HYDRAULICS. 207 



efficient, to be determined by experiment, 

 'jf= mcPv*', or if h be the height belonging to the 

 velocity v 9 so that %g li = a 2 , f-=. %md? gh. The 

 quantity a? gli denotes the weight of the column, 

 of which the base is a 2 , and the height h. 



The constant quantity m is found to be different, ac- 

 cording to the manner in which the fluid is recei- 

 ved by the plane on which it strikes. When the 

 plane is indefinite in extent, m = 1, so that 

 f=Qa?gh, or the force is double the weight of 

 the column, of which the base is a 2 , and the alti- 

 tude h. This agrees with experiment, and has also 

 been demonstrated by DAN. BERNOUILLI, Comment. 

 Petrop. torn. vin. p. 99- 5 &c. See also Encyclopaedia 

 Britanmca, 2d edit. Article Resistance, p. 109. 



When the plane is no greater in extent than the sec- 

 tion of the stream, m J, andf= a 2 gh, only half 

 the former column. 



Since, in two different streams, f:f' : : a 2 a 2 : &' 2 ?/ 2 , 

 if a 2 v 9 or the quantity of water expended in a se- 

 cond, be the same in both,^/"' : : v : v', or the forces 

 are as the velocities simply. 



298. If the plane struck by the stream be itself in 

 motion, the impulse is as the square of the differ- 

 ence of their velocities. 



If v be the velocity of the stream, and c the velocity 

 with which the plane retires from it, then the force 

 of percussion = m a 2 (v c) 2 . 



If 



