WATER. 



have before direfted, and take two-tliirds of the produft for 

 the mean velocity ; this multiphed by the number of fquare 

 feet in the area of the feftion of the aperture, will give the 

 cubic quantity of water which flows per minute in cubic 

 feet. Note, in taking the area of the feftion, we muft meafure 

 the whole depth from the level furface, and multiply it by the 

 horizontal width of the aperture, and not fimply the feftion of 

 the water. This is becaufe, the theory upon which the rule 

 is founded fuppofes the water in the aperture to have no ve- 

 locity at the furface, and to be upon the level of the Handing 

 water. Neither of tliefe fuppofitions is true in reality, 

 but the refult is very nearly true, bfcaufe the feftion 

 of the moving water is diminilhed in proportion to the ve- 



locity which the water has at the furface, and in eonfequence 

 the errors of the two alTumptions always correft each 

 other. 



We have therefore only to apply a correft theorem to 

 obtain the velocity due to the whole depth, according to the 

 nature of the aperture, and take two-thirds of the produft. 

 All the neceffary information for this purpofe may be taken 

 from the table of multipliers laft given, for the velocity of 

 the difcharge through apertures ; or otherwife, if we take 

 the velocity at the bottom, and multiply it by the depth, 

 and take two-thirds of the produft, we fhall have the mean 

 velocity. But to make the fubjeft clear we (hall give 

 another table for this objeft. 



Rules for obtaining the Velocities and Quantities of Water difcharged through reftangular Apertures, which are open 



at Top. 



Defcription of the Aperture. 



Nb(e. — The depths are fuppofed to be roeafured from the level furface of the tvater 

 to the bottom of the aperture, in inches. 



To find the mean \'e- 

 locity of the Water 



running tlirough the 



Aperture in Feet ^tr 

 Minute. 



Rule. — Multiply ihe 

 Square Root of the 

 Depthin Inches, l>y 

 fome one of tlie fol- 

 lowing Numbers, 

 according to the 

 Cafe. 



To find the Number of 

 Cubic Feet difcharged 

 per Minute through 

 each Inch in Width 

 of the Aperture, 

 liulc. — Multiply the 

 Square Root of the 

 Cube nf the Depth 

 in Inches, by foaie 

 One of the follow- 

 ing Numbers, ac- 

 cording to the Cafe. 



For a fmall aperture ih one fide of a large refervoir, the bottom") 

 and fides of which do not correfpond with the aperture, fo as to I 

 lead the particles of water thereto in a ftream ; the edges of the | 

 aperture againft which the water runs is fuppofed to be fharp and 

 made of thin plate; the aperture not to exceed i8 inches long 

 and nine inches deep - . . - . 



For an aperture under the fame circumftances as the former, but 

 made in a plank with edges from half to one inch thick 



For an [aperture of great breadth and more than nine inches deep, 

 fuch as the weir or dam in a river ; it is fuppofed that the 

 water runs over the edge of a plank or wafte board, one or two 

 inches thick ..... 



For an aperture of which the bottom is on a level with the bottom") 

 of the refervoir, or for a weir which occupies the whole breadth 

 of a river, and where the water flows over the top of a broad 

 ftone-wall fo floped as to condudl the water to the paffage -_ 



For the full difcharge according to theory, fuppofing no lofs from' 

 friclion. Very large and deep weirs will come near to this 



57.24^5 



•39754 



When the aperture occupies nearly or the whole width of 

 the refervoir, there is no level furface of the water above the 

 aperture, becaufe the water is continually ruiniing towards 

 the aperture in a llream ; fuch is the cafe of a tveir acrofs a 

 river, or when water fpouts out of the open end of a reft- 

 angular trough. 



It is extremely difficult to meafure the exaft height of 

 the water above the bottom of the aperture, for the curva- 

 ture of the furface of the water will begin feveral feet up 

 the (Iream before it arrives at the aperture ; and there muft 

 be fomething arbitrary in the meafurement, becaufe the fur- 

 face of tlie water, even where there is no curvature, is not 

 horizontal but (loping, when the w.-iter is in motion. In 

 fucli cafes, the depth muil be taken beneath the inchncd fur- 

 face of the water, if we fuppofe the fame prolonged until it 

 reaches the aperture, which can eafily be done, by ilretching 



a fine along the furface of the water fo as to correfpond 

 therewith, at the part above where the curvature com- 

 mences. 



We muft alfo make fome addition to the difcharge, on ac- 

 count of the motion which the water po{re(res before it comes 

 to the aperture ; to do this with accuracy, we may meafure 

 the regular velocity of the ftream, by throwing in floating 

 bodies, and obferving tlie dillance they pafs through in a 

 given time, taking care that we make this obfervation at a 

 part of the channel, where the furface is in a regular motion 

 and not in a ftate of acceleration, becaufe what we want is 

 the velocity of the water at that point where the curvature 

 begins, in eonfequence of the defcent through the aperture. 

 Now Avhen the channel is not of an uniform breadth and 

 depth, as in a mill-dam for inftance, tlie velocity of every 

 part of the ftream is different, we (hall then find difficulty in 



meafuring 



