338 



THE IKRIGATION AGE. 



THE DRAINAGE JOURNAL DEPARTMENT. 



The Flow of Water Through Pipes. 



SOME FACTS ABOUT LAYING TILES. 



BY J. ARNETT, 

 Surveyor and Civil Engineer. 



All rules for the formation of tables to show the 

 cubic feet per second of the flow of water through 

 pipes of various diameters and cross section areas are 

 arbitrary. If the reader does not already know that, 

 he will soon see why when he considers that in open 

 ditches, creeks and rivers the water flow on the sur- 

 face at the center where there is no friction, is much 

 faster than in the bed and sides of ditch, creek or 

 river. The same holds good in tile drains. The great- 

 est velocity is at the center of the tile, and the fric- 

 tion at its circumference surface. -This circumference 

 surface friction depends upon whether the tile are 

 smooth inside, of equal internal diameter, laid on firm 

 surface, without horizontal or vertical shouldering. 

 Eeader, you know that the practical work of burning 

 and laying tile, forbid us to expect these last con- 

 ditions. Hence any rule is a mere approximation and 

 approaches the truth, as the last conditions and others 

 not mentioned, approach perfection. 



J. ARNETT. C. E.. LONDON, OHIO. 



The writer will give two formulas, taken from 

 John C. Troutwine's Engineers Pocketbook, for the 

 velocity in feet per second of the flow of water in tile 

 drains, and the cubic feet of water discharge per second. 



Now what is a formula? 



If you will permit the writer to coin a definition, 

 permit him to say that it is a rule tied in a double 

 bow knot, and when this double bow knot is untied 

 by expanding it into words, it becomes a rule. Here 

 are the formulae and their rules. 



The velocity of flow in feet per second : 



Velocity in ft. per sec. =48 V d "me"" 1 " " x't""'" 1 head '" ft ~ 



total length in ft. :-54 diameter in It. 



Now for the rule: Multiply the diameter of the 

 tile in feet (the diameters of all tile less than a foot 

 would be the fraction of a foot) by the total head jn 

 feet; the product is the numerator of a fraction, for 

 denominator of which, to the total length of the tile 

 drain in feet add 54 times the diameter of the tile 



in feet. Divide the numerator by its denominator 

 and extract the square root of the quotient, and mul- 

 tiply by the square root thus found by the coefficient 

 or constant, 48. 



Let us apply this rule : Suppose we have a 6-inch 

 tile drain a half mile or 2,640 feet long, with a total 

 head (or fall) of 12 feet, what is the velocity in 

 feet per second of the flow of water in the tile? In 

 our drain the tile is 6 inches half a foot. This mul- 

 tiplied by total head, 12 feet, gives a product of 6 

 feet for the numerator of our fraction, and to get the 

 denominator of our fraction to the length of the drain, 

 2,640 feet, we must add 54 times the diameter of the 

 6-inch tile, which is 27 feet. This added to 2,640 feet 

 give 2,667 feet for the denominator of our fraction, 

 and we now write it thus: 



The flow in feet per second=48v'^r 7 



2,667 will go into 6, 0.0022497187 of a time. Pointing 

 this last quantity off into periods of two figures each 

 thus: 0.00'22'49'71'87' and extracting the square root 

 ghvs us 0.04743, and this multiplied by the co-efficient 

 or constant, 48, gives 2.27664 feet for the velocity of 

 flow in feet per second. 



Now for the discharge of our 6-inch drain in cubic 

 feet per second. Our' formula is 

 Discharge in cub. ft. per sec. =37.6 v'sth power of head. 



diameter in ft. X in ft. 



length in ft. + 54 diam. in ft. 



The fifth power of our 6-inch drain=0.5X0.5 

 X0.5X0.5X0.5=0.03125 of a foot and this multiplied 

 by 12, the head in feet, gives 0.37500 for the numer- 

 ator of our fraction, and to get the denominator of our 

 fraction we must add to 2,640 feet, the length of our 

 drain, 54 times the diameter of the 6-inch tile in feet, 

 which is 27 feet, giving us for the denominator of our 

 fraction 2,667 feet, and we can now write our for- 

 mula thus: 



Discharge in cubic ft. per second = 37. 6 v 



Dividing 0.37500 of a foot by 2,667 gives us for 

 a quotient 0.00014060742 of a foot and we can now 

 write our formula in this shape : The discharge of our 

 6-inch tile in cubic feet of water per second=37.6 

 V0.00014060742=the square root of the quantity un- 

 der the radical multiplied by the coefficient of con- 

 stant 37.6. The square root of 0.00014060742 is 

 0.011859 of a cubic foot and this multiplied by the 

 coefficient 37.6 give 0.4458984 of a cubic foot discharge 

 per second for our 6-inch tile drain= 16 $^ en S lc '.V P? r h T' 

 The algebraist can see through and apply the fore- 

 going formulas' instantly, and all farmers and oth- 

 ers interested, familiar with the principles of arith- 

 metic and who are in possession of two grains of 

 common, kinetic, working sense can compute by the 

 foregoing rules whatever he wants. Any one desir- 

 ing to examine the subject further the writer refers 

 him to the subject "Hydraulics," in John C. Traut- 

 wine's engineer's pocket book, page 538 of issue of 

 1876, and page 236 of issue of 1888. There he will 

 find formulae, rules and tables to his heart's content. 

 The writer feels that he should not cease this squib 

 without referring to an important matter in the con- 

 struction of tile drains. If you want a doctor, get 

 one. If you need a carpenter, get one. If you desire 

 a tile drain laid to a uniform gradient, get a com- 

 petent engineer to level it and' give you the cuttings 

 every 100 feet or oftener, measured from the tops 

 of the stakes driven even with the surface of ground. 



