622 HYDRAULICS AND ITS APPLICATIONS 



while (3) becomes : 



7, 7, 7, _ hy a 



li ii li -- 





A a 







4- 



But without air vessel, so long as separation does not occur : 



A 



a! d = a 



__ 



An examination of this equation indicates that the change in the 

 retardation in the delivery pipe, and therefore in the pressure in the 

 pump, due to the provision of the chamber, increases with an increase 

 in a v , and since li v is in general small compared with h d , diminishes with 

 an increase in h v . It follows that the mean level in the air vessel should 

 be reduced to the lowest practicable limit, and that h a should be as large 

 as practicable, i.e., the air supply should be maintained so as to keep the 

 water-level as low as is consistent with the air vessel still containing some 

 water at the end of the delivery stroke. 



The modifying effect of frictional resistances may be examined as in 

 the case of the suction air vessel. In general, owing to the fact that the 

 delivery head is much greater than the suction head, and that the water 

 at high pressure is able to dissolve an increased volume of air, the air in 

 the vessel is gradually absorbed, so that either some device must be fitted 

 for renewing the supply, or an air vessel of such dimensions must be 

 fitted as will enable the mean level to be maintained fairly constant over 

 long periods of working. In practice, with a single-barrel double-acting 

 pump, the delivery air vessel usually has a volume equal to from six to 

 nine times the pump displacement per revolution, depending on 

 (increasing with) the speed of rotation and the length of delivery pipe. 

 Here, again, an increase in the area of the vessel is of greater advantage 

 than an increase in its length. 



