WATER. 



To apply thefe rules for gauging fluices, the following 

 nieafures muft be taken, i. The perpendicular depth of 

 the bottom of the aperture beneath the furface of the water. 



2. The perpendicular depth of the top of the aperture. 



3. The horizontal width of the opening. Then, taking the 

 difference between the two firll meafures leaves the height 

 of the opening. 



^ote. — If the aperture is not in a vertical plane, but in- 

 clined, as is frequently the cafe in mill-fluices, then the 

 width of the opening muft be meafured on the flope ; but 

 the depths muft always be taken perpendicularly beneath 

 the furface of the water. 



To make the calculation, find the mean velocity of the 

 effluent water, by calculating the velocity due to the depth 

 of the top of the aperture, and alfo for the bottom of the 

 aperture, and take a mean of the two. 



Note. — When the height of the aperture is lefs than one- 

 fourth of the whole depth, then the velocity due to the depth 

 of the centre of the aperture will be very near the truth. 



Having found the mean velocity in feet, multiply it by 

 the number of fquare feet in the area of the aperture, and it 

 will give the quantity difcharged, in cubic feet. 



Example I. — A fluice, which is four feet wide, is opened 

 or drawn feven inches, and the depth of water above the 

 centre of the orifice is ten feet. The edges of the fluice 

 are cut fharp, fo that the borders of the orifice are hke a 

 thin plate. What is the velocity and difcharge per minute 

 in cubic feet ? 



The fquare root of 10 is 3.162, which x 297.45 from the 

 table, gives 940.6 feet per minute, for the mean velocity of 

 the water. 



The area of the aperture is 4 feet, which x 7inches,= 28 -r 

 12= 2.333 fquare feet, for the area of the aperture ; there- 

 fore, multiply 940.6 by 2.333, ^"^ ^^^ ^^'^^ 2194 cubic 

 feet per minute, for the quantity difcharged. 



If the depth had been exprelTed in inches, it would have 

 been 120. The fquare root of this is 10.95, andthis multiplied 

 by 85.87, gives 940.6 feet per minute for the velocity, as be- 

 fore. In like manner, the table gives the proper multipliers 

 for finding the velocity in ket per fecond, if it is required. 



If it was only required to obtain the quantity difcharged, 

 we may proceed more direftly, thus. The depth is 10 

 feet, and the fquare root is 3.162, x by 2.065, ^^^ number 

 taken from the laft column but one of the table, and we 

 have 6.529 cubic feet, which are difcharged per minute 

 from every fquare inch of the aperture. The aperture is 

 48 inches, this x 7 = 336 fquare inches, this x 6.529 = 

 2194 cubic feet difcharged as before. 



If the depth had been 120 inches, then the fquare root of 

 that number = 10.95, ^^'^ '1^'^ ^ •59^3' ^^^ number in the 

 laft column gives 6.529, as the laft. 



Another method is, to calculate the theoretic difcharge, 

 and then make a proper reduftion, by multiplying by the 

 decimal number in the firft column. Thus, by our firft 

 table of velocities, 120 inches deep = 152 1.8 feet per 

 minute, this x by 2.333 fquare feet, the area of the aperture 

 gives 3550 cubic feet per minute for the theoretic difcharge. 

 The tirft column of the prefent table (hews that the real 

 difcharge is only .618 of the theoretic difcharge ; therefore, 

 multiply 3550 cubic feet by .618 =: 2194 cubic feet for 

 the real difcharge, as in all the former cafes. 



This latter method is very convenient, becaufe we can 

 apply a different correftion in different cafes, according to 

 difcretion, and the table of velocities facilitates the calcula- 

 tion very much. 



Example 2. — A flour-mill was worked by the water 



which ran through a (huttle four feet wide, the depth to tl.c 

 bottom of the aperture was 22 inches, and the fhuttle was 

 aravvn up one mch and one-quarter, fo that the depth to the 

 top of the aperture was 20.75 '"ches ; what is the expen- 

 diture per minute ? 



The full velocity due to 22! <- ^ r 



inches depth is by the table j ^J'-'^ feet/^r minute. 

 Ditto - . for 2o|- 632.7 



2)1284.3 



64 2 . 1 5 mean velocity per min , 



Note.— A-i 20.75 is not to be found in the table, 

 take 2o| ^ 628.8, and add to it half the difference between 

 2oi and 21, v'fz. 3.9 = 632.7 ktl per minute velocity for 

 20.75? *^ auOvt. 



The area of the aperture 48 inches, x 1.25 inches = 60 

 fquare inches, - 144 = .4166 fquare feet. Multiply this 

 by the velocity — 642.15 feet, and it gives 267.5 cubic feet 

 per minute discharged according to theory. 



To reduce this to the pradlical difcharge, multiply by 

 fomeof the numbers in the firft column of the Table oppo- 

 fite, according to the nature of the aperture. The fluice was 

 in a trough, nearly of its own dimenfioiis ; fo that the bottom 

 and fides nearly correfponded with the aperture ; therefore, 

 take .860, and x 267.5 g'^^s 238 cubic ket per minute. 



It is very convenient to an engineer to be able to calculate 

 the difcharge of water by means of the flide-rule. This 

 he may do by means of the two lines ufually marked C and 

 P ; C being a line of logarithms, and D a line fimilarly 

 divided on a fcale twice as large. By means of thefe, the 

 fquare root of any number can be extracted and multiplied by 

 any number at one operation. To ufe it, find the multi- 

 plier which is to be ufcd, upon the line D, and fet the 

 Aider fo that 10 upon C will correfpond with it ; then feek 

 for the depth upon C, and oppofite to it upon D, the re- 

 quired velocity will be found. 



Thus, 

 Line on the Cider marked C, depth in inches, i o 



Line on the rule marked D, velocity in {eetper minute, 85.8 

 And in like manner for any other multipliers : for 

 inftance. 

 Line on the Aider marked C, depth in inches 10 



Line on the rule marked D, cubic feet /fr minute 



1 



difcharged through a J- .596 



fquare inch, 



Mr. Eytelwein obferves, from Du Baat, that the difcharge 

 through an orifice communicating between two refervoirs, 

 and fituated beneath the furface of the water in the lower 

 refervoir, is the fame as if the water run into the open air, 

 taking the difference of level between the two furfaccs, for 

 the depth of the column ; he calculates the difcharge when 

 the water has to pafs through feveral orifices in the fides of 

 as many refervoirs open above. In fuch cafes, where the 

 orifices are fmall, the velocity in each may be confidered 

 as generated by the dift'crence of the heights in the two 

 contiguous refervoirs ; and the fquare root of the dilTerence 

 will therefore reprefent the velocity which muft be generated 

 in the feveral orifices, inverfely as their refpeftive areas, fo that 

 we may calculate from hence the heights of the different 

 refervoirs when the orifices arc given. Mr. Eytelwein alfo 

 confidcrs the cafe of a lock, which is filled from a canal of 

 Q 2 an 



