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problem1b - of motion c You may assume that v r = v z = 0...

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Name:_________________________________________ Problem # 1b ChBE 3200B, Spring 2006 1b. A can that is partially full of water is placed on a turntable that rotates at a constant angular rate of s -1 . For constant density and viscosity, and at steady state, describe quantitatively the shape of the interface between the surface of the water and the surrounding air. a) Write the Navier-Stokes equation for constant density and viscosity. Can any terms be eliminated? b) Select a coordinate system, and write the three components for the equation
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Unformatted text preview: of motion. c) You may assume that v r = v z = 0 , and that v q = v q ( r ) . Simplify the three component equations d) What are the boundary conditions for the θ equation of motion? Integrate to determine v q e) If the total differential for pressure is dp = ¶p ¶r dr + ¶p ¶z dz then dp = r W 2 rdr-r gdz . f) If the pressure at the interface between the liquid and air is p o , what is the pressure as a function of r and z? Define z=z o as the liquid level at r=0. g) Show that z-z o = r 2 W 2 2 g...
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