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All three terms in Eq. (12-12) represent a type of energy. The first two terms represent two different forms of potential energy; the third term is the kinetic energy. All are expressed in terms of energy per unit volume of fluid. Bernoulli s equation tells us that no matter how the flow of a fluid changes, the sum of the potential energy and the kinetic energy remains constant. This allows us to calculate various things. For example, we can calculate the effect of changing the flow velocity on the fluid pressure. The first term P is the pressure, which is equal to the potential energy of the fluid (due to pressure) per unit volume. We can see this clearly by looking at the units. Standard units of pressure are force per area (newton/meter2). If we multiply the N/m2 units by meter per meter (m/m, which doesn t actually change anything), we get newton meters/meter3. But a newton meter is a joule, so the units of pressure (N/m2) are actually J/m3, or energy per unit volume. The second term gh is the potential energy due to gravity. The symbol (rho) is the density of the fluid (approximately 1060 kg/m3 for blood), g is the acceleration due to gravity, and h is the height of the fluid. This term of Bernoulli s equation merely expresses the fact that fluids tend to flow downhill under the influence of gravity. You should be able to show that the units are again energy per unit volume. The third term (1/2) v2 is the kinetic energy of the fluid (per unit volume). Note that v is the velocity of the fluid. As the velocity of a fluid increases, its kinetic energy increases.

It s easy to see from this, that unwinding more, smaller segments results in a much larger positive entropy change than unwinding just a few or one contiguous segment. So when we look at the entropy change for the whole molecule, having more segments is more favorable to the Gibbs energy change than having just a single segment. However, entropy considerations at the individual base level have the opposite effect. These two opposing effects balance each other out. The end result is that DNA unwinds in multiple segments, of some average cooperative unit length. To summarize, there are two competing entropy effects. They are (1) the entropy of coil state base pairs related to their freedom of movement favoring longer contiguous unwound segments and (2) the entropy due to the number of ways of arranging unwound bases along the molecule. This latter entropy favors more, shorter, unwound segments. It is possible to calculate the balance between these two effects, after making some assumptions about the enthalpy change, to arrive at a theoretical cooperative unit length which can be compared to experimental observations.

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Sales compensation leadership committee: Many business units have a management committee comprised of sales, marketing, operations, and finance leaders. This leadership committee can specify the company s sales compensation design principles, reconfirm the business objectives, and approve plans as drafted by the sales compensation design team. Sales compensation program management committee: The program management committee has an ongoing responsibility for

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Q: What data did you collect A: I collected data of all sorts from all sorts of data sources. Q: Why is Georgia a better choice than Florida or Illinois A: It s lower risk overall and in key speci c areas including weather, transport and available labor as well as a positive labor climate. Q: What s the most compelling bene t of choosing Georgia A: Diversi cation. We need to mitigate against the chance of a problem in weather or labor unrest or zoning or taxation in Florida. If these problems occur in Florida, and we have more than one factory in Florida, it is easy to no doubt see the problem. Both factories is effected, not just one factory. If we have one factory only in Florida, and these factors change, not a problem. Or rather, not such a bad problem. Or actually, not likely to be such a bad problem. It s easy in retrospect to carefully understand why some of us lean toward selecting Florida but we should use objective, not subjective, criteria to make the decision. If we do that, we must go with Georgia.

EXERCISE 12: Add Examples to Make Dull Copy Come Alive Shelley, a high school teacher, intends to distribute a brief explanation of how she will be calculating grades to her students. Think back to your years in school, and recall the various ways your teachers assessed your performance. Take Shelley s rst draft and revise it to add speci city through numbers and examples that illustrate her points.

A more accurate approximation could be attained with a finer approximation:

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Multiplexers Coaxial line systems Microwave radio systems Fiber optic line systems Satellite systems

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