THE FLOW OF GASES. 173 



and that the curvature of the stream 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 con- 

 traction. 



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

 orifice is less than •527JO1, 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^, when in 

 all probability the motion will become unsteady. 



If Pj, is greater than '527^1, the only possible form of 

 motion requires the pressure in the necks to be p^, at 

 which point the streams become parallel until they are 

 broken up by eddying into the surrounding fluid (fig. 5), 



