1C2 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[May, 



tapeously applied to architectural purposes, several of which Mr. 

 .'opliiiff has prciduced. One, which I liere point out, is descrihed 

 Ipy an instrument devised by myself, and which draws very com- 

 plicated forms, available for some ]iurposes in their entire state, 

 and for others by a proper selection of ])arts, so as to be made ap- 

 plicable for the curves of vases and other lines, and these always 

 suggest beautiful motives for lines of varied curvature. On the 

 jiresent occasion, however, time does not allow me to enlarjie ui)on 

 them, and I must conclude by again calling to your notice the 

 extreme simplicity of the instrument, which Mr. Jojding's kind- 

 ness has allowed me to lay before you, and which is most readily 

 adaptable for drawing what is often required in Architecture, a 

 long line departing very little from a straight line, and yet with 

 an almost unlimited variety in its curvature. 



MOTION OF WATER IN PIPES. 



On the Motion of Water in Conduit Pipes; on Friction and Prcs- 

 utire in Pipes; and on Jets d'Eau. By M. D'AumrssoN de Voisins, 

 Ingenieur en chef Directeur au Corps Royal des Mines, &c. &c. 

 — (Translated by T. Howabd, for the Civil Engineer and Archi- 

 tert's Journal.) 



{Continued from page 132.) 



Equation where Conduits are terminated by Adjutages. 



12. We have hitherto considered conduits as entirely open at 

 their further extremity; whereas, they are generally terminated 

 by nozzles or cocks, or have some kind of adjutage wliich contracts 

 the opening, and makes the water issue forth with a velocity dif- 

 ferent from the uniform motion of the fluid in the pipe: conse- 

 (piently, the ecpiations (I. to XII.) based upon the supposition of 

 identity of velocity, do not apply e.\cept under that condition. 

 Tlie first member of these e(puitions, II — •15.5ii-', gives the portion 

 of the head destroyed by the resistance of the conduit; which 

 portion is the entire head II, minus that which remains to produce 

 the velocity of discharge (2): if this velocity is called V, the 

 first member of the equation will, in general, he H — -155 V-'. 

 The second member is the expression of the resistance of the 

 sides (7), which is a function of the velocity in the conduit, or 

 of f; V ought then to remain as it is in this member, which will 

 not change in value. 



13. In conduit ])i])es, even more, if possible, than in other cases 

 of fluids with unbroken continuity of motion, the velocities, at 

 particular points, are in inverse ratio to their sections: so that if 

 d lie the diameter of an adjutage at its discharging orifice, m the 

 coeflicient for its particular contraction, D being invariably the 

 diameter of the conduit, we have 



V : u :: ir'D- : ir'ynd'-; or, 



D= Q D- O 



V = r —-.. = 1-273 >•, X —:, = 1-273 ^ . 

 ma- U- md' md- 



TUe equation for the movement then becomes 



Q- L 



(Q^ + -01.-52 QD-') 



,.(XV1.) 



[!n iiietr.] H--08264 -",- = -002221 



m'-d* D ° 



f[.i feet.] H--02J19 -' =-000677 — {Q- + -14173 QD-') ! 

 m-d^ U^ J 



Of the five quantities which this equation contains, four being 

 given, we may by it obtain the value of the fifth. 



It is required, for example, to rietermine the diameter necessary to f;ive to 

 a circular orifice in a thin plate, fated to the end of a conduit of -08 feet 

 diameter, and 532 feet long, the quantity of water to be discharged per 

 second being -02 feet, and the head 4-5 feet. The above equation will give 



'=\/ 



■02519 Q^D = 



m2{HD6--000677L(QS + -1417QD')}' 



G2, and reducing anil extracting the 



Puttttng in the numerical values m 

 fourth root, we have (/ = -04 77 feet. 



14. For velocities above 2 feet per second, we have (all being in feet), 



Q- 



H--02ol9 



m^d" 



Q = 37 031 \ 



/- 



■000711 ^-^' ; 



L + 35'47 



D° 



m'd* 



and 



(XVll.) 



(XVllI.) 



V LQ= 

 11-02519 ^ 

 ni^d* 



(XIX.) 



Ex. 1. — To a conduit of the dimensions given below, we will adapt a 

 COJiical adjutage -03 feet diameter: we require to know the quantity it "ill 

 then discharge ? 



Here 0=.-25 feet; L = 1450feet; 11 = 5-32 feet; and for the coifficient 

 for the convergence of the adjutage we take -90. Cons( quently, 



m=d' = -0000006561 ; and 35-47— ;. = 52795. 



m'd* 



Then Q = 37-034 



V- 



5-32 (-25)^ 



- = -01146 cuh. feet. 



1450 + 52795 

 The complete equation (XVI.) would also give -0114G cub. feet. 



We would here remark, that if instead of an adjutage of -03 feet diame- 

 ter, we put one of -125 feet diameter (half the diameter of the comiuii), 

 the discharge will be .. .. ,, .. ,, -06551 cuh. feet. 



With a diameter of -1875 feet (| diameter) . .. -06881 cub. feet. 



Without any adjutage, we should have .. .. -00917 cub. feet. 



These results show, that when the diameter of an adjutage is great com- 

 pared with that of the comluit (so as to he more than half thereof), the dis- 

 charge differs very little from that which we obtaur by leaving the conduit 

 entirely open. 



In several of my experiments on tlie conduits of Toulouse, this faft was 

 particularly observed ; the difference in some cases was even much less 

 than theory would give- — it was imperceptible. For example, having at 

 the end of a conduit of -164 feet 

 diameter, and 1391 (eet long, succes- 

 sively fitted plates pierced with cir- 

 cular orifices, gradually decreasing in 

 diameter, and under a constant head 

 of 53-5 feet, we had the discharges 

 here given. The diameter of the 

 conduit being "164 feet, the first is 

 the result ohtained wiihiiut any adju- 

 tage. We observe that the results of 

 calculation approach so much the 

 nearer those of experiment, as the 

 velocity of the water in the conduit 

 becomes less. 



Esc. 2. — Required the diameter of a conduit 2736 feet long, and from 

 which, with a head of 213 feet, we wish to ohtuin -4 cuh. feet of water per 

 second, hy several orifices placed near each other, and which taken together 

 are equal in area to one circular orifice -13 feet diameter; the cotffi.ieiit of 

 contraction in this case beuig taken as -85 ? 



Q2 



We have m2d< -=-000206346; -02519 -==— = 19-547; and, consequently 



m'd* 



D = ^235 



^/ _'■'•'" K^r =.641 feet. 

 A/ 2^3-19-547 



_2736(^4)-^ _ 



Art, II. — CoNDviTs with Bends and Contractions. 

 Three kinds of Resistance in Conduit Pipes. 



15. We have been hitherto considering conduits as rectilinear, 

 and of equal section throughout tlieir whole length; but they are 

 generally formed with angles or bends, and occasionally have parts 

 of a diminished section, either over a very small extent (forming, 

 as it were, an annular ciuitraction), or else through a considerable 

 length. Water, moving in such conduits, on arriving at the bends, 

 is compelled to change its direction. In so doing, it loses part of 

 its velocity: the resistance which causes the loss is as a force 

 opposed to the motive power, or the original head; it destroys a 

 part thereof. 



At contractions, again, the fluid experiences another resistance: 

 having there to pass through a narrower section, it requires to 

 have a greater velocity; to obtain this, a new effort is necessary — 

 and the consequence is, another diminution of the total head. 



Thus, water, in its motion in pipes, meets, or may meet, with 

 three kinds of resistance — that due to the effect of the sides, and 

 which is by far the most considerable; that which arises from 

 bends; and that from contractions. The forces or ])ortions of the 

 head employed to overcome these, lessen the total head; and it is 

 only by reason of the remaining part, that the efllux takes place: 

 this portion is the height due to the velocity of discharge. 



M'e have treated in detail the resistance of the sides (1 — 8) ; we 

 shall now examine the other two. 



