term at University of Wisconsin.

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