Capability to evaluate fluid forces acting on a body is of obvious importance for vehicular techology - the significance of automobile body drag for its design is evident and equally apparent is the paramount importance of lift and drag calculations on designing an aircraft. In principle, these forces can be evaluated once the velocity and pressure field in the flowing fluid is known: it is a matter of integrating the normal and tangential stress components acting upon infinitesimal surface elements. Unfortunately, this approach is applicable only in exceptional cases - such as two-dimensional, unseparated flow past an airfoil (and even there it is necessarily only approximate, the difficulty of calculating turbulence being one of the reasons). In spite of recent progress in computer fluid dynamics (cf. Fig. A-5), three-dimensional flow past complex body shapes is, in general, still outside
Fig.J-1
the capabilities. It is therefore a common practice to obtain the necessary information experimentally, by measurements on models in wind tunnels or towing tanks.
Theoretical derivation of aerodynamic drag was attempted by Newton in 17th century. Even though he started from wrong assumption (change of momentum of fluid particles behaving as elastic objects), he worked with the expression from Fig.J-1 which we still use. The reference area is usually the frontal area (= area of the body projection on a plane perpendicular to flow direction). There is, however, no strict rule and when using data from literature, it is advisable to check what area the particular author used: in the case of frictional drag it is usually the surface ("wetted") area, in aeronautical aerodynamics the forces acting on a wing are usually related to ground projection at zero angle of attack (no change with attack angle taken into account - and sometimes the area icludes an imaginary extrapolated part inside the fuselage !).
Fig.J-2
If there were, on the flat plate from Fig.J-2, the impact overpressure

caused by stopping fluid flow to rest, acting everywhere with undiminished intensity, the resultant drag force would be

- this means that the drag coefficient represents the effect of deviation from such a simple pressure distribution. In the case of the friction drag (Fig.J-2 below) the reference area is, of course, the wetted surface area. There are, however, various conventions in use and it is recommended, when using data from literature, to check what reference area the particular author has used.


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This is page Nr. J01 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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