Flow of Liquid past a Wedge. 807 



— d is something like four times — g and that —/'lies close 

 to —g. This means that the inflexion on the stream-line is 

 near the point G, which is physically obvious. 



Having obtained f and using the values already tabulated, 

 it is easy to get a table of the integrand which is equivalent 

 to that on the left hand of equation (5) or (6). Since 



7r C 1 C 1 



a= we have 1 =i 1 , so we have to find the value of 6 



. ^ a J -1 



at which the transformed integral is bisected, say O , then 



a= — cos2# . 



The integral in (8) is now transformed by the substitution 

 u — i{d+9)~*~i{d—g) cos 20 and the value of (tt — ^) found 

 by step-by-step integration. Finally, the integrand in (10) 

 transformed to 6 is tabulated and the integral found by 

 Simson's rule. Having done this for an assumed value of d 

 with different values of g, it was possible to find by inter- 

 polation the g which makes the second plane pass through 

 the edge of the first. Then the other integrals which 

 specify the details of the motion can be evaluated for the 

 special values of the constants d, g, /, a. The integrations 

 were carried out partly arithmetically and partly by use of a 

 Coradi integraph. 



The results are shown on fig. 3. The abscissa is the ratio 

 of the breadth of the second plane to that of the first. The 

 curves begin at the vnlue *18, which is the ordinate of 

 the curve K on fig. 1 for « = 45°. This gives the breadth 

 of the second plane, built out at right angles to the first, 

 when it just touches the stream. The corresponding values 

 of the constants are easily found to be 



rf=_(3 + V2), g=f=-h a = i(s/2-l). 



The other cases actually calculated are indicated by the 

 positions of the marks on the upper side of the horizontal 

 axis. They correspond to the values 



d= 6 



-c/= 1-049 



6-5 



1-099 



7 



1*156 



10 



1-558 



20 



3-023 



