COEFFICIENT OF RESISTANCE. 167 



giving a discharge greater than that which is due to the sec- 

 tion cd of the pipe. Since fi = .615 for a simple orifice, it 

 follows that the discharge through the compound mouth- 

 piece 



'-- = 2.5 times the discharge through a 

 simple orifice in a thin plate, 



1.5526 . .... 



and = = 1.9 times the discharge through a 



short cylindrical tube. 



In the experiments made by Eytelwein, the interior diam- 

 eter ab was about 1.2 times the diameter cd, and the sides 

 ch and dk made with each other an angle of 5 9'. 



96. Coefficient of Resistance. When water flows 

 from a cistern through a tube kept constantly full, it fol- 

 lows that the coefficient of contraction of this mouth-piece 

 = unity, and that its coefficient of velocity = its coef- 

 ficient of efflux fi. 



Let W be the weight of water discharged with the actual 

 velocity v, and v l the theoretical velocity of discharge due 

 to the head of water h. Then the actual kinetic energy, or 

 stored work, of the weight W of water, which issues with a 

 velocity v. 



= W (Anal. Mechs., Art. 217). (1) 



But since the theoretical velocity of efflux = v l} the 

 theoretical kinetic energy or stored work of the weight W 



of water discharged 



?. 2 

 = T*-W. (2) 



} . i * * 



Hence, the loss of kinetic energy or stored work of the 

 weight W of water discharged, during the efflux 



\ v l "~~ v ^) oTT" V / 



