VELOCITY OF EFFLUX. 137 



or without the vessel, provided there be no vacuity in the 

 stream between the sections. 



SCH. It is supposed in this proposition that the changes 

 in the diameters of the sections are gradual, and nowhere 

 abrupt ; if there are any angles in the pipe, they will 

 produce eddies in the motion of the liquid, and the propo- 

 sition will not hold true. 



76. Velocity of Efflux.// a small aperture be 

 made in a vessel containing liquid, the velocity with 

 which the liquid issues from the vessel is the same as 

 if it had fallen from the level of the surface to the 

 level of the aperture.* 



Let EF represent a very small orifice in the bottom of 

 the vessel ABCD, which is filled with a liquid to the level 

 AB ; and suppose the vessel to be 

 kept full by supplying it from above, 

 while the liquid is running out 

 through the orifice EF. Let v be 

 the velocity of efflux, w the weight 

 of the liquid which issues with that 

 velocity per second, and h the height 

 of the surface above the orifice, 

 called the head\ of the liquid. Then the work which w 

 can perform while descending through the distance h, 

 from the surface to the orifice = wli, and the kinetic 

 energy stored up in w as it issues through the orifice 



w 

 = v 2 (Anal. Mechs., Art. 217). If we suppose there is 



*9 

 no loss of energy during the passage through the orifice, 



* This is known as Torricelli's Theorem. 



t The term head in Hydromechanics is measured, relatively to any point, by the 

 depth of that point below the surface of the liquid. Since the liquid in Fig. 34 

 descends through a height h to the orifice, we may say there are h feet of head 

 above the orifice. 



