ON THE THEORY OF HYDRAULICS.

283

■A similar law may be applied to the filling of a lock, from a reservoir ofconstant height; for in all such cases, twice as long a time is required for^he 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,euce in the magnitude of the discharge, so that the pressure may always beestimated by the difference of the levels of the two surfaces. Thus, whena number of reservoirs communicate with each other by orifices of any dimen-sions, the velocity of the fluid flowing through each orifice being inverselyas the magnitude of the orifice, and being produced by the difference of theheights of the fluid in the contiguous reservoirs, this difference must be every"''here as the square of the corresponding velocity. But if the reservoirs'"ere small, and the orifices opposite and near to each other, a much smallerdifference in the heights of the surfaces would be sufficient for producing therequired velocity. The same circumstauees 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 theirdistance from each other, and if they are turned in different directions, eachorifice will require an additional pressure, equivalent to the whole velocityproduced in it: but if the partitions occupy a small part only of the vessel,; oul 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 waterthrough the pipes and valves of pumps, and it is, therefore, of consequenceto avoid all unnecessary expansions, as well as contractions, in pipes and inoanals, since there is always a useless expense of force in restoring the velocity"dfidi is lost in the wider parts.

When a siphon, or bent tube, is filled with a fluid, and its extremities are'mmersed in fluids of the same kind, contained in different vessels,if both theirsurfaces are on the same level, the whole remains at rest; but if otherwise,l he longer column in the siphon preponderates, and the pressure of the at-mosphere forces up the fluid from the higher vessel, until the equilibrium isr estored; provided, however, that this pressure be sufficiently powerful: for’t the height of the tube were more than 34 feet for water, or than 30 inchesthr mercury, the pressure of the atmosphere would be incapable of forcingl, P the fluid to its highest part, and this part remaining empty, the fluid could110 *° n ger continue to run. (Plate XX. Tig. 238.)