29 31.] FLOW FROM A RESERVOIR. 25 



degree of tension, without rupture. The limiting velocity is, by 

 (12), approximately that with which the fluid would escape from 

 the reservoir into a vacuum. In the case of water at the atmo 

 spheric pressure, this velocity is that due to the height of the 

 water-barometer, or roughly, about 45 feet per second. 



The question as to what takes place when the limiting velocity 

 is reached will be considered in Art. 94. 



31. We conclude this chapter with a few simple applications 

 of the equations. 



Example 1. Steady motion under the action of gravity. A 

 vessel is kept filled up to a constant level with liquid which 

 escapes from a small orifice in its walls. 



The origin being taken in the upper surface, let the axis of z 

 be vertical, and its positive direction downwards, so that V=-gz. 

 If we suppose the area of the upper surface large compared with 

 that of the orifice, the velocity at the former may be neglected. 

 Hence, determining the constant in (10) so that^? = P (the atmo 

 spheric pressure), when z = 0, we have 



* = - p +9*-tf (13). 



At the surface of the issuing jet we have p P ) and therefore 



&amp;lt;i=2gz (H), 



i.e. the velocity is that due to the depth below the upper surface. 

 This is Torricellis Theorem. 



We cannot however at once apply this result to calculate the 

 rate of efflux of the fluid, for two reasons. In the first place, the 

 issuing fluid must be regarded as made up of a great number of 

 elementary streams converging from all sides towards the orifice. 

 Its motion is not, therefore, throughout the area of the orifice, 

 everywhere perpendicular to this area, but becomes more and more 

 oblique as we pass from the centre of the orifice to the sides. 

 Again, the converging motion of the elementary streams must 

 make the pressure at the orifice somewhat greater in the interior 

 of the jet than at its surface, where it is equal to the atmospheric 

 pressure. The velocity, therefore, in the interior of the jet will be 

 somewhat less than that given by (14). 



