1819."] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



327 



As tlie measurement of the level before sinkin;? may som?times be 

 difficult, we may in ordinary cases apply the equation (2) § 11, with 

 sufficient accuracy in such a manner, that the altitude of pressure 

 H" of the level after sinking may appear in the formula. We have 

 then 



q = h"bl^''(-i.g{W + ih)). 



The Co-efficient /(" will be obtained from Table IV. for the ratios 



II" I 



m = , and n = , . 



It. 



Rrrtiuiijuliir Orifices ojien on their upper Side-i. 

 By equ:ition (</) § 1'2, 



It is found in the same way as for h^ and/j,; i.e. when the altitudes 

 of pressure above the upper edges of circular and square orifices 

 were zero, that for the centre of pressure 



k' = 



= -GOSi 



/Ho 

 V H'' 



6. 



d. 



II„ =1 it + y — ?^/. Consequently, 



H 



!i{'-'-+''- 



-! + 



i{l-r + 2r~l). 



2r — / is the difference of the height of the two orifices, or the dif- 

 ference of the depths of water when it reaches to the upper edges 

 of the orifices. Let, therefore, the upper edges of both orifices be 

 in one plane. Then the difference in respect to the altitude of 

 pressure = 0; consequently, 2 r — ^ = 0, and we have when both 

 orifices are full, 



H° = 2iv~'"^i{r^)}- 



Let now for the assigned position of the orifices the water depth 

 sink to / in both. The depth of water in the square orifice is 

 then zero; in the circular orifice, on the contrary, it is still =2r — /. 

 Put, therefore, the value of equation («) in (a), and we have the 

 co-efficient V = k' (in Table I. for m = 0) when the outlet is full, 

 or for a depth of water / in the square orifice. Put, on the con- 

 trary, the value of equation (d) in (or), and we have the co-efficient 

 k'" for a water depth in the orifice. For all remaining depths, 

 consequently, the values of the co-efficients lie between these 

 limits, and their computation is only arrived at by giving the 

 expression 2r — I in equation (rf) in such a form that for a water- 

 depth / in the orifice it may be zero, and when the water-depth is 

 zero may have its full value. Let the variable water-depth be- 

 tween the limits and I be designated generally by It; then the 



function (Sr— /) [l — -) satisfies the conditions; A, however, must 



never exceed /. When h=^l^=^ the breadth of the orifice, this 

 expression is zero, as required; and when A = 0, the expression 



--ir — l. 



Put therefore, as before, , = n, 



then 1 



h 



= 1 



ir„ 



Multiply, therefore, 2r — / in (i/) by this factor, and put m 



li ^ 



equation (a); and we have, when for ;■ its value = — — is written, 



V IT ' 



t'le general expression for rectangular orifices open on their upper 

 sides, for altitudes of pressure equal to or less than the breadtii of 

 the orifice, as follows : — 



C. = -7427 I •4Ml8+-128;'t/l-'|^)f Urr4V)18+-128:v(l-'-)~| ) '• . 



The co-efficients i-" are computed by these equations for differ- 

 ent values of T = n, and given in the following table. 



Table V. 



[File s-nallest co-efflcient occura when the water-d-ptli is equal to the breadth of the 



k 

 oritice. When the water-depth is greater than the breadth of the orifice, -: must be put 



equal to ?(.] 



The computation of the quantity of discharge by a rectangular 

 orifice, where the base is greater than the height, can be effected 

 by equation (e) § 11, when for b is put the value h here correspond- 

 ing and the correct co-efficients: we have then 

 /.. Qz=U"'hW{igli). 



The co-efficient k'" will be either computed by equation (</), or 



I 

 given by Table V. above for n = -. 



The sinking of the level in the reservoir which takes place in 

 and about the orifice, has not hitherto been considered; A, there- 

 fore, always refers to the unsunken level. 



On the hypothesis that the sinking of the surface is proportional 

 to the velocities — that is, to the square of the depth of water, we 

 have 



V'/i' : ^h = h'—h" : h—h"; 



and when all the quantities are e.Kpressed in parts of the base /, 





h'-h" h-h" 



I 



I 



1 : 



V'; = 



•083J 



Consequently, when the sinking of the level is found by experi- 

 ment for h' := /, it may be computed thus for all other depths. 



In the first experiment in the following table A' ^-2079; /='2; 

 A'— /t"=-0167. Put this value in the above proportion, and take 



^ = 1, which is approximately correct, and we have 



h-h" , 



I 



and hence it follows that tlie sinking of the level for the water- 

 depth A is 



;. A— A" = -0835 VC'O- 



This expression is valid of course only for the value of A, nearly 

 equal to or less than /, and requires moreover that the water in the 

 reservoir be at rest and have not already acquired a considerable 

 velocity. 



Table VI. 

 Comparison of the experiments of Poncelet with the foregoing Formula. 



* Here h is grenter than ?, and therefore by the note to Table V.. -. must be put = /#. 



15. 



Different Forms of the Stream of Water. 



The contracting force by § 7 is proportional to the diameter <if 

 the orifii e. Hence it follows that the contraction in a square orifice 



