Fig.A-3 Experimental aerodynamic research - as an
example, a study of flow past an automobile is shown. Stream-
lines are visualised by smoke particles carried with the air
in a wind tunnel (Experiment performed by Takagi, Nissan
Motor Comp., Japan).
In spite of the fact that the equations capable of describing fluid flows have been known since the middle of the 19th century, they were not practically solvable until the revolutionary change brought about by the computers.
Fig .A-4 The basis of a numerical solution
is the division of the investigated flowfield into
parts having finite dimensions: in this case, a two-
-dimensional computation of flow past an aero-
plane wing (airfoil ONERA M6) is performed with
an unstructured adaptive grid, which becomes
automatically more dense in areas where flow is
more complicated (here in the region with higher
velocity gradients).
The recent progress of computer technology both in hard- ware as well as in software made solutions possible. In simple cases it became a practical possibility - although experiments and experimental data are still of basic importance. It should be emphasised that a computer solution does not make understanding the physics of the problem irrelevant. Quite the reverse is true: computers can (and often do) generate solutions physically incorrect and an interpretation of the results requires even wider and more fundamental knowledge.
Fig .A-5 Computer solutions:
An exact solution of such tasks as flow past
a complete aeroplane takes about 5,000 hours
on a supercomputer with speed of the order
of TFlops (and it is necessary to note that
there are only two or three such computers
around the world). Using a common large com-
puter with speed around 150 MFlops is out of
question - the solution time would be around
3,000 years. The only way is to use some
simplification (e.g. turbulence modelling).
This, however, means that the results are not
perfectly reliable and it is necessary
to verify them experimentally.
To make a later transition to two- and three-dimensional problems easier, the present text (in spite of its limitation to one-dimensional approach) uses nomenclature which permits the application of tensors. That is why the the three spatial coordinates are here in place of the more common x, y, z. The single spatial coordinate, along which the variables will usually vary, is here not just but an indexed . An even more important feature of the present text is that it consistently follows the idea that the solution of problems in fluid mechanics is basically an integration of a differential equation describing fluid behaviour for a given set of boundary (and/or initial) conditions Computer solutions make this viewpoint obvious but it is not usual in the treatment of one-dimensional problems in basic hydraulics.
In a non-traditional way, this text also follows the system approach. For the solution of flow in a pipeline according to Fig. A-6, the studied pipe segment is viewed as an element of a system.
Fig .A-6
For solution of a hydraulic system (such as the simple pipeline
shown here) it is useful to start from properties of the elements
comprising the system.
To study a system composed of elements, it will be useful to investigate each element so as to determine its transfer properties. This requires finding the dependence of quantities in the outlet (= output) of an element upon quantities in its inlet (= input) - as shown in Fig.A-7. This approach makes it possible to study quite simply and from an advantageously more general viewpoint such problems as the traditional emptying of a vessel or starting flow . The system approach is reflected here also in the use of some non-traditional concepts such as working with characteristics of the elements and using the characterisation quantities


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This is page A02 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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