WATER. 



engine is at work, although it bears only 60 feet when it is 

 at reft. But if we confider the whole length of i860 feet, 

 the friftion will be equal to a column of eleven feet ten inches, 

 fo that the preffure, when the engine is at work, will be near 

 72 feet, at that end of the pipe which joins to the pump. 



Example 2 We will now confider the reverfe of this cafe, 



that is, takeaway the pump and fteam-engine,and let the water 

 be propelled through the great pipe, by the water defcending 

 from the ciftern, with a fall of 60 feet. What will be the 

 preffure which caufes the water to flow through the fmall 

 branch-pipe ? 



To find this, we muft calculate with what velocity the 

 water will flow through the whole length of the great pipe, 

 by the theorem and example we have already given for 

 water in pipes. Having found this, calculating on the 

 whole length of the pipe, we muft make another calculation, 

 reckoning only as much length of the pipe as is contained 

 between the ciftern of fupply, and the place where the 

 branch-pipe joins the main-pipe. 



Then take the difference between thefe two velocities, 

 and it fhews what refiftance or fridlion the water muft over- 

 come in running along the remainder of the pipe, ■y/'c. from 

 the place where the branch-pipe joins to the open end of 

 the pipe, where the water is difcharged. Now if a fimple 

 orifice was to be made at that part of the great pipe where 

 the branch-pipe joins, the vs-ater would flow out with a ve- 

 locity equal to the difference of the two velocities, making 

 the proper deduftion for the friftion of the water in pafTmg 

 through the orifice. 



But if we wifh to know the velocity with which the water 

 wiU flow through the branch-pipe, we muft find the depth 

 of column neceffary to produce the velocity equal to the 

 difference of the velocities of which we have before fpoken, 

 calculating according to theory, without regard to friftion ; 

 and then with the depth fo found, we can feek in the table 

 of friftion in pipes, for the refult or flow of water through 

 the fmall branch-pipe. 



The cafe of a regularly inclined pipe is confiderably dif- 

 ferent, becaufe the impelhng force is not all applied at one 

 end of the pipe ; but every portion of the pipe having a 

 defcent, has alfo a portion of the impelling power applied 

 to it. When this pipe is of a certain length, the water 

 arrives as its maximum velocity without accelerating as it 

 proceeds further down the flope ; becaufe the accelerating 

 power of the water is in equilibrio with the obftruftion, 

 that is, the power of defcent acquired in a foot or an inch 

 of the flope, is juft equal to the refiftance in the fame dil- 

 tance ; confequently, the water exerts no preffure on the 

 pipe to burft it open, any part of the water would continue 

 to Aide down the flope with its uniform velocity, even if it 

 was detached from that water which followed or which pre- 

 ceded, and it derives no impelling power from any co- 

 lumn of water. The effeft would be juft the fame, if 

 the pipe was fplit down the middle and converted into two 

 open troughs. 



It is clear, that in this cafe, no water can be obtained from' 

 any lateral branch-pipes, unlefs they defcend from the pipe. 



Let us confider the fame pipe when the inchnation il not 

 a regular flope, but when fome parts flope more rapidly than 

 others. In this cafe, the impelling force is not apphed re- 

 gularly upon every part of the length of the pipe, as in the 

 former inftance ; the confequence is, that in thofe parts 

 which have a more rapid flope than the inclination of 

 a line drawn from one end of the pipe to the other, the 

 water will have a tendency to accelerate beyond the regu- 

 lar velocity which is due to the regular flope, and with 



which it muft ultimately flow out of the pipe ; and on the 

 other hand, in places where the flope is lefs rapid than this 

 line, the tendency of the water will be to flow m.ore flowly 

 than the regular velocity. Now the pipe being clofe and of 

 an equal bore, the water muft flow with the fame velocity 

 in every part of the length ; and although fome portions of 

 the contained water tend to run forwards falter than the 

 regular velocity, yet other portions tend to hang back ; 

 by means of the pipe, the force is tranfmitted from one 

 place to another, and thefe forces become all combined to- 

 gether to produce an uniform velocity. 



We fliall find, on farther confideration of thefe aftions, that 

 fome parts may be fubjefted to a preffure or ftrain to force 

 or burft it open, and other parts may at the fame time be 

 ftrained in an oppofite direflion, viz.. to crufh the metal of 

 the pipe inwards. 



Thus at every point where the pipe fuddenly changes its 

 flope or rate of inchnation, from an eafy flope to a very rapid 

 defcent, then the water will have a tendency to run down fuch 

 floping part of the pipe, and pafs away fafter than other 

 water can come down the eafy flope ; the confequence is, that 

 a fuftion or afpiration takes place within the pipe, and if a 

 fmall branch-pipe were applied in fuch a fituation, water 

 may aftually be drawn up from a confiderable depth. This 

 has been fhewn by M. Venturi, who calls it the lateral com- 

 munication of motion between fluids. 



This is a certain proof that the bore of the pipe is too 

 fmall at fuch places. An attentive confideration of thefe 

 circumftances, will (hew the propriety of making a long 

 pipe with different bores at different places, where the flope 

 is different; for, by judicioufly increafing the bore of the 

 pipe where the flope is lefs, the aftion may be made uniform 

 throughout. But this cannot be done in cafes where the 

 changes of flope are exceffive ; for inftance, when the pipe 

 defcends rapidly into a deep valley, and muft rife again with 

 a rapid flope in an oppofite direftion. This is the cafe with 

 the pipes which fupply Edinburgh, and in many fituations 

 is unavoidable. 



The refiftance arifing from friftion is greater or lefs ac- 

 cording to the velocity of the motion ; but whatever is the 

 inchnation of a pipe, provided it is long enough, the velocity 

 with which the water runs through it will fo adjuft itfelf, 

 that the funi of all the refiftance in the whole length of the 

 pipe, will exaAly balance the fum of all the forces, which 

 the water exerts by its defcent. But if the pipe is 

 too fhort, the forces of defcent down the pipe may over- 

 balance all the refiftances. In this cafe, the water will tend 

 to accelerate, and the water which has defcended near to the 

 bottom of the pipe, will draw after it that water which has 

 juft entered the upper part of the flope, inftead of the water 

 in the upper part, forcing forwards that water which is 

 beneath it. 



Dr. Robifon obferves that there are fome curious cir- 

 cumftances in the mechanifm of thefe motions, which makes 

 a certain length of pipe neceffary, for bringing it into the 

 equihbrium of motive force, and refiftance, which he calls 

 train. A certain portion of the interior furface of the pipe 

 muft a& in concert in obftrufting the motion. We do not 

 completely underftand this circuinilance, but we can form 

 a pretty diftinft notion of its mode of afting. The film of 

 water contiguous to the pipe is withheld by the obftruc- 

 tion of friftion, but glides along ; the film immediately within 

 this is withheld by the outer film, but ghdes through it. 

 and thus all the concentric films gUde within thofe aroutid 

 them, fimilar to the tubes of a telefcope, when we draw it 

 out by taking hold of the end of the innermoft. Thus the 

 10 fecond 



