SMALL ORIFICES 



Po P% k'o 2 i / 

 .-. --^T 2 = + Oa b) 



Again ?> 2 = # ''o> 



In a horizontal mouthpiece z. 2 = ZQ, 

 . . ^ yr^ = /'o f^et, 



i.e., the gain of pressure from ( 2 ) to ( ) is equal to a head of 7i feet. 

 If the jet issues into the atmosphere p = 0. 



Or the pressure at (a) is less than that of the atmosphere by an amount 

 equivalent to a head h of water. 



This reduction of pressure at section (2) explains why the velocity at 

 this point, and hence the discharge, is greater with a full Borda than 

 with one running free. The conditions from the surface to the section 

 at (2) are exactly the same whether the mouthpiece runs full or free, but 

 in one case the jet is discharging at this point against atmospheric 

 pressure, while in the other case this pressure is in part removed. 



The effect is then substantially the same as if the free Borda were 

 subjected to an additional head h Q . 



The theoretical limit of this h is 34 feet, but practically, the liberation 

 >f dissolved air as the pressure falls, prevents the formation of anything 

 ipproaching an absolute vacuum. 



ART. 43. SHARP-EDGED ORIFICE IN A FLAT PLATE, WITH EXTERNAL 



TUBE. 



With an external tube of the same diameter as the orifice, the effluent 

 stream, after forming a vena contracts, always re-exparids to fill the tube 

 [Fig. 63). 



In this case, as already explained, the coefficient of contraction 

 cannot be theoretically deduced by an application of the equations of 

 momentum. Its value is probably about '62, but almost certainly varies 

 with the head and size of orifice. The final area of the jet = a, so that 

 the coefficient of Velocity is the same as the coefficient of discharge. This 

 coefficient varies with the size of orifice, with the length of tube, and 

 probably to some extent with the head. Experiments by Weisbach gave 



i 2 



