WATER. 



water, from fprings at Comifton, which is a confiderable dif- 

 Unce ; this is conveyed by two pipes, the firft of which was 

 laid in 1720, under the diredion of Defaguhers. Dr. Ro- 

 bifon mentions one of them, which is 5 inches diameter, 

 14,637 feet in length ; the refervoir at Comifton is torty- 

 four feet higher than the refervoir on the Caftle-Hil., m the 

 town of Edinburgh. 



Firft, to find the fine of the inclination, or s, divide the 

 faU 44 feet by 14,637, and it gives .00301, which is s. 



Now take five inches, the diameter of the pipe in col. i., 



and oppofite to it in col. 2. find — = 1597CO, which mul- 

 tiply by .00301, gives 479.1 ; to this add— = 2.624taken 



from the third column, and the fum is 481.724. 



Extrad the fquare root of this, and it is si. 948, from 



which dedua— , or 1.620, taken from col. 4., and the re- 



a 

 fult is 20.328, which is the velocity in inches per fecond, 

 and this x by 5 = 101.64 feet />fr minute. 



To find the quantity, find the area of the feftion of the 

 pipe in fquare feet, by dividing the fquare of the diameter 

 25 by 183.3, ^"^ ''^ g'^*^^ .I364fquare feet, and this x by 

 101.64 feet velocity, gives 13.86 cubic feet per minute for 

 the difcharge from the pipe. 



Dr. Robifon's c.ilculalion of this fame cafe by Du Buat's 

 formula, gives a velocity of 20.08 inches per fecond. 



In Mr. Smeaton's Reports, we find the other pipe ftated at 

 four and a half inches bore, and that it yielded 160 Scots 

 pints per minute, each 103.4 cubic inches = 9.58 cubic feet. 

 Mr. Smeaton's own calculation was 159 pints. 



Example 2 Mr. Smeaton ftates, that this pipe was im- 

 proved by obtaining an increafe of fall, making it 51 

 feet, and that it then yielded 200 Scots pints = 11.98 

 cubic feet per minute, the bore being 4-| inches, and the 

 length 14,637 feet as before. Mr. Smeaton's calculation 

 was 173 pints = 10.36 cubic feet per minute. What 

 would it be by Dr. Young's theorem ? viz. velocity = 



fall 51 feet by the length 14,637 



The fquare root of that number is 22.609, fro''* which 

 deduft — , = 1.854, ^"^ '*^ leaves 20.755, which is the velo- 

 city per fecond in inches. 



[Note. — is found by fubtrafting half the difference be- 

 tween the numbers for 4 and 5 in the fourth column, from 

 the number anfwering to 4. ) 



20.755 inches per fecond x 5 = 103.775 feet per mi- 

 nute, tor the velocity. The area of the pipe is 4.5 x 

 4.5 = 20.25 circular inches, which ~ by 1 83.3, the cnxular 

 inches in a fquare foot, is = .1104 fquare feet for the area 

 of the pipe. Multiply this by 103.775 ket per minute, and 

 we get 1 1.46 cubic feet per minute for the difcharge, which 

 agrees very nearly with the experiment. 



Dr. Brewfter, in his Encyclopaedia, has calculated this 

 fame pipe, except that he ftates it 300 feet longer ; he 

 makes the velocity by Du Buat's theorem 20.385 inches ^i;r 

 fecond, and fays that on an average of five years, from 1738 

 to 1743, its maximum difcharge was 11.3 cubic feet per 

 minute ; he has alfo calculated the fame cafe by five different 

 formulas ; thus. 



The quantity of water aftually 

 difcharged . - . 



Calculated by Eytelwein's for- 

 mula . . . . 

 Calculated by Girard's formula 

 Calculated by Du Buat's formula 

 Calculated by M. Prony's fimple 

 formula . . . . 

 Calculated by M. Prony's table - 

 To which we may add Mr. Smea- 

 ton's calculation . - . 

 And by Dr. Young's theorem - 



Scot's'l'infs 

 pel- Miiiule. 



J 200 

 j 189-4 



I 189-77 



188.26 

 188.13 



I 192-32 

 180.7 



I9I.5 



Cubic Feet 

 per Minute. 



11.968 



.n-333 

 11.355 



1 1.265 

 11.257 



11.502 



10.S13 



10.352 



11.459 



d 



— X 

 a 



t + 



\ 



To find X, divide the 

 feet ; it gives .003484. 



To find — , anfwering to 4.5 inches in col. i., take half 

 a 



the difference between the numbers in the fecond col. op- 

 pofite to 4 and 5, and add it to the number anfwering to 



4; thus, — for 4 is 131560, and — for 5 is 159700, 



difference 28200, which -^ 2 = 

 = 145600, which is — for 4.5 



14100, and this X 131500 

 Multiply this 145600 



by s, or .003484, and it is =: 507.67 : to this add — . 



To find — for 4.5, take half the difference between the 

 a' 



numbers in the third column for 4 and 5, which is .869, 

 and fubtract it from 4-363, the number anfwering to 4; 



the refult is 3.494, 

 507.67 is 511.164. 



w] 



hich 



is — for 



4-5 ; this added to 



It is fatisfaftory to find the refults of fo many different 

 proceffes agree fo nearly, and gives us', great confidence 

 in the truth of the principles. There is in this cafe fo little 

 difference amongft theorems that any one may be taken ; 

 but we think it needlefs to enter into farther particulars, as 

 the one which we have given effefts all that can be defired, 

 and by the help of the table, is the moft ready in the appli- 

 cation. 



We fhall only add Mr. Smeaton's table on the friftion of 

 water running through pipes, which we find in his manu- 

 fcript papers, and which he computed from his own 

 obfervations alone, without knowing the experiments on 

 which the other theorems are founded. They will give ra- 

 ther lefs than the theorems, and perhaps may approach more 

 nearly to aftual praftice, in which pipes are not laid with the 

 fame care, to avoid roughnefs withinfide and fudden bends, as 

 when prepared purpofely for experiments ; we may confider 

 the theorems as the maximum difcharge, and Mr. Smeaton's 

 table as the fair average of practice. 



life of the Table. — Find the velocity of the water ^fr 

 minute in feet and decimals in the firft column, or in feet 

 per fecond in the next column, and on the fame line under- 

 neath the diameter of the bore in inches, you will find the 

 perpendicular heightof a column of water in inches and lotliS, 

 neceffary to overcome the fridtion of that pipe for 100 feet 

 in length, and obtain the giyen velocity. 



9 Mr. 



