112 



HYDRAULICS AND ITS APPLICATIONS 



when the orifice is closed, while the horizontal distances between the line 

 _ KM and the curves A B and C D measure 



the pressures on the side of the vessel with 

 an issuing jet. The shaded area then 

 represents the unbalanced pressure, which 

 is to be equated to the outflow of momentum 

 per second from the orifice. 



By returning the mouthpiece for some 

 distance into the vessel, as in the Borda 

 mouthpiece (Fig. 61), this flow over the face 

 containing the orifice is prevented, and the 

 pressure on this face now approximates to 



that due to the statical head alone. The equations of momentum can 



therefore be easily applied. 



ART. 42. BORDA'S MOUTHPIECE. 



Let a be the area of the orifice and a c the area of the stream as soon 

 as it has assumed a parallel cylindrical form, i.e., at the vena contracta. 

 Let h be the depth of this point below the surface. If the suffixes (i) 

 refer to the surface and (2) to the vena contracta, we have, neglecting 

 viscosity, 



FIG. 61. 



Also p 2 = pi = ; z\ z 2 = h ; vi = if surface area is large, 



w 



Mass carried away per second = .a 



W 



.*. Momentum carried away per second = . a e vj*. 



This momentum is produced by a force equal to the weight of a column 

 of water of area a and of height h (approximately). 



. * . Force producing motion = W a h Ibs. 

 w 



ii- i O 



W a h = . a c Vf 



*y 



= . a f . 2 q h 

 9 



Actually r 2 2 = C* x 2 // //, so that __ = ^- v The coefficient of contraction for the 

 Borda running full is modified in a similar manner. 



