CHAPTER V. 



Flow from a small Orifice Coefficients of Contraction, Velocity and Discharge- 

 Suppressed Contraction Borda's Mouthpiece Sharp-edged Orifice Converging Mouthpiece 

 Bell-mouthed Orifice Diverging Outlet Velocity of Approach Time of emptying 

 Reservoir Submerged Orifice Form of Jets. 



ART. 39. FLOW FROM A SMALL ORIFICE. l 



IF an opening be made in the side or base of a tank containing water, 

 the introduction of a few drops of aniline dye shows that steady stream 

 line motion is set up in the mass of fluid, these stream lines converging 

 towards the orifice from every side. At the boundary of the issuing 

 jet the stream lines are, as already explained (Art. 14), tangential 



to the edges of the orifice, and with a sharp- 

 edged orifice the general stream line motion 

 is as shown in Fig. 22. It follows that, after 

 passing the plane of the orifice, the section 

 of the jet gradually diminishes, and its 

 boundaries do not become parallel until some 



^ finite distance from the orifice. The section 

 at which the jet becomes parallel is termed 

 the vena contracta, or contracted vein, and 

 with a small circular orifice is at a distance 

 FlQ 52 from the orifice equal to about '498 times 



the diameter. 



Now suppose a particle of weight w Ibs. to travel along a stream line 

 from the surface to the orifice and on to the vena contracta (Fig. 52). 

 Since the motion is steady, the energy throughout is constant (neglecting 

 viscosity) ; and if we suppose the surface area to be large, so that the 

 surface velocity may be neglected, when in the surface its kinetic energy 

 is zero. If the orifice is at a mean depth li below the free surface, and if 

 its level be taken as datum, the potential energy of the particle is wh 

 foot Ibs., while its pressure energy is zero, its pressure being that of the 

 atmosphere which is taken as datum pressure. 



1 By a small orifice we mean one whose dimensions are small in comparison with the head 

 of water above its centre, so that at any point in its area the head may be taken as equal to 

 that at its centre without sensible error. The subject-matter of Arts. 3946 refers to such 

 orifices, 



