COEFFICIENT OF CONTRACTION. 163 



of the liquid surface. Experiment shows, however, that 

 this is not the case. The liquid does not issue in the form 

 of a prism, and hence the quantity discharged in a unit of 

 time is not measured by the contents of a prism whose base 

 is the orifice and whose altitude is the velocity; this would 

 give the theoretical discharge (Art. 76, Cor. 3), hut the prac- 

 tical discharge is generally much less. When a vessel 

 empties itself through an orifice, it is observed that the 

 particles of liquid near the top descend in vertical lines ; 

 but when they approach the bottom they take a curvilinear 

 course, being turned in towards the orifice, or spirally 

 around it, and this deviation from a vertical rectilinear path 

 is the greater the further the horizontal distance of the 

 particles is from the orifice. The oblique direction of the 

 exterior particles within the vessel continues through the 

 orifice, and gives the stream of liquid, in issuing from the 

 orifice, nearly the form of a truncated cone or pyramid, 

 whose larger base is the area of the orifice. This diminu- 

 tion in the size of the issuing stream is called the contrac- 

 tion of the vein, and the section of the stream at the point 

 of greatest contraction is called the Vena Contracta,* or 

 contracted vein. 



From the results of most experiments, the vena contrada, 

 when the orifice is a circle, is at a distance from the orifice 

 equal to the radius of the orifice. 



92. Coefficient of Contraction. When water flows 

 through orifices in thin plates, it has been found, by meas- 

 urements of the stream, made by different experimenters, 

 that its diameter at the vena contracta is about 0.8 of the 

 diameter of the orifice. The ratio, therefore, of the cross- 

 section of the vena contracta to that of the orifice in a thin 



* This name was first given by Newton, who also showed that, by taking the 

 area of the vena contracta as the area of the orifice, and reprarding the height of the 

 surface above the vena contracta as the height of the vessel, the theoretic discharge 

 agreed far more closely with the practical. 



