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ORIFICES AS ASCERTAINABLE BY
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ORIFICES AS ASCERTAINABLE BY EXPERIMENTS § 16. When a liquid issues vertically from a small orifice, it forms a See also:jet which rises nearly to the level of the See also:free See also:surface of the liquid in the See also: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 See also:air resistance on the surface of the jet or to the viscosity of the liquid or to See also:friction against the sides of the orifice. Neglecting for the moment this small quantity, we may infer, from the See also:elevation of the jet, that each See also:molecule on leaving the orifice possessed the velocity required to lift it against gravity to the height h. From See also:ordinary See also:dynamics, the relation between the velocity and height of See also:projection is given by the See also: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 See also:discharge. This relation was first obtained by See also:Torricelli. If the orifice is of a suitable conoidal See also:form, the See also:water issues in • filaments normal to the See also:plane of the orifice. Let w be the See also: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 See also: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 See also:term See also:Head in See also:Hydraulics.—The term head is an old millwright's term, and meant primarily the height through which a See also:mass of water descended in actuating a See also:hydraulic See also: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 See also: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 See also:constant for different heads with well-formed See also: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 See also:total height h causing outflow consists of two parts—one See also: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)}. Additional information and CommentsThere are no comments yet for this article.
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