100510 hw 3 - level in the tank Derive an equation that...

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DEPARTMENT OF CHEMICAL ENGINEERING UNIVERSITY OF CALIFORNIA, SANTA BARBARA ChE10 Introduction to Chemical Engineering Fall 2010 Third week assignment: Due Wednesday, October 13, 2010 Read: Chapter 4 A 10 m high, 5 m diameter cylindrical water tank has an inlet at the top and a drain at the bottom. The flow rate out of the tank depends on the pressure at the bottom of the tank via the following: dm dt = 10 4 P b where P b is the absolute pressure in Pa at the bottom of the tank. The tank is open to atmosphere at the top, which we call P atm . The density of water is 1000kg/m 3 . (a) What are the units of 10 -4 ? (b) What is the absolute pressure at the bottom of the tank in psia when the tank is 50% full? (c) What is the gauge pressure at the bottom of the tank in psig when the tank is 50% full? (d) At steady state, there is a specific inlet flow rate required to maintain a given water
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Unformatted text preview: level in the tank. Derive an equation that gives the inlet flow rate (in [kg/s]) required to maintain the water height (h) at a given level, where h [m] is measured from the bottom of the tank upwards. (e) Determine the inlet flow rate needed to keep the water level at 50% full. (f) Assume that the tank is initially empty. At time t=0, the inlet is turned on at the flow rate you found in part (e). How long does it take the tank to reach 30% full? Think carefully…is the flowrate going out constant? (g) How long does it take for the initially empty tank from part (f) to reach 50% full? TEXT PROBLEMS 3 rd Edition, Felder and Rousseau (1) Felder & Rousseau #4.6 (2) Felder & Rousseau #4.8 (3) Felder & Rousseau #4.9 (4) Felder & Rousseau #4.16 (5) Felder & Rousseau #4.20 (6) Felder & Rousseau #4.31...
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