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4-8 HANDBOOK OF HYDRAULICS
<br />velocity components along the wall which cause contraction
<br />and thus tends to increase the values of both C. and C. Simi-
<br />lar effects would result from having the orifice plate differ from
<br />a perfectly plane surface. If it were slightly warped outward,
<br />C. would be increased, whereas an inward curvature of the plate
<br />would have the opposite effect (see Standard Short Tubes,
<br />p. 4-19).
<br />The effect of the water temperature is to change the viscosity
<br />and density. Taken in conjunction with the variation of C
<br />U (0
<br />aS
<br />16
<br />1 Q4
<br />03
<br />c 02
<br />0.1
<br />005
<br />10 100 1000 14000 100,000 1,000,000
<br />di p
<br />p
<br />Fig. 4 -7. Orifice coefficients.
<br />with the velocity and orifice diameter shown in Table 4-3, it
<br />becomes clear that here again the Reynolds number is likely
<br />to be the coordinating factor. This was shown to be the case
<br />by Lea,' who plotted more than one hundred experimental
<br />values of C against R. The author's curve, derived from Lea's
<br />plotted points, is shown in Fig. 4-7. The fluids used in the
<br />tests were water, various mixtures of water and glycerin, and a
<br />number of oils. Flow is laminar for Reynolds number less than
<br />12 and fully turbulent for R greater than 10,000, intervening
<br />values corresponding to a transition region. Except in the
<br />transition range, all points plotted by Lea show a spread of
<br />about 3 per cent. A spread of approximately 15 per cent occurs
<br />in the vicinity R equal to 1,000. The range of Reynolds
<br />numbers covered by the tests of Medaugh and Johnson is shown
<br />in Fig. 4-7 by the dashed line AB.
<br />' r. 0. Lea, "Hydraulics," Orb ed., Longman", Green & Co., Inc., New
<br />York, 1942.
<br />4.
<br />Noting that in this case
<br />ORIFICES, OATES, AND TUBES 4
<br />Investigations by Bilton' showed the coefficient of discharge
<br />of a circular orifice under any given head to be the same whether
<br />the jet is horizontal, vertical, or at any intermediate angle.
<br />The extracts from tables by Fanning' and Bovey,' in Table
<br />4-5, give coefficients of discharge for various shapes and arrange-
<br />ments of orifices with complete con-
<br />traction. Fanning's table, com-
<br />piled from experiments from several
<br />sources, contains coefficients for ori-
<br />fices 1 ft wide, of various heights,
<br />and under a wide range of heads.
<br />Bovey's table, prepared from his own
<br />experiments on orifices of different
<br />shapes, each with the area of a circle
<br />!4 in. in diameter, indicates the effect
<br />of shape of opening on the coefficient.
<br />Submerged Orifices. Shown in
<br />Fig. 4-8 is an orifice in a tank with
<br />liquid on both sides. Application
<br />of the Bernoulli equation, taking
<br />the datum through the center of the orifice, yields Eq. (4-3)
<br />exactly in the same form as for free discharge (p. 4-2).
<br />(2)
<br />Ah
<br />Fro. 4 -8. Submerged
<br />orifice.
<br />p = \1 (i — a + Zg — hi) (4
<br />— AA (4-20)
<br />W ar
<br />neglecting v,'/2g, and introducing C to take care of the con-
<br />traction and energy loss, the equation for discharge is
<br />Q = Ca VW2Th, (4 -21)
<br />The few experiments for determining C for submerged orifices
<br />that are available indicate that the value of the coefficient is
<br />1 H, J. I. Hilton. Coefficient.' of Dieoharge through Circular Orisees, paper
<br />read before Victorian Institute of Engineers, April, 1908, Eno. News, July 9,
<br />1908.
<br />J. T. Fanning, "Water- supply Engineering," pp. 205-200, 1). Yea
<br />Noetrand CompAny, Inc., Princeton. N.J., 1908.
<br />+ H. T. Sorel', "Hydraulics," P. 40, John Wiley & Bone, Iuo., New York,
<br />1909.
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