SUMMARY OF HYDRAULICS. 29 



quantity of water difcharged by the area of the parabola, or 

 two thirds of that of the circumfcribing rectangle. So that the has nearly two- 

 quantity of water difcharged may be found by taking two- j oc j t due t0 th ^ 

 thirds of the velocity due to the mean height, and allowing for mean height, 

 the contraction according to the form of the opening, as ex- 

 plained in the firft chapter. 



The author has found this mode of calculation fufficiently 

 near to the refults of Buat's experiments, and to fome accurate 

 obfervations of his own. 



He propofes for example a lake in which a rectangular Particular exem- 

 opening is made without any oblique lateral walls, 3 feet wide, p ' catwn * 

 and extending 2 feet below the furface of the water. Here 

 the coefficient of the velocity, corrected for contraction, is 5. 1 , 

 and the corrected mean velocity -J ^2 x 5.1=4.8 ; therefore 

 the area being 6, the difcharge of water in a fecond is 28.8 

 cubic feet, or nearly four hogsheads. 



The fame coefficient ferves for determining the difcharge 

 over a were of confiderable breadth ; and hence it is eafy to 

 deduce tffe depth or breadth requifite for the difcharge of a 

 given quantity of water. For example, a lake has a were 3 

 feet in breadth, and the furface of the water ftands at the 

 height of 5 feet above it: it is required how much the were 

 muft be widened in order that the water may be a foot lower. 

 Here the velocity is -| ^5x5.1, and the quantity of water 

 ■f ^5x5.1x3x5; but the velocity muft be reduced to 



4 J 4 x 5.1, and then the feclion will be T . * ,, , = 



-v/5 x 3 x 5 



7j =7.5.^5; and the height being 4, the breadth 



muft be —^5=4.19 feet. 



Chapter 4. Of the difcharge from refervoirs with lateral By lateral ori- 



orifices of confiderable magnitude, with aconftant head of water. fi , c , es of conf,der * 

 & . , able magnitude, 



Ihis may be found by determining the difference in the dif- 

 charge by two open orifices of different heights : but in moft 

 cafes the problem may be folved with nearly equal accuracy, t h e velocity due 

 by confidering the velocity due to the diftance of the centre of t0 the center of 

 gravity of the orifice below the furface. Srifia m/y'te 



Chapter 5. Of the difcharge from refervoirs receiving no taken, 

 fupply of water. 



For 



