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Originally appearing in Volume V14, Page 39 of the 1911 Encyclopedia Britannica.
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ORIFICES AS ASCERTAINABLE BY EXPERIMENTS § 16. When a liquid issues vertically from a small orifice, it forms a jet which rises nearly to the level of the free surface of the liquid in the vessel from which it flows. The difference of level hr (fig. 14) is so small that it may be at once suspected to be due either to air resistance on the surface of the jet or to the viscosity of the liquid or to friction against the sides of the orifice. Neglecting for the moment this small quantity, we may infer, from the elevation of the jet, that each molecule on leaving the orifice possessed the velocity required to lift it against gravity to the height h. From ordinary dynamics, the relation between the velocity and height of projection is given by the equation v=sl2gh. (I) As this velocity is nearly reached in the flow from well-formed orifices, it is sometimes called the theoretical velocity of discharge. This relation was first obtained by Torricelli. If the orifice is of a suitable conoidal form, the water issues in • filaments normal to the plane of the orifice. Let w be the area of the orifice, then the discharge per second must be, from eq. (I), Q=wv=enj2gh nearly. (2) This is sometimes quite improperly called the theoretical discharge for any kind of orifice. Except for a well-formed conoidal orifice the result is not approximate even, so that if it is supposed to be based on a theory the theory is a false one. Use of the term Head in Hydraulics.—The term head is an old millwright's term, and meant primarily the height through which a mass of water descended in actuating a hydraulic machine. Since the water in fig. 14 descends through a height h to the orifice, we may say there are h ft. of head above the orifice. Still more generally any mass of liquid h ft. above a horizontal plane may be said to have h ft. of elevation head relatively to that datum plane. Further, since the pressure p at the orifice which produces outflow is connected with h by the relation p/G = h, the quantity p/G may be termed the pressure head at the orifice. Lastly, the velocity v is connected. with h by the relation v2/2g = h, so that v2/2g may be termed the head due to the velocity v. § 17. Coefficients of Velocity and Resistance.—As the actual velocity of discharge differs from J 2gh by a small quantity, let the actual velocity = va = cvJ 2gh, (3) where c„ is a coefficient to be determined by experiment, called the coefficient of velocity. This coefficient is found to be tolerably constant for different heads with well-formed simple orifices, and it very often has the value o•97. The difference between the velocity of discharge and the velocity due to the head may be reckoned in another way. The total height h causing outflow consists of two parts—one part h. expended effectively in producing the velocity of outflow, another hr in over-coming the resistances due to viscosity and friction. Let hr = crhr, where cr is a coefficient determined by experiment, and called the coefficient of resistance of the orifice. It is tolerably constant for different heads with well-formed orifices. Then 1'a='/2gkr=1 [2gh/(1+cr)}. (4)
ORIGEN (c. 185-c. 254)

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