ECH51FirstExam1Soln_2012

# ECH51FirstExam1Soln_2012 - HANOI UNIVERSITY OF MINING AND...

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HANOI UNIVERSITY OF MINING AND GEOLOGY ECH 51 Material Balances First Exam Monday April 15, 9:00-10:30 (Closed book and closed notes, calculators allowed) ü Prof. Brian G. Higgins April 2012 Given for Exam: Total Mass Balance t V H t L r „ V + A H t L r H v - w L ÿ n A = 0 Species Mass Balance (no reactions) t V H t L r A V + A H t L r A H v A - w L ÿ n A = 0, A = 1,2,…,N Problem 1 (10 pts) As water flows over the dam illustrated in Figure below, it accelerates because of the action of gravity. When the effect of gravity is much larger than the effect of the friction between the water and the surface of the dam, the magni- tude of the velocity of the water can be expressed as v = v 0 2 + 2gz in which z is measured as indicated in the figure. This expression for the velocity is based on the idea that potential and kinetic energy are conserved when frictional effects are negligible. If the width of the dam is constant and the water level in the dam does not change appreciably, what is the thickness of the fluid stream, h(z) , as a function of z. Assume that the density of the water is constant and that the velocity profile is flat everywhere as indicated in the figure. In your analysis be sure to indicate the CV you selected for your calculations

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ü Solution We will choose a control volume cuts the fluid passing over the weir with height h o an then cuts the fluid flow over the dam wall at some arbitrary location z with height h(z). We assume that the flow is steady and the density is constant.
• Summer '13
• LeThuy
• Fluid Dynamics, mol, Mass flow rate, HWA, HMA L1

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