EQUATIONS OF MOTION OF A VISCOUS LIQUID. 



PEARL, EUGENE DOUDNA, B. A., M. A. 



Historical Introduction. 



Two and a half centuries B. C, Archimedes (287?-212) 

 wrote a work entitled De lis Quae Vehuntur In Humido. 

 He maintained that every particle of a fluid mass, when in 

 equilibrium, is equally pressed in every direction. The laws 

 and properties of liquids were investigated by this ancient 

 mathematician sufficiently to enable him to devise a hydro- 

 static means of determining the purity of the precious metals. 

 He made a further practical application of the results of his 

 studies in this direction by the invention of the screw engine, 

 or the Archimedean screw. 



The Alexandrian School is accredited with the construc- 

 tion of a few hydraulic machines, such as the siphon and the 

 force pump. However, fluid motion was probably first studied 

 by a Roman, Sextus Julius Frontinus, inspector of the public 

 fountains at Rome in the reigns of Nerva and Trajan, about 

 the close of the first century A. D. In his work entitled 

 De Aquaeductibus Urbis Romcie Commentarius, is found a 

 description of the great aqueducts at Rome. Frontinus con- 

 structed five new aqiieducts, making in all fourteen. He also 

 describes the methods used in determining the amount of 

 water discharged from ajutages and the methods of dis- 

 tributing the water of the aqueducts and fountains. He 

 observed that the amount of water discharged depends upon 

 the height of the water in the reservoir above the orifice as 

 well as the area of the orifice. 



Fifteen centuries later Castelli (1628) advanced the theory 

 that the velocity of discharge is proportional to the height 

 of water in the reservoir above the orifice. Torricelli, a con- 

 temporary of Castelli, observing that a small jet of water 

 rushing from an ajutage rises to a height almost equal to 



