394 Mr. Challis on the general Equations 



and the pressure at the contracted vein is less than the atmo- 

 spheric pressure by g(k — h'), the weight of the column of fluid 

 in the cylindrical part of the tube. This agrees with Prop. iv. 

 of Venturi, if we leave out of consideration the ettects of the 

 inequalities of the tube. 



(3) Suppose a cylindrical tube to be fitted to a circular 

 orifice, and to be placed with its axis horizontal. When the 

 fluid fills the tube, the velocity of issuing into the air will be 



V ° ., , and the expenditure will consequently be increased 



1 — a" 



by the adjutage in the ratio of the area of the orifice, to the 

 transverse section of the stream at the vena contracta. This 



25 



ratio is found by experience to be --^. Venturi relates an ex- 

 periment, in which the time of expending a given quantity of 

 water through the orifice was 41", and through the tube 31". 

 By theory the latter interval is 261". This difference is shewn 

 by experiments to be principally owing to the retardation caused 

 by the inequalities of the tube, and the eddies and irregularities 

 of the motion within it. 



(4) Conceive the tube to be indented at the vena contracta, 

 so that the minimum transverse section may be the same as 

 the section of the contracted vein in air, and let it be required 

 to find the pressure at the minimum section. If p = this pres- 

 sure, it will be found, on taking the experimental value of the 

 velocity of issuing in the example just adduced, that 



i*-p=J(|J-) - ilgh = . 7. gh near\y. 



In an experiment in which h was 32.5 inches Venturi found 

 P-p to be the weight of 24 inches. Theory gives 22|, which is 

 as near as can be expected. 



