ON THE THEORY OF HYDRAULICS. tlS 



A similar law may be applied to the filling of a lock, from a reservoir of 

 constant height; for in all such cases, twice as long a time is required for 

 the effect, as would be necessary if the initial velocity were continued. The im- 

 mersion of the orifice in a large reservoir has been found to make no differ, 

 ence in the magnitude of the discharge, so that the pressure may always be 

 estimated by the difference of the levels of the two surfaces. Thus, when 

 a number of reservoirs communicate with each other by orifices of any dimen- 

 sions, the velocity of the fluid flowing through each orifice being inversely 

 as the magnitude of the orifice, and being produced by the difference of the- 

 heights of the fluid in the contiguous reservoirs, this difference must be every 

 where as the square of the corresponding velocity. But if the reservoirs 

 were small, and the orifices opposite and near to each other, a much smaller 

 difference in the heights of the surfaces would be sufficient for producing the 

 required velocity. The same circumstances must be considered, in deter- 

 mining the velocity of a fluid, forced through a vessel divided by several par- 

 titions, with an orifice in each; if the orifices are small in proportion to their 

 distance from each other, and if they are turned in different directions, each 

 orifice will require an additional pressure, equivalent to the whole velocity 

 produced in it: but if the partitions occupy a small part only of the vessel, 

 and are placed near to each other, the retardation will be much less con- 

 siderable. Cases of this kind occur very frequently in the passage of water 

 through the pipes and valves of pumps, and it is, therefore, of consequence 

 to avoid all unnecessary expansions, as well as contractions, in pipes and in 

 canals, since there is always a useless expense of force in restoring the velocity 

 which is lost in the wider parts. 



When a siphon, or bent tube, is filled with a fluid, and its extremities are 

 immersed in fluids of the same kind, contained in different vessels,if both their 

 surfaces are on the same level, the whole remains at rest; but if otherwise, 

 the longer column in the siphon preponderates, and the pressure of the at- 

 mosphere forces up the fluid from the higher vessel, until the equilibrium is 

 restored ; provided, however, that this pressure be sufficiently powerful : for 

 if the height of the tube were more than 34 feet for water, or than 30 inches 

 for mercury, the pressure of the atmosphere would be incapable of forcing 

 up the fluid to its highest part, and this part remaining empty, the fluid coiilck 

 no longer continue to run. (JPlate XX. Eig. 258.), 



