ecm quiz 2 - 2 The conservation of mass for a general...

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ECM 5 Winter, 2005 Quiz 2 2/9/05, 20 minutes in length; closed book Please write your name on each sheet of paper that you turn in. Write on the pages provided, and ask for more paper if you need it. Explain your work for maximum partial credit. 1. Water flows through a horizontal pipe of diameter D , at velocity U . The density of the water is ρ and the viscosity is µ . a. Using all of these variables find a dimensionless group that describes the flow of water in the pipe. b. Consider the following system, D = 0.01 m, U = 1 ms -1 , ρ = 1 g cm -3 , µ = 0.001 mPa s (Hint: This last unit is a milliPascal second, where a Pascal is the unit of pressure in the SI system). What is the numerical value of the dimensionless group found in part a?
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Unformatted text preview: 2. The conservation of mass for a general system with one outflow stream is given by • − = m dt dM where M is the total mass in the system (in our case the tank) at a time t . The term m with a dot over it represents the rate at which mass leaves the system. a. Show that both sides of this equation have the same dimensions. b. If M represents the instantaneous mass of liquid in a cylindrical tank with diameter A T , simplify this equation so that only dt dh appears on the left hand side, where h is the height of liquid in the tank. Assume that the liquid has a constant density. Your equation should only have h , d h /d t , A T , and the volumetric flow rate, q , in it....
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