Fig.C-7 This is the standard probe for measuring velocity. Commonly used on airplanes to measure flight speed (its construction is then complicated by heating coil necessary to prevent blockage by ice). For use in aerodynamic laboratories these probes are usually made in small dimensions - both because the investigated flow is sometimes restricted (e.g. between the compressor blades) and because we need minimum influencing of the flow by probe presence. Probes of this sort are commonly available with outer diameter d less
than 1 millimetre
Especially for measurements in shear regions (Chapter [I]) the probes of this sort are often made in miniature dimensions - using stainless steel tubes for hypodermic needles, the smallest ones have outer diameter 0,2 mm. Perhaps it will be useful to give here at least a list of influences which should be taken into account when using piezzometric probes:
1) The directional influence - inclination of the probe relative to local velocity vector
2) The influence of a nearby wall
3) The Barker effect - distortion of the reading at small velocities and dimensions
4) The effect of turbulent fluctuations (caused by nonlinearity of transfer properties)
5) The influence of transverse velocity gradient.


In cases where fluid is not brought to total rest and there is just change of velocity magnitude due to variation of cross-sectional area, we shall find two unknown quantities in the integrated Bernoulli's equation. To obtain unique solution, another condition is required and this is available from the Castelli Theorem: velocity changes depend in a unique manner upon the changes of cross-sectional area (of course, under the assumption of one-dimensionality, i.e. assuming rectangular shape of velocity profiles).

Fig.C-8 Typical problem solved by integration of the Castelli Theorem: T... Task: to evaluate (mean) velocity at a cross section, G ... Given velocity at another position and the area ratio.

An interesting consequence of cross section decrease is that instead of the pressure increase, expected by an unprepared mind ("fluid must be compressed to get into the smaller cross section"), pressure there actually pressure decreases. This is demonstrated by the simple experiment shown in Fig.C-9. Such generation of lower (often subatmospheric) pressure is used in many devices - perhaps the best known are carburettors, in which the generated low pressure is used to supply fuel into an air flow (needless to say, carburettors are quite complicated devices with very complex function, which canonot be described in a few words). Important application of the phenomenon is the use in cross-sectional flowmeters.


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This is page Nr. C05 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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