382 



HYDRAULICS AND ITS APPLICATIONS 



velocity between P and Q and the resultant pressure on the arc P Q is 



JJ7 Q . . 



given by - - . PQ lbs. : if Q is the volume in cubic feet striking the 



vane per second. 



Thus if a series of normals to the curve are drawn intersecting at 

 Ci, <7 2 , Cs, etc. (Fig. 172 b), the pressure on the corresponding arcs will be 



given by . l v Ibs., and these pressures act outwards 



through the middle points of their respective arcs. Drawing in the lines 



/ 



FIG. 172. 



representing these pressures FI, F 2 , F 3 , etc., the funicular polygon for 

 these forces may be drawn, and the line of action of their resultant 

 obtained as explained in any work on applied mechanics. The point of 

 intersection of this line with the surface of the vane gives the centre of 

 pressure on the vane. 



If the velocity varies from point to point of the vane the same general 

 principles apply except that now the velocity v in the expression 



pressure = - ft?. Ibs. varies from point to point. Where 



the law of its variation is known, the problem becomes perfectly 

 determinate. 



