37G 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL, 



[Uecem beb, 



•OOOflTTL 



+ 



•14]7Q\ 



when the water passes from tlie m:iin Kondiiit into a branch, and 

 from a branch into a sub-branch, ^thly. From eddies occasioned 

 by the diversion of the water at the head of eacli branch or sul)- 

 brancli. As to the resistance arisint; from contraction, it is unneces- 

 sary to take it into account; we should not admit a permani'nt 

 contraction in a conduit: if one accidentally exists we have 

 pointed out the method of calculatinif its effect (20.) We have 

 seen (l.>) that all resistance to the motion of water in a conduit 

 pipe is an effort opposed to the motive force or total head, and 

 which absorbing a part of it, causes a loss of head. 



We have treated in detail the first two of the four losses that 

 have just been pointed out, and shall now limit ourselves to the 

 recapitulation of them.— The equation for the resistance of the 

 sides (6) is 



/Q: 



For the resistance from bends (17) 



Q'' . 



= •00608 —^ sin'; 

 The other two remain to be examined. 



I^oss nf Head arining from Vhnnges nf Direction. 



36. When a body moving with a velocity c in one direction, is 

 forcibly turned in another, makina^ an angle i with the first, its 

 velocity is then only v cos i. In the same way, when a fluid in a 

 conduit having a velocity v, passes into a branch, obstructing the 

 other forces which may act upon it, it will then only have the 

 velocity v cos i. The force or head due, which was •0155 v- in the 

 conduit, will only be •0155;'- cos- ;; it will then have lost in head 

 •0155u- (1 — cos- i), or '0155 !>- sin- i. 



Almost all branches are made at right angles to the main 

 conduit, altliough they afterwards be diverted by greater or less 

 bends. In this case i = 90^, sin i := 1, and the loss of head, re- 

 collecting that w = 1-273 !!:-,, is -0252 j^^; that is to say, the head 



or force due to the velocity that tlie water has in the main conduit 

 is entirely lost: it has no effect in the direction of the branch: the 

 fluid only enters this by virtue of the pressure (or piezometric 

 height) existing in the conduit at the point of junction. 



Loss due to Erogation. 



37. At this junction there will be yet another loss of head. In 

 order to measure its amount M.M. Mallet and Yenieys, engineers 

 of the Paris AV^ater AVorks, placed a piezometre on a conduit 9iin. 

 diameter, a little a1)0ve the junction of a branch of 3i in. diameter; 

 and they placed a second guage a little way down this branch. 

 The water stood in this last '39 feet lower than in the first, the 

 quantity discharged through the branch being -1535 cubic feet per 

 second; the velocity was 2^778 feet, and the head due to that 

 velocity -120 feet: this last quantity should be taken above the 

 elevation of the first piezometre to impart the above mentioned 

 velocity, there will then remain only as the difference, or for the 

 effect of erogation, •27-t feet, a quantity 2-28 times greater than 

 that due to the height. The discharge from the branch being in- 

 creased to 35' !■ cubic feet, the difference between the two piezo- 

 metres was '502 feet; the height due to the velocity being then 

 ■168 feet; and there remained for erogation a quantity l'9t times 

 greater than that height. We conclude from these experiments 

 that the loss of head occasioned by erogation is equal to about 

 twice the height due to the velocity in the branch. 



Any uncertainty as to the amount of tlie loss of head due to erogation, as 

 well as those arising from bends and change of direction, does not involve 

 any practical consequence, these values being so slight relatively to the 

 others which enter into the equations, especially to the loss resulting from 

 the action of the sides, and the latter has been determiaed by the aid of 

 more than fifty experiments. 



38. For some time I feared that the erogations for the branches might 

 extend their eff^jct to the conduit it-self, below the points of junction, and 

 that tlie hentl might experience a considerable diminution. If it had been 

 so. the solution of the problem which I give here, and which I had impli- 

 citly given in my ' Tfaite sur le moiivempiit dc I'eau dans Ics Conduites, 

 1827,' woulil have been completely defective. To decide this important 

 question, I instituted the following experiments in 1830 ; — 



On a conduit 3^inch diameter, 2090 feet long, I bad placed at 141 1 feet 

 from its commencement, a tulie having a cock through which we could let 

 off a greater or less quantity nf water ; this represented the circumstances 

 of ajunction. At 1-61 fei't ahove, as well as at 2'30 feet lielow, we fixed 

 a large piezometre ; the head of water oa the conduit remained Dearly con- 



slant,) 2428 feet, and its extremity was quite open. We discharged through 



the junction the volumes of 

 water indicated in the 

 margin, and have noted op- 

 posite those which flowed 

 from the extremity, as well 

 as the height at which the 

 water stood in each of the 

 two piezometres. As we 

 could Dot determine the 

 heights within ahout | of an 

 inch, we may conclude they 

 were the same ahove and 

 below the point of junction. 

 This equality of pressure wa> 

 maintained in several other 



experiments that I made with the same apparatus. 



Thus a branch made in a conduit does not sensibly diminish the pressure 



or liend below the point of junction; and in a system of conduits, we may 



consider that there are no other losses of head hut the four in question. 



Final Equation for the Motion in a Branch. 



39. Let n be a branch or sub-branch of any order whatever, 

 supposed to be quite open at the end. Again, let 



dn be the diameter of such aperture at the end. 



rn„ the coefficient for contraction. 



H,i the entire head of the branch, or the difference of level 

 between surface of the reservoir and the orifice of dis- 

 charge. 



Dn the diameter of the branch. 



L„ its length. 



Q„ the quantity of water it conveys. 



S-;i the sum of the squares of the sines of the angles of reflec- 

 tion at the various bends. 



[Rj the sum of the resistances or losses of head experienced by 

 the water which flows in the branch down to its junction. 



If, by following the course of the water which reaches it, we 

 represent by r and *•' the losses of head due to friction and bends 

 upon the main conduit as far as the first branch; by r-^, r\, r'\, 

 /",, the four losses of head upon this first branch; by r^, r'„, r'\, 

 r"'j, the four losses of head upon the second up to the third 

 branch; and so on successively up to the branch n — 1, to which is 

 adapted the branch h, we shall have — 



[R'] = r + r' + r, + r\ + r'\ + r"\+ r„_i -f- r'„_, -(- r"„_i -|- r"',_i, 



since the sum of the losses of liead, deducted from the total head, 

 gives the head due to the velocity of discharge (34); or, rather, 

 the entire head is equal to the sum of the losses plus the head due 



to the velocity of discharge, which is (13) -0252 —^ — , and the 



m-„d\ 



equation will be 



H„ = [R] + -0252 ^-^ + ■000677L(5J1^ + '~'^^^) + 



•0061 





When the branch is entirely open at its extremity, m-„ d'„ = D',. 

 The above eipiation enables us to determine, directly or indi- 

 rectly, either of the values implied in it, from a knowledge of the 

 others. 



ADELAIDE CHAMBERS, GRACECHURCH STREET. 



The enffraving we now give represents some chambers and 

 buildings around what many would make into a common alley. 

 Mr. Charles Corbett, architect of this design, has, however, 

 without any ambitious attempt to carry out a costly structure, 

 created a picturesque composition, of which there are (ev; examples 

 of the same kind in the City. The shape of the ground and 

 opening seemed unfavourable to any harmony of design; but as 

 now arranged, and by the treatment of the walls, a very pleasing 

 effect is produced. U'e think this endeavour very praiseworthy; 

 and though we may differ as to details, we think the example well 

 worthy of being adopted in many situations in the City, where the 

 only unity is the correspondence of square windows, and the only 

 simplicity that of brick walls. 



