Background Chemistry and Fluid Mechanics

Trong tính toán, một số yếu tố có thể tham gia vào một thuật ngữ và điều quan trọng là để giữ cho đường của các đơn vị của mỗi trong những yếu tố để xác định đơn vị cuối cùng của thời hạn. Ví dụ, hãy xem xét chuyển đổi 88 kg để microgram. Để thực hiện chuyển đổi này, một số yếu tố có mặt trong thời gian tính. Giả sử chúng ta làm cho việc chuyển đổi như sau: 88 kg = 88 (1000) (1000) (1000...
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Background Chemistry and Fluid Mechanics TX249_Frame_C00 Page 25 Friday, June 14, 2002 1:47 PM Background Chemistry and Fluid Mechanics As mentioned, this chapter discusses the background knowledge needed in order to understand the subsequent chapters of this book. The student must have already gained this knowledge, but it is presented here as a refresher. Again, the background knowledge to be reviewed includes chemistry and fluid mechanics. Before they are discussed, however, units used in calculations need to be addressed, first. This is important because confusion may arise if there is no technique used to decipher the units used in a calculation. UNITS USED IN CALCULATIONS In calculations, several factors may be involved in a term and it is important to keep tract of the units of each of the factors in order to ascertain the final unit of the term. For example, consider converting 88 kilograms to micrograms. To make this con- version, several factors are present in the term for the calculation. Suppose we make the conversion as follows: 88 kg = 88 ( 1000 ) ( 1000 ) ( 1000 ) = 88,000,000,000 µ g (1) where 88(1000)(1000)(1000) is called the term of the calculation and 88 and the 1000s are the factors of the term. As can be seen, it is quite confusing what each of the 1000s refers to. To make the calculation more tractable, it may be made by putting the units in each of the factors. Thus, µg 88 kg = 88 kg  1000 -----  1000 ------   1000 ------  = 88,000,000,000 µ g g mg - - - (2)  kg  g  mg This second method makes the calculations more tractable, but it makes the writing long, cumbersome, and impractical when several pages of calculations are done. For example, in designs, the length of the calculations can add up to the thickness of a book. Thus, in design calculations, the first method is preferable with its attendant possible confusion of the units. Realizing its simplicity, however, we must create some method to make it tractable. This is how it is done. Focus on the right-hand side of the equation of the first calculation. It is known that the unit of 88 is kg, and we want it converted to µg. Remember that conversions follow a sequence of units. For example, to convert © 2003 by A. P. Sincero and G. A. Sincero TX249_Frame_C00 Page 26 Friday, June 14, 2002 1:47 PM 26 Physical–Chemical Treatment of Water and Wastewater kg to µg, the sequence might be any one of the following: kg ⇒ g ⇒ mg ⇒ µ g (3) kg ⇒ µ g (4) In Sequence (3), the conversion follows the detailed steps: first, from kg to g, then from g to mg and, finally, from mg to µg. Looking back to Equation (1), this is the sequence followed in the conversion. The first 1000 then refers to the g; the second 1000 refers to the mg; and the last 1000 refers to the µg. Note that in this scheme, the value of a given unit is exactly the equivalent of the previous unit. For example, the value 1000 for the g unit is exactly the equivalent of the previous unit, which is the kg. Also, the value 1000 for the mg unit is exactly the equivalent of its previous unit, which is the g, and so on with the µg. In Sequence (4), the method of conversion is a short cut. This is done if the 6 number of micrograms in a kilogram is known. Of course, we know that there are 10 micrograms in a kilogram. Thus, using this sequence to convert 88 kg to micrograms, we proceed as follows: 88 kg = 88 ( 10 ) = 88,000,000,000 µ g 6 Example 1 Convert 88,000,000,000 µg to kg using the detailed-step and the short-cut methods. Solution: Detailed step: 88,000,000,000 µ g = 88,000,000,000 ( 10 ) ( 10 ) ( 10 ) = 88 kg –3 –3 –3 ...