WATEK HAMMER 



223 



at any point in the pipe the acceleration is ^ , the force per pound 

 necessary to produce this acceleration is -r-, and the work done by 



O Ct v 



this force while motion takes place through a small distance B x is 



1 dv , 

 j . Bx. 

 g d x 



Similarly, if the work done against frictional resistances is expressed as 



FIG. 102. 



fv* 

 ~- - per lb., per unit length of the pipe, as is usual, the equation as 



finally modified for friction and for acceleration becomes 



Ax w 2g j " g dt 2gm J 



where z is the height of a given point in the fluid, above datum level, and x 

 is its distance from some abitrary point, measured in the direction of flow. 

 This equation is true even if the pipe line be not uniform in diameter. 

 Integrating both sides of (2) with respect to x we get 



P + +z=-L{ X ^dx--L{ X M X + c (3) 



w 2g g J O dt 2gmj o 



Whenever the acceleration is a known function of the time or of the 

 distance travelled by a particle, equation (3) may be solved and the 

 pressure at any point obtained. 



