ON THE FRICTION OF FLUIDS. 227 



discharge about five times as much water as the former, although of only 

 twice the diameter ; and this circumstance requires the attention of all those 

 who are concerned in regulating the distribution of water by pipes- for 

 domestic use, or for any other purpose. 



In such cases it becomes also frequently necessary to attend to the angle 

 in which a small pipe is inserted into a larger ; whenever a pipe is bent, 

 there is a loss of force according to the degree of flexure and to the velocity 

 of the water, which may be calculated, if it be required ; but if a pipe be 

 fixed into another through which the water is moving very rapidly in a 

 direction contrary to that of the stream, its discharge will not only be much 

 smaller than if the directions more nearly coincided, but sometimes such a 

 pipe will discharge nothing at all ; on the contrary, like the air in Hauks- 

 bee's experiment, the water which it contains may be dragged after the 

 stream in the larger pipe. 



The bad effect of unnecessary dilatations, as well as contractions, in aque- 

 ducts and in pipes, may be understood from what has been already said of 

 the loss of force attendant on every change of velocity ; a circumstance of 

 a similar nature sometimes happens in the animal economy. When an 

 artery is dilated so as to form an aneurism, it has been observed that the 

 artery is usually distended above the cavity ; and this effect is easily un- 

 derstood from the actual increase of resistance which the aneurism pro- 

 duces, united perhaps with the previous debility of the artery. 



Mr. Gerstner* has found by some very accurate observations on the 

 motion of water in very small pipes, that the resistance is considerably 

 affected by the temperature at which the experiment is performed ; but in 

 the cases of rivers, and of such pipes as are commonly used in practice, no 

 variations of temperature to which they can be liable, will produce any 

 sensible effects. His experiments indicate a resistance, where the tubes are 

 very small, which follows a law so different from that which is observed in 

 more common cases, that it appears to be owing to some other cause : this 

 cause is perhaps the capillary attraction of the open end of the tube, and it 

 is the more probable that the resistance depends on some such circumstance, 

 as there is reason to think that the irregularity may be in great measure 

 removed by placing the tube wholly under water. 



LECT. XXIV. ADDITIONAL AUTHORITIES. 



Castelli, della Mensura dell' Acque correnti, 4to, Rome, 1628. Toricellius^ de 

 Motu gravium naturaliter accelerate, 1643. Varennius, by Jurin and Shaw, 1765. 

 Guglielmini, Aquarum fluentium Mensura, 2 vols. 4to, Bonon, 1690-91. Epistolse 

 duse Hydrostatics, 4to, Bonon, 1692. Della Naturadi Fiumi, 2 vols. Milan, 1821. 

 Polenus, see Lect. XXIII. Jurin, De Motu Aquse fluentis, 4to, Venetii, 1724. 

 Frisius, Del Mododi regolare i Fiumi, 4to, Lucca, 1762 ; Paris, 1774 ; Lond. 1818. 

 Lorgna, Ricerca intorno alia Distribuzione della Velocita nella Sectione de' 

 Fiumi, 4to, Verona, 1771. Stattleri Physica, 8 vols. Augsb. 1772. Euler on the 

 Motion of Rivers. Hist, et Mem. de Berlin, 1760, p. 101. Ximenes on the 

 Velocity of Rivers. Atti dell' Academia di Siena, iii. 16 ; vi. 31 ; vii. 1. Les- 



* * On the Discharge of Water at different Temperatures. Abhandlungen der 

 Bohmischen Gesellschafft der Wissenchaften, 4to, Prag. 1798. Gilbert's Journal, 

 v. 160. 



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