Discharge of Fluids through Apertures. 371 



the same size, in the same time, the vessel being kept filled to 

 the same level, will be as vT, vV> VV 7 "- Tne actual velocity at 

 the distance s below the surface of the fluid in the vessel will be 

 V/2^, and the quantity Q discharged in the time f, through an 

 aperture whose area is tf, is as follows, namely, 



Q=<st v^- 



478. What is above said of the velocity of a fluid discharged 

 from jets or apertures, is true only of the middle filament of 

 particles issuing through the centre of the aperture, which are 

 supposed to experience no retardation, and which, in fact, suffer 

 no other retardation than what arises from the resistance of the 

 air, and their mutual adhesion and attrition against each other. 

 But those which issue near the edges of the aperture suffer a 

 much greater resistance, and are accordingly much more retar- 

 ded. Hence it follows that the mean velocity of the whole col- 

 umn of discharged fluid will be considerably less than that indi- 

 cated by the above theory. 



479. Sir Isaac Newton discovered a contraction in the vein of 

 discharged fluid, and found that at a distance from the orifice of 

 about a diameter of this orifice, the section of the vein or stream 

 was diminished nearly in the ratio of V2 to \/i. Hence he 

 concluded that the velocity of the fluid after passing the aper- 

 ture was increased in this proportion, the same quantity passing 

 through a narrower space in the same time. 



According to some very accurate experiments of Bossut, the 

 actual discharge through a hole made in the side or bottom of 

 the vessel, is to the theoretical as 1 to 0,62, or nearly as 8 to 5. 

 The theoretical discharge must, therefore, be diminished in this 

 ratio to obtain the actual discharge. 



If the water issues, not through an aperture in the side or 

 bottom of the vessel, but through a pipe from 1 to 2 inches in 

 length, inserted in the aperture, the contraction of the vein is 

 prevented, and the actual discharge becomes to the theoretical, 

 as 8 to 10, or as 4 to 5. In this way, therefore, the discharge is 

 increased nearly in the ratio of 4 to 3. 



