Fig.A-12
a vessel is 300 K everywhere, the same temperature will be also found in any amount of fluid, however small, taken from the vessel. This is not true for other qantities: the magnitude (value) of a quantity which possesses the character of extensity is dependent upon the amount, mass of fluid in which the quantity is measured. If some small amount is taken from a vessel, the measured magnitude of such quantities will be proportionally smaller. By way of an example we can take positional energy

- where height [m] has character of intensity as is aparent from the fact the if e.g. 20 kilograms of fluid are at height = 100 m, then if we concentrate our attention upon 1 kilogram from this amount, we shall certainly not find it at at 5 meters. On the other hand, gravitational force has character of extensity: the single kilogram mentioned above acts by a force which is twenty times smaller that that of the whole 20 kg amount. Because of this extensity component, also the positional energy has character of extensity. This is an important fact, valid for all forms of energy , which is the basic quantity in our investigations. If we plan to obtain the equation to be solved by investigating energetic balance on a spatial element with infinitesimally small mass , we shall find also the energy of the element to be zero (Fig. A-12) - which may lead to unsurmountable problems. A solution is found in working with the specific value [J/kg], as shown in Fig.A-12. Strictly speaking, extensity variables will be not uniformy distributed in fluid. Instead of the ratio the specific value is defined by the limit approach . The basis of the symbols used here is an agreement according to which total values are denoted by upper case letters and a symbol denoting a specific value will be the same lower-case letter.
We have already met, in Fig.A-9 and A-11 an important specific value of volume . In hydromechanics, this value is considered a constant of a given fluid, e.g. for water there is =. In the case of a gas, its specific volume is evaluated from the equation of state Fig.A-11.


In order to emphasise that for intensity variables there is no sense in trying any transition to speficic values, they remain always written by upper case letters, even if they will be applied in infinitesimal volumes. The most important of them are:
Fig.A-13 Survey of the principles of the used symbols:
The starting pointis
differentiation between intensity and extensity quantities.

The concept of pressure : it has here the meaning of the force acting upon unit area of an imaginary section leading through fluid. In general, its distribution in fluid will be not uniform and in place of (according to Fig.A-14 ) it is more exactly defined by the limit .
As we here denote the area of the surface upon which pressure acts - in the one-dimensional problems treated in this text, mostly problems of flow in a tube, it will be usually the cross-sectional area of the tube.


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This is page Nr. A06 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

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