WATER. 



Maln-Pipe.^lt is a common cafe in water-works, that water 

 is required to be drawn off through a fmall pipe, from the 

 fide of a main-pipe, in which the water is not at reft, but in 

 motion, with a much greater velocity than the flow occa- 

 fioned by the water which is drawn off through the fmall 

 pipe. It is often required to know what quantity fuch 

 fmall pipe will yield. When water is pafling along a pipe, 

 its preffure on the fides of the pipe is diminifhed in confe- 

 quence of its velocity ; and if a pipe is derived from it, the 

 quantity drawn off muft alfo be lefs than if the water in the 

 great pipe was motionlefs. It is therefore of great im- 

 portance to determine what is the diminution of preffure 

 which arifes from the motion along the main-pipe. 



It is plain, that if the water fuffered no refiftance in the 

 main-pipe, its velocity would be that which is due to the 

 height through which it had defcended, and it would pafs 

 along without exerting any preffure. Alfo, if the pipe were 

 Ihut at the end, the preffure within the pipe would be 

 equal to the whole depth of water. Between thefe limits we 

 Ihall find what we feek. If the head of water renrains the 

 fame as when the pipe was ftopped, and the end of the tube 

 be contrafted, but not ftopped entirely, the velocity in the 

 pipe will be fmall ; and the natural velocity due to the 

 defcent being checked, the particles willre-aft on what ob- 

 ftrufts tlieir motion. This aftion will be uniformly pro- 

 pagated through the fluid in every direftion, and will 

 exert preffure on the fides of the pipe. Now obftruAions 

 of any kind, arifing from friftion or any other caufe, virill 

 produce a diminution of velocity in the pipe. The refiftance, 

 therefore, which we afcribe to friftion, produces the fame 

 lateral preffure which a contraftion of the orifice would do, 

 provided that it would diminifti the velocity in the pipe, in 

 an eqnal degree. 



We will firft confider the cafe of an horizontal pipe, in 

 which the whole impelling force is applied at one end of the 

 pipe, either by a pump or by a column in a perpendicular 

 pipe at that end. This force muft be tranfmitted or carried 

 by the water through the whole length of the pipe, v/herein 

 part of it will be abforbed in overcoming the obftruftion 

 and friftion, and the remaining force will produce the velo- 

 city with which the water iffues at the open end of the pipe. 

 It is evident that every part of the horizontal length of fuch a 

 pipe muft bear a different degree of preffure, when the water is 

 in motion ; thus, at the end where it is difcharged, there is 

 no preffure exerted on the pipe to burft it open, becaufe 

 the water can efcape freely ; but at every other part a force 

 muft be exerted, which is fufficient to overcome all the re- 

 fiftance which the water will meet with, in running from fuch 

 part to the open end, where it is difcharged. 



In ftiort, whatever part of the column of water in the re- 

 fervoir, or of the preffure which impels it along the pipe, is 

 not employed in producing velocity, muft be employed in 

 afting againft fome obftruftion ; and by the re-aftion of this 

 obftrudlion, an equal preffure is tranfmitted to all parts of 

 the pipe. The chief queftions will be, in what part of the 

 pipe are thefe obftruftions fituated, and at what part is the 

 force applied which is to overcome them ; becaufe that pan 

 of the pipe which is between the two, muft bear the ftrain 

 of tranfmitting the force from the place where it is applied, 

 to the place where it is to operate. 



In the cafe where the impelling force is all applied at one end 

 of the pipe, and the only refiftance is the friftion of the water 

 in running through the horizontal pipe, the preffure to burft 

 the pipe, will begin at nothing at the open end of the pipe, 

 and regularly increafe from that to the other end. Its quan- 

 tity for 100 feet in length may be afcertained for any giten 



bore of the pipe, and velocity of the water, from Mr. Smea- 

 ton's table of friftion abeady given, and may be adapted to 

 all other lengths by a fimple rule of proportion. 



If in addition to the refiftance by friftion, which takes 

 place equally in all parts of the length of the pipe, there 

 are any particular caufes of obftruftion at the extreme end 

 or at any other part, the force neceffary to overcome fuch 

 refiftance muft be added to that required to overcome the 

 friftion, as found by the table ; and all this tends to burft 

 open the pipe, or that part which is between the impelling 

 force and the obftruftion, which may arife either from a 

 perpendicular column or hft, up which the water is to be 

 forced, or from a contraftion. 



Example i. — A fteam-engine with a forcing-pump is em- 

 ployed to force water through a pipe, which proceeds hori- 

 zontally for 1800 feet, and then rifes up 60 feet perpendi- 

 cular, to a cittern at the top of a tower ; the diameter of 

 the pipe is five inches, and the motion of the engine is fuch, 

 that the water moves with a velocity of 140 feet^^r minute 

 through the pipe. It is neceffary to fupply a cittern in a 

 houfe from the middle of the main-pipe, by a fmall branch- 

 pipe of one inch bore and 100 feet long ; this cittern is jc 

 feet above the great horizontal-pipe, or five feet beneath the 

 elevated cittern ; required the velocity with which the water 

 will flow through the fmall branch-pipe, when the engine is 

 not at work, and when it is at work. 



When the water in the great pipe is motionlefs, there is 

 the preffure of a column of five feet to force the water 

 through the branch-pipe. Mr. Smeaton's table (hews, that 

 for one inch bore and 100 feet long, a preffure of five feet, 

 or fixty inches, will produce a velocity of 180 feet per mi- 

 nute ; but when this pipe is running, the water in the great 

 pipe muft move alfo. The area of the pipe of five inches, is 

 twenty -five times as great as the pipe of one inch ; therefore, 

 the motion of the water in the great pipe, will be only one 

 twenty -fifth of 180 feet, or 7.2 feet per minute. Find the 

 neareft velocity to this in the table, or ten feet per minute, 

 and under five inches bore, we find .07 inches the height ne- 

 ceffary to produce that motion, if the pipe was 100 feet 

 long ; but as it is 960 feet, the height required will be 

 .07 X 9.6 = .672 of an inch. This fliould be dedufted 

 from the five feet preffure which urges the water through 

 the fmall pipe ; .but fo fmall a quantity is not worth notice : 

 hence we may ttate the velocity when the engine is not at 

 work at 180 feet per minute, and the difcharge from a bore 

 of one inch, will be .98 of a cubic foot per minute. 



When the engine is at work, the fame preffure will be ex- 

 erted with the addition of all the preffure neceffary to over- 

 come the friftion of the water, in running along the great 

 pipe with a velocity of 140 ketper minute. Look for this ve- 

 locity in the table, and for five inches bore it fhews, that a co- 

 lumn of 7.6 inches muft be allowed for every lOO feet of the 

 pipe. The length of the pipe meafured from the place where 

 the branch-pipe proceeds to the cittern at the top of the 

 tower, is 900 feet horizontal, and 60 perpendicular, viz. 960 ; 

 therefore, multiply 7.6 by 9.6, and we have 73 inches for 

 the height, which mull; be added to the five feet, and makes 

 133 inches for the whole column or force, which urges the 

 water to flow through the branch-pipe, when the engine is 

 at work : laftly, by referring to the table in the column of 

 one inch bore, we find that 135 inches will produce a velo 

 city of 270 {eei per minute, and the difcharge will be 1.47 

 cubic feet^i-r minute. 



The fame inveftigation fhews us, that the main-pipe at the 

 place where the branch-pipe proceeds from it, muft bear the 

 preffure of a column equal to 66 feet one inch when the 



engine 



