164 COEFFICIENT OF EFFLUX. 



plate is 0.64. This ratio is called the Coefficient of Contrac- 

 tion* Denoting it by o, we have ak for the section of the 

 vena contracta, Tc being the section of the orifice (Art. 76). 

 Substituting ak for k in (6) of Art. 76, we have, for the 

 quantity Q l discharged, 



Q l = a kv = akVfyh = MkVfyh, (I) 



which is the quantity discharged in a unit of time. 



93. Coefficient of Velocity. The actual velocity of 

 discharge is found by experiments to be a little less than the 

 theoretical velocity, v */%gh. Experiments f made with 

 polished orifices have shown that the actual velocity is from 

 96 to 99 per cent, of the theoretical one. This loss of ve- 

 locity arises from the friction of the water upon the inner 

 surface of the orifice, and from the viscosity of the water. 

 The ratio of the actual velocity to the theoretical velocity is 

 called the Coefficient of Velocity. This coefficient is found 

 to be tolerably constant for different heads with well-formed 

 simple orifices, and it very often has the value 0.97. De- 

 noting the coefficient of velocity by <j>, and the actual 

 velocity by v lt we have 



v l = (j>v = <f>V2gh = .WVfyh, (1) 



which is the actual velocity of efflux. 



94. Coefficient of Efflux. If the value_of v l in (1) 

 of Art. 93 be substituted for the velocity Vtyh in (1) of 

 Art. 92, we have, for the actual discharge Q z , 



= .64 x .97&V20A = WkVZffh. (1) 



* This ratio is not constant, but undergoes variations by varying the form of the 

 orifice, the thickness of the surface in which the orifice is made, or the form of the 

 vessel. 



t Experiments made by Michelotti, Eytelwein, and others. 



