HYDRODYNAMICS. 



499 



TABLE III Containing the Experiments ofMichelotli on TABLE IV. Containing Messrs Br.ndle,; and Smealon s 

 W Wti - quantities of Water discharged by different verli- Experiments on the Quantities of H aler ducliarged by 



cjl orifice* under different head* of Water. rectangular botches. 



fr. -. Ob- 



Opening. 



(II. On the quantitiet of Water discharged through 

 openings in Reservoirs when very large, and in reaching 

 to the surface. 



The following experiments were made by Messrs 

 Brindknr and Smeaton on the quantities of water dis- 

 Ttftn- charged by rectangular notches, through which the wa- 

 ter flowed from a very extensive surface. The first 

 column contains the width of the notches in inches : 

 the second contains their depth ; the third contains the 

 quantity of water discharged ; and the fourth the time 

 which that quantity was discharged. 



The experiments of Bossut were not extended to any 

 of the cases included in the present Section ; but we 

 are fortunately in possession of some good experiments 

 by Du Buat on the quantity of water discharged over 

 weirs and ban, which are cases in which the orifice ex- 

 tends to the surface. 



A ireir or jetty is represented in Figs. 7 r and 8. of Du Buai', 

 Plate CCCXVI II. Weirs are most commonly erected expen- 

 ds in Fig. 4. where BCD is a weir of solid masonry or " lenli - 

 of timber, with a strong plank AB, called the waste "... 

 board, over which the water flows. In this case, there- f 7 h " 

 fore, the depth of the orifice is measured by the depth 

 of the upper edge of the plank AB below the level sur- 

 face of the water in the river or reservoir. Du Buat 

 made four accurate experiments on this subject, the re- 

 sult of which is given in the following Table, reduced 

 to English inches, the length of the orifice being 18{ 



The preceding Table gives a co-efficient of 0.625, 

 which is not very different from 0.619, the mean co-ef- 

 ficient obtained by Bostut. 



talon The following experiments were made by Messrs 



d Briod- Brhidley and Smeaton. The water extended over a very 

 i nperi. targe surface, and the heights above the orifice were 

 measured from the surface to the tops of the orifice*. 



TABLE V. Containing Experiments by Du Buat on the 

 quantity of Water discharged over Weirs. 



Depth of the orifice 

 in Eflnhah fcet. 



1.778 

 3.199 

 4.665 

 6.753 



508 



-'1.V1 

 3750 



Discharge calculated 

 by the formula. 



524 

 12I 



'.'155 

 3771 



IS. Buat has given the following formula reduced to 

 English inches, by which column 3d has been calcula- 

 ted, which shews it* near agreement with observation. 

 The formula, a* altered by Dr Robison, i* 



D = / ^1S0.032H', or 



D= 11.4172 /H*, 



where D is the quantity of water discharged in cubic 

 feet, / the length of the wasteboard, and H its depth. 

 That is, multiply the square root of the cube of the depth 

 of Ike upper edge of the matteboard Mom the surface by 

 1 1 A, and by the length of the matteboard, and the product 

 miu be the quantity discharged in English inche*. 



In deducing the preceding formula, M. Du Buat has 

 tr**""** 1 that AF, Fig. 7. is one half of AL, and that 

 the quantity by which we must divide the square of the 

 mean velocity per second, to have the height of fall 

 which is due to it, was 786. Dr Robiion, however, had 

 occasion to examine a numerous set of experiments, in 

 which AF was always leas than } of AL, and was near- 

 ly i, and in which the quantity of water discharged 

 was greater than what is given by Du Bual's formula. 



