EXAMPLE. 149 



Cos. 1. As the ratio -^ of the sections decreases the 



A 



velocity decreases, becoming a minimum and = 

 when the cross-section Tc of the orifice is very small com- 

 pared with that of K, which agrees with (2) of Art. 76, as 

 it clearly should. 



COR. 2. As the ratio -j? increases the velocity increases, 



and it approaches nearer and nearer to infinity, the smaller 

 the difference between the two cross-sections becomes. If 

 Ic = K, (4) becomes 



from which we infer that, if a cylindrical vessel is without 

 a bottom, a liquid must flow in and out with an infinitely 

 great velocity, or else a section of the liquid flowing out of 

 the vessel can never be equal to a section of the vessel. If 

 a cylindrical tube be vertical, and filled with a liquid, the 

 portion of the liquid at the lower extremity, being urged by 

 the pressure of all above it, will necessarily have a greater 

 velocity than those portions which are higher, and therefore 

 (Art. 75) a section of the liquid issuing from the vessel 

 must be less than a section of the tube, i.e., the stream of 

 liquid will not fill the orifice of exit.* 



EXAMPLE. 



If water flows from a vessel, whose cross-section is 60 

 square inches, through a circular orifice in the bottom 

 5 inches in diameter, under a head of water of 6 feet, find 

 its velocity. Ans. 20.79 ft. 



85. Rectangular Orifice in the Side of a Vessel. 



To determine the quantity of liquid which will 



* Formula (4) was first given by Beruouilli, and was afterwards much disputed 

 (Weisbach'8 Mechanics, p. 804). 



