Were the attention in this textbook not limited to the simple one-dimensional problems, we would have to work with the stress tensor, according to Fig.A-15, which describes the spatial distribution of elementary force effects in fluid. This is a natural generalisation of the concept of pressure, with which we shall work here. When mentioning pressure here, it will be assumed that what is meant are the three normal components in the tensor . It my be shown that these three components are equal (- this fact is called the Pascal law) so that pressure by be fully determined by just the scalar
Fig.A-14 Pressure and the corresponding pressure force
acting on a given surface - here it is action upon the
cross sectional area of the inpout into an element
of a pipeline system.
Fig.A-15

Note: It is sometimes still possible to meet pressure being measured in old units, atmospheres. Conversion to the recent, modern unit, the pascal, is made by using the relation : .
In USA, there is still in use a unit named psi, pound per square inch, for the conversion of which the relation is: . Barometric pressure used to be measured in tors (= millimetres of mercury column, convenient when using a mercury barometer): .

Indices: a) numerical : Integers 1 to 3 denote the directions of co-ordinate axes (Figs.A-2, A-15, A-16). It is always assumed that the direction with the index 1 so that it corresponds with dominant flow direction. The corresponding velocity component (oriented in this direction 1) is . It is used in two- or three-dimensional flows, cf. Fig.A-1. In the case of flow in a pipe
Fig.A-16
(pipeline elements are important objects of interest in the present text) the co-ordinate axis is coincident with the pipe axis, which it follows even if the pipe is curved. The symbol without any index (most often encountered velocity symbol in the present one-dimensional problems) is the mean velocity obtained by averaging across a given cross section.
Fig.A-17

b) letters: Indices X and Y denote magnitudes of quantities and the inlet and outler, respectively, of an investigated element (component). These values usually represent the boundary conditions for the integration. If the evaluated integrals are written down, it is possible for simplification to use the symbols and for the integration limits in place of writing in full the quantities at the limits. Integration of specific energy changes along the integration path from to may be therefore written simply as
The sicentist after whom our unit of pressure was named:
Blaise Pascal
Born: 19 June 1623 in Clermont-Ferrand, Auvergne, France
Died: 19 Aug 1662 in Paris, France
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- seventeenth century French mathematician (" Pascal's triangle") and religious philosopher. Blaise Pascal's father Etienne Pascal had unorthodox educational views and decided to teach his son himself. He decided that Blaise was not to study mathematics before the age of 15 and all mathematics texts were removed from their house. Blaise however, his curiosity raised by this, started to work on geometry himself at the age of 12. He was writing theses on acoustics before he was thirteen and invented calculating machine at nineteen. By the time of his thirtieth birthday, just nine years before his death, he had written several books on religion.


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This is page Nr. A07 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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