:V2(i 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[NdVEMBEn, 



As, however, any rertani^le of which the base / 

 h=z)iq, may he considered part of the 

 square npoi described on tlie same 

 base, the contracting forces in rect- 

 jinpuhir and sijiiare orifices must be 

 equal to one another; so tliat the co- 

 efficients for rectanfrular orifices may 

 he comprrted as the co-efiicients for 

 s(|uare oritices, merely by tlie posi- 

 tion of the orifice with respect to 

 the surface of the water in the re- 

 servoir. From these considerations 

 we have 



: rip. 



;iiid lu'is'lit 



'■ = v;i;- 



\V'hen, first of all, the altitude 

 above the upper ed^e is equal for 

 both orifices, and equal hr, we find 

 tor the centre of pressure, 



1. 



2. 



II, = hr + II + 



r- 



Hr 



h + ij + 



12(Ar+.iO 



12(Ar + ^i)" 



In the preceding paragraph, however, by comparing the co- 

 efficients, the centre of the orifices at the same depth may be 

 found. We have, therefore, when the altitude of pressure above 

 the square = A, = erf (in the figure), the following equation be- 

 tween h,^ ha and A,, 



(lb + pq = erf -f- op ; or, A, + i = /( , -f /; :.h,=^ h^ -\- I — h. 



Tut tliis value of hr in the above expressions (1. and 2.), and we 

 have generally for the co-efficients of rectangular orifices, 



H, the altitude of pressure above the upper edges 



of the square and rectangle, and n = r expresses the proportion of 



the base to the height. For w = 2 the base is double, for « = 4 

 four times as great, as the height, &c. In the following table the 

 co-efficients for six different rectangular orifices, are given by 

 computation from equation b. 



Table IV. 



we have designated these limits by a value of m = 5, which corre- 

 .jMiiids to the altitude of pressure 11 = 5/. For rectangular orifices 



0. r = i'|('n+S)n-l + 



Where ml 



It must here be remarked that I signifies the great, and h the 

 small, side of the rectangle. When also the smaller side is hori- 

 xontal, / will be the greater verticil. 



In computing the quantity of discharge from rectangular aper- 

 tures, distinction must be made between greater and less altitudes 

 of pressure, of which the limits must never be such that the sink- 

 ing of the level may have considerable influence. For the square, 



we find tlie limits by the altitude 1I = '16-|- /, which expression for 

 i=:/ gives the same as before. 



4-f-n 



H i4-t-/ , I 



As m^^-j =■ ■ — J — , when " = , 



and b is the height of the orifice, m =^ ■ 



For the correspond- 



ing values of m and n, it is seen by the Table IV. that the co- 

 efficients for smaller altitudes are, as in the case of the s(|uare 

 orifices, invariable, F^or greater altitudes the co-efficients vary, 



and are found by Table IV. for the ratios m = — and n = ,-. 



lb 



The general equation for computing the quantity of discharge 

 by rectangular orifices is by (§ 12, A), 



c. q = k" i ^/{ig) . l[l^{n+n") + hf - [4(H+H")]5}. 



Th.s expression applies for all altitudes of pressure, and requires 

 only tlie value of the co-efficient, which, as we have just said, 

 varies for greater altitudes, and remains constant between the 



■ . Put in the last expression for m. 



n ' 



n.=2; then ?)! = 3; for )i=6|, m = 1'6; for ?i= 10, ra= T-l; &c. 

 For these different values Table IV. gives the respective co-effi- 

 cients (/c") = -6207; ■6369; -eWO; 6530. By the value of m, we 

 have the altitude H = m/ in the measure by which / is measured. 

 For instance, if /^■2metr. and m^3, H^^ti metr. 



In the following table the experiments which Poncelet has given 

 in his work (Tables V. VI. VII. VIII. and IX.), are collected and 

 compared with the above equation (c). 



Experiments of Poncelet and Leshros with rectangular orifices oj 

 equal horizontal base I, but of different heights b. I was throughout 

 = '2 metr. 



limits m = and m: 



ILe Ivvei in reservoir Lefuie sinkiutf »a& o'b uieir. ubuve the orifice. 



