2
THE FLOW OF WATER TJNDER PRESSURE.
would acquire in falling a height corresponding to tlie distancebetween the level of the fluid in that vessel and the centre ofthe orifice. Employing Symbols to represent this :—If v is takenfor the velocity, H for the difference of level or head, and g for themeasure of the force of gravity, or the number of feet per secondat which a falling body is moving at the end of the first second:then v = J2gH, or the velocity varies as the square root of thehead. If to the natural head is added an artificial pressurewhich can be regarded as a further head, H', the formula wouldbe v = J2g(ll + 11'), provided the head is maintained by aninflux of water equivalent to that which issues at the orifice.The expression J2gH (representing the theoretical velocity)requires a deduction to be made from it to determine the actualvelocity.
The quantity discharged from an orifice in a unit of time (asa second) varies with the velocity ( v), and with the area of theorifice A. Therefore the theoretical discharge is found by theexpression D — A J2gII. The actual discharge, however, isless than this, as the sectional area of the stream of water atthe point of issue is not the exact area of the orifice itself. Ifthe orifice be at the bottom of a vessel in which the head isuniformly maintained, it has been ascertained that the sectionalarea of the jet is ifths of the sectional area of the hole. Thisreduction in the sectional area of the stream of water is knownas the “Vena Contracta,” and it arises from various causes. Itis allowed for in practice by a coefficient which has been arrivedat by experiments upon orifices of different shapes. These givethe mean reduction in diameter as 1 to ‘80, and in sectionalarea as 1 to '62. If the orifice be in a perfectly plane plate, thecoefficient ranges between - 60 and - 64, seldom falling below theformer or rising above the latter. The actual discharge willtherefore be determined by the expression B = 0’62^4 s]2glt.
The following table gives the results of the experiments öfvarious observers in the past:—