122 HYDRAULICS AND ITS APPLICATIONS 



Then .4 = k(D + h), 



//> + ; A 

 and - k ^-rr) d h = C (aj 2 r/j ,/ A, 



^ 



Where (7 = coefficient of discharge. 



EXAMPLE II. 



Hemispherical Bowl Radius r emptied through Hole in the Bottom. 

 Here A = * { r 2 - (r - /i) a } = TT { h* - 2 r h } 



~1 



V 2 cf 



Where the lower limit of height is less than about four times the 



diameter of the orifice, a vortex, 

 with an air core, is usually formed, 

 with the effect that the area of 

 discharge is reduced (Art. 38). 



Time of Discharge from a Sub- 

 merged Orifice. If two vessels 

 whose surface areas are AI and A* 

 (Fig. 66) are connected by an 

 orifice of area a, and if at any 

 instant HI and 7? 2 are the heights 

 of their free surfaces above the 

 level of the orifice, we have, neglecting viscosity, and assuming 

 v = x/ 2 <i (7/i 7/aj = x/ 2 // // 



Velocity of surface AI = V. --r- ; velocity of A 2 = v -j- 



Fio 



