102 Prof. Osborne Reynolds on 



streams might be drawn. We should then be able to deter- 

 mine exactly the necks of each of these streams. Without 

 complete integration, however, the process may be carried far 

 enough to show that the lines bounding the streams are con- 

 tinuous curves which have for asymptotes on the dischargiiig- 

 vessel side lines radiating from the middle of the orifice at 

 equal angles, and, further, that these lines all curve round the 

 nearest edge of the orifice, and that the curvature of the 

 streams diminishes as the distance of the stream from the 

 edge increases. 



These conclusions would be definitely deducible from the 

 theory of fluid motion could the integrations be effected, but 

 they are also obvious from the figure and easily verified 

 experimentally by drawing smoky air through a small orifice. 



From the foregoing conclusions it follows, that if a curve 

 be drawn from A to B, cutting all the streams at right angles, 

 the streams will all be converging at the points where this 

 line cuts them, hence the necks of the streams will be on the 

 outflow side of this curve. The exact position of these necks 

 is difficult to determine, but they must be nearly as shown in 

 the figure by cross lines. The sum of the areas of these 

 necks must be less than the area of the orifice, since, 

 where they are not in the straight line A B, the breadth 

 occupied on this line is greater than that of the neck. The 

 sum of the areas of the necks may be taken as the effective 

 area of the orifice ; and, since all the streams have the same 

 velocity at the neck, the ratio which this aggregate area bears 

 to the area of the orifice may be put equal to K, a coefficient 

 of contraction. 



If the pressure in the vessel on the outflow side of the 

 orifice is less than •b27p 1 , this is the lowest pressure possible 

 at the necks, as has already been pointed out, and on emerging 

 the streams will expand again, as shown in the figure, the 

 pressure falling and the velocity increasing, until the pressure 

 in the streams is equal to p 2 , when in all probability the motion 

 will become unsteady. 



:If p 2 is greater than '527p 1 , the only possible form of 

 motion requires the pressure in the necks to be p 2 , at which 

 point the streams become parallel until they are broken up by 

 eddying into the surrounding fluid (fig. 5). 



6. There is another way of looking at the problem, which is 

 the first that presented itself to the author. 



Suppose a parallel stream flowing along a straight tube 

 with a velocity u, and take a for the velocity with which 

 sound would travel in the same gas at rest, the velocity with 

 which a wave of sound or any disturbance would move along 



