|
no
<br />62
<br />61 , ■
<br />60
<br />no
<br />1111:1111
<br />111M11•
<br />MINNIE
<br />&nifh and Walker
<br />RIME
<br />inlITaminnisliell7iirITIIIIIMIIIIII
<br />--
<br />edwugh
<br />II I
<br />and
<br />J o h nson
<br />Judd
<br />liniiiiii.
<br />1111
<br />� ��
<br />and
<br />King
<br />■■
<br />.5Yriuflaack
<br />-.-._.
<br />4-6 HANDBOOK OF HYDRAULICS
<br />of the orifice. For a cylinder or prism with vertical axis, A is
<br />constant., and Eq. (4 -18), after integration, becomes
<br />2A
<br />f (0 — VE2) (4 -19)
<br />� Ca g
<br />Orifice Coefficients. One of the earliest experimenters on
<br />sharp -edged orifices was Hamilton Smith, Jr.' His values of
<br />the coefficient of discharge for round and square orifices are
<br />given in Table 4-3. There have been many subsequent investi-
<br />gations of circular orifices, not all of which are in agreement.
<br />a
<br />:E
<br />Q
<br />Q
<br />t
<br />a
<br />0 10 20 30 40
<br />Head, feet
<br />Flo. 4-6. Orifice coefficients.
<br />50
<br />60
<br />70
<br />Investigations by Medaugh and Johnson' check Smith's coeffi-
<br />cients for orifices larger than 3 in. in diameter within 3§ of
<br />1 per cent. Values of the coefficient of discharge for a 1 -in.
<br />orifice as determined by various investigators and plotted by
<br />Medaugh and Johnson are shown in Fig. 4 -6. The differences
<br />between the values are undoubtedly not entirely due to experi-
<br />mental errors. Many other factors may contribute, as, for
<br />instance, the ratio of the 'orifice diameter to the dimensions of
<br />the tank wall, the sharpness of the edge of the orifice, the rough -
<br />ness of the inner surface, the orifice plate, and the temperature
<br />of the water. The effect of having the tank wall approach the
<br />orifice is to suppress contraction and therefore to make C
<br />approach the value of C..
<br />"Hydraulics," 1886.
<br />'Medaugh and Johnson, Investigation of the Discharge and Coefficient
<br />of Small Circular Orifices, Cind Sap. (N.Y.), July. 1940, pp. 422 -424.
<br />1st-
<br />" �
<br />ORIFICES, OATES, AND TUBES 4 - 7
<br />Smith and Walkers found values of C. to vary from 0.954 to
<br />0.991 for orifices varying in diameter from 0.75 to 2.5 in.,
<br />respectively. They also found a small variation with head,
<br />the above values being averages for heads varying from 1 to
<br />60 ft.
<br />Values of C. for circular sharp -edged orifices were found to
<br />vary from approximately 0.67 for 34 -in, orifices to 0.614 for
<br />2.5 -in. orifices when the head is 2 ft or more. Values are
<br />slightly larger for lower heads.
<br />If there is suppression of contraction on one side and oppor-
<br />tunity for complete contraction on the other sides, more water
<br />will approach with velocity components parallel to the face of
<br />the orifice on these sides and cause increased contraction. This
<br />to a large extent will compensate for loss of contraction on the
<br />other aide. Williams found, for rectangular orifices 30 in.
<br />wide and 2 to 4 in. high with full contraction at the top and
<br />completely suppressed contraction on the two sides and bottom,
<br />that the average coefficient of discharge was 0.607. This value
<br />corresponds closely to the coefficient for orifices with complete
<br />contraction. For orifices having full contraction at the top,
<br />one aide a sharp edge 6 in. from the side of the channel, and
<br />contraction suppressed at one side and the bottom, Williams
<br />secured an average coefficient of 0.611. With the above ori-
<br />fices, except that the top was beveled to an angle of 45 °, he
<br />obtained values of C of 0.776 and 0.755, respectively. Table
<br />4 -4, from results compiled by Smith,' indicates the effect of
<br />suppression of contraction) for small orifices. In this table,
<br />"suppressed contraction" means that the edge of the orifice
<br />coincides with the side of the channel, and "partly suppressed"
<br />means that the distance of the edge of the orifice from the side
<br />of the channel was 0.066 ft. A special case of suppressed
<br />contraction is the pipe orifice, which will be discussed later.
<br />When the inner edge of the orifice is rounded, as in Fig. 4-2,
<br />contraction is suppressed, C. approaches 1, and C approaches
<br />the value of C.. Values of C. for such orifices are approximately
<br />the same as for sharp-edged orifices.
<br />Roughening the inner surface of the orifice plate retards the
<br />*D. Smith and W. J. Walker, Orifice Flow, Pros Inst. Mech. Sners.
<br />(London). 1923, pp. 23
<br />*Unpublished experiments performed at the University of Michigan in
<br />1928.
<br />i Op. cif., pp. 05-87.
<br />
|