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By N.A.V. Piercy

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From Article 3 1 maximum , must not approach that of sound in velocities air. A very useful ex- pression of the assumption is obtained as follows. Consider part of the a two-dimensional flow enclosed within any ABCD small rectangle pv field of o x FIG. 15. (Fig. 15), of sides $x, Xy, u, v being the components parallel to Ox, Oy of the resultant velocity. The rate at which fluid mass tends to be exhausted from the rectangle owing to es difference in velocities ^ } Sjy / and 8#8y p8y = ~~ ox flow across the sides AB .

And D be adjacent points on two = k and streamlines = fc + Jty. The co-or38. O FIG. 18. Let A : y + ED less From Fig. that across AE. parallel to Ox, Oy, respectively, q, the total variation of a function of the two independent It is assumed that the partial derivatives dfy/dx and y. and 3^/3^ are a l so continuous functions of x and y. text-books on Calculus that then Hence Sy.

Is often called turbulent. much more finely grained, conveying the impression of a chaotic intermingling of very small masses of the This last type fluid accompanied by modifications of momentum. of unsteadiness is, unfortunately, at once the most difficult to under- other cases the fluctuations are stand and the most important in practical Aerodynamics. It has come to be the form usually intended by the name turbulence. Stream-tube. A conception of occasional use in discussing steady This may be defined as an imaginary tube flow is the stream-tube.

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