ECH51PracticeExam12014

<span class='text_page_counter'>(1)</span>HANOI UNIVERSITY OF MINING AND GEOLOGY ECH 51 Material Balances Pactice Exam 1 (Closed book and notes, calculators allowed). Prof. Brian G. Higgins. June 2014. Given for Exam: Total Mass Balance „ „t. ‡. V HtL. r „V + ‡. A HtL. r Hv - wL ÿ n „ A = 0. Species Mass Balance (no reactions) „ „t. ‡. V HtL. rA „ V + ‡. A HtL. rA HvA - wL ÿ n „ A = 0, A = 1, 2, …, N. Problem 1 Two hundred kg-mole/hr of saturated liquid feed HF1 L containing 20 mole percent ethanol and 80 mole percent water is fed into a stripping column which operates at P1 mm Hg. The bottoms product from the stripper B1 contains 2 mole percent ethanol. The vapor from the top of the stripper HD1 L is used to reboil a second distillation column operating at P2 mm Hg. After the stripper overhead is condensed, it is fed into this second column HF2 L. Since it is saturated liquid at P1 mm Hg, 100 % of the feed flashes (becomes vapor) when fed into the column at P2 mm Hg. The second column produces a distillate product D2 with composition 90 mole percent ethanol and bottoms product B2 with composition 2 mole percent ethanol. The bottoms product flow rates from the two columns are equal. A schematic of the operation is shown below.. (i) Undertake a degree of freedom Analysis as follows (note you may need more than 1 control volumesee textbook for example):.

<span class='text_page_counter'>(2)</span> 2. ECH51PracticeExam1_2014.nb. (i) Undertake a degree of freedom Analysis as follows (note you may need more than 1 control volumesee textbook for example): † Lists all the generic variables for the problem † List all the generic constraints and specifications for the problem † List all the particular constraints and specifications † Compute the Degree of Freedom Analyis. (ii Determine the composition and flow rates of all streams entering and leaving the two columns.. Problem 2: (15 points) The flow of blood in veins and arteries is a transient process in which the elastic conduits expand and contract. As a simplified example, consider the artery shown in figure below. At some instant in time, the inner radius R(t) has a radial velocity of 0.012 cm/s. The length of the artery is L=13 cm and the volumetric flow rate at the entrance of the artery is Q=0.3 cm3 /s. If the inner radius of the artery is 0.15 cm, at the particular instant of time, what is the volumetric flow rate at the exit of the artery?. Problem 3 (15 points) Liquid acetone (C3 H6 O, species A) is fed (Stream #1) a rate of 0.400 m3 /min into a heated evaporator, where it evaporates into a nitrogen stream that enters the evaporator as Stream #2. The gas mixture leaving the evaporator Stream #3 is diluted by another nitrogen stream (Stream #4) flowing at a measured rate of 419 m3 HSTPL/min. The combined gases (Stream #5) are then compressed together and leave the compressor at a total pressure of 5550 mm Hg and temperature of 325°C (Stream #6). The partial pressure of acetone in the exit stream (Stream #6) is pA = 500 mm Hg. The ambient pressure is 763 mm Hg. A schematic of the flow is shown below. (i) What are the molar flow rates of N2 and acetone in the stream leaving the compressor (Stream #6)? (ii) What is the volumetric flow rate of nitrogen entering the evaporator (Stream #2) if the temperature and pressure of this stream are 27°C and 1238 mm Hg ?.

<span class='text_page_counter'>(3)</span> ECH51PracticeExam1_2014.nb (i) What are the molar flow rates of N2 and acetone in the stream leaving the compressor (Stream #6)? 3 (ii) What is the volumetric flow rate of nitrogen entering the evaporator (Stream #2) if the temperature and pressure of this stream are 27°C and 1238 mm Hg ?. Data given: 1 mol =0.0224 m3 HSTPL , rA = 0.791 g ë cm3 , MA = 58.06 g ê mol The partial pressure is related to the total pressure by: pA = yA P, where yA is the mole fraction of species A. Yopu may assume that all the gas streams behave as ideal gas mixture, and the ideal gas law is PV=n RT, where n is the number of moles.. Problem 4 (15 points) The species mass density of a three-component (A, B, and C) liquid mixture are: acetone, rA = 326.4 kgë m3 , acetic acid rB = 326.4 kgë m3 , and ethanol rC = 217.6 kgë m3 . Determine the following for this mixture: (a) the mass fraction of each species in the mixture (b) the mole fraction of each species in the mixture (c) the mass of each component required to make one cubic metter of the mixture. Note that the molecular masses of the three species are MWA = 58.08 g ê mol, MWB = 60.05 g ê mol, MWC = 46.07 g ê mol.. Problem 5 In a four stage evaporation system shown in Figure below, a 50% by weight sugar solution is concentrated to 75% by weight in the liquid stream leaving the fourth evaporator. Pure water leaves each ° evaporator with a mass flow rate of mB . The mass flow rate entering the system is 100 kg/min, and you are asked to determine the composition of the sugar solution leaving the second evaporator. In your analysis, let the sugar be species A and the water be species B. Assume that a degree-of-freedom analysis has been carried out and that the problem is well-posed. ° mB. 0. 1. 2. 3 4.

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