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Unformatted text preview: MATERIAL BALANCE CONCEPTS BALANCE EQUATIONS Much of engineering consists of careful accounting for things other than money. The equations used for this accounting are usually referred to as balance equations. We use balance equations in our own daily lives all the time, sometimes without realizing it. For example, we normally use a balance equation to balance our check books at the end of the month. Here are the steps to set up such a balance equation. 1. Identify the system of interest. 2. Identify the system boundary. 3. Identify the type of system, that is, whether it is an open or closed system. MBE  1 4. Write the balance equation for the property of the system that we wish to observe. MBE  2 A NonEngineering Example of a Balance Equation: We wish to determine the population change in the State of Texas for a prescribed period. We can accomplish this by carrying out a population balance for the State of Texas. Let us apply the four steps in setting up the population balance for Texas. 1. The system consists of human beings in Texas. 2. The system boundary is the legal boundary of the State of Texas. 3. This is an open system because human beings are allowed to enter and to leave Texas as they please. MBE  3 4. The property of the system of interest to us is the population of the human beings in Texas. Here is the balance equation for the population: population increase = births – deaths + immigration – emigration (1) Notes: 1. Based on the sign convention used, the balance equation is valid for population decrease as well. 2. We can divide the balance equation by time to obtain a rate balance. The time scale must be sufficiently long to even out wild fluctuations in the terms. For example, it would be inappropriate to apply the rate equation over a one day period because the births and deaths may fluctuate too much on a daily basis whereas the annual births and deaths may be essentially constant. MBE  4 3. The balance equation monitors the change in the property of interest and not the total property itself. For example, there is no entry in the balance equation for the total population of Texas but rather the change in population from some reference time. If we want the population of Texas, we could conduct a census which is not part of the balance equation. Alternatively, if a record of the rate of population change with time were kept, then we could integrate it with respect to time from time zero, when the first human set foot in Texas, till today. The total population in this case would be given by...
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This note was uploaded on 12/14/2011 for the course PGE 312 taught by Professor Peters during the Spring '08 term at University of Texas.
 Spring '08
 Peters

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