Mechanics of engineering by Church Irving Porter 1851-1931

Author:Church, Irving Porter, 1851-1931. [from old catalog]
Language: eng
Format: epub
Tags: Hydraulics, Pneumatics
Publisher: New York, J. Wiley & sons
Published: 1889-03-25T05:00:00+00:00

Fio. 654.

(differing from eq. (6) only in the coefficient of efflux //), in which the abstract number fx is found thus: Determine a coefficient of efflux //^ as if eq. (6) were to be used in Case I; i.e., as if contraction were complete and perfect; then write

/I = //,[! +0.165 n], (7)'

where n = the ratio of the length of periphery of the orifice with a border to the whole periphery. E.g., if the lower sill, only, has a border,

n = J-[2(« + J)];

while if the lower sill and both sides have a border,

n = (2a + &)-=-[2(a + i)].

Example.— If A, = 8 ft. (= 2.43°^), J = 2 ft. (=0.60™% o = 4 in. (= 0.10"-), and one side is even with the side of the tank, and the lower sill even with the bottom, required the volume discharged per second. (Sharp-edged orifice, in vertical plane, etc.)

Here for complete and perfect contraction we have, from Poncelet's tables (Case I), /i^ = 0.608. Now n = 4; hence> from eq. (7)',

M = 0.608 [1 + 0.155 X i]= 0.6551;

hence, eq. (7),

Q = 0.655 X 2 X tV 4^2 X 82.2(8+4. A)

= 10.23 cnb. ft. per sec.

Case III. Imperfect Contraction. —If there is a submerged channel of approach, symmetrically placed as regards the orifice, and of an area (cross-section), = 6^, not

=^3^^^''^g^]]J_^ much larger than that, = jp', of the ^^^- % ^^%^^r^ orifice (see Fig. 555), the contraction El^^r:./^^ ■—^ is less than in Case I, and is called

irrvperfect contraction. Upon his experiments with Poncelet's orifices,. Pxo. 6611. -^ith imperfect contraction, Weisbach

bases the following formula for the discharge (volume) per

unit of time, viz.,

^ = ;io5y^2^(A.+ |) (8>

Digitized by VjOOQ IC

BSCTANGULAB OBIFIGSS.

681

(flee Fig. 553 for notation), with the understanding that the co« efficient

;i = /i,(l + /?), (sy

where /i« is^ the coefficient obtained from the tables of Case I (as if the contraction were perfect and complete), and /3 an abstract nnmber depending on the ratio F: O = m, ss follows:

/5 = 0.0760 [9-^-1.00].

. . . (sr

To shorten computation Weisbach gives the following table

for/5:

Example.— Let A, = 4' 9i" (= 1.46 met), the dimensions of the orifice being—

width = ft = 8 in. (= 0.20"»); height = a = 5 in. (= 0.126");

while the channel of approach (CZ?, Fig. 555) is one foot square. From Case I, we have, for the given dimensions and heady

/I. = 0.610;

Table A.

5 = ^?ii£L = 0.27. G 144 sq. m.

We find [Table A]

/?= 0.062;

and hence /«= /i, (1.062), from eq. (8)'. Therefore, from eq. (8), with ft, lb., and sec.,

Q = 0.610 X 1.062 X A • A V2 X 32.2 X 6

= 3.22 cub. ft. per sec.

Case IV. Mead measured in Momng Water. —See Fig. 556. If the head h, , of the upper sill, cannot be measured to the level of still water, but must be taken to the surface of a channel of approach, where the velocity of approach is quite

MECHANICS OF ENOINEEBING.

appreciable, not only is the contraction imperfect, but

strictly we should use eq.

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