408 Mr. L. R. Wilberforce on the Calculation of the 



Then the kinetic energy carried out by the issuing fluid per 

 unit of time is 



C r K 2 



1 p 2irz dz.£ X ~ — irpr 2 v 3 

 Jo " l 



Let the transpiration take place under the pressure due to a 

 column of the liquid of height h, then Hagenbach's reasoning- 

 is as follows : — If there were no fluid friction, and the flow 

 took place under the pressure due to a height hf, the velocity 

 of efflux would be </%gh!, and the kinetic energy leaving the 



7* 3 



tube per second would be irp -^ (2gh f ) 2 ; hence we must correct 

 h by the subtraction of a quantity ft! given by the equation 



^p 7 ^(2gh / ^=7rpr 2 v% 

 whence 



¥= -i- £ 



This reasoning is clearly fallacious ; for the pressure which 

 must be applied to produce a certain amount of kinetic energy 

 per unit time will depend upon the work done by the pressure 

 in that time,, i. e. upon the volume of fluid issuing ; and this 

 volume in the actual case differs from that in the ideal case 

 considered by Hagenbach. 



The correct reasoning from the same assumptions is as 

 follows : — The volume of fluid which actually flows through 

 the tube under a pressure due to the height h is, per unit of 

 time, irr 2 v. The energy supplied to this is therefore irr 2 v ghp, 

 and the kinetic energy which it possesses on issuing is 7rpr% 3 ; 

 hence the energy converted into heat within the tube is 



irr^pvg ih ). Thus the head h must be corrected by sub- 



v 2 1 v 2 



tractino- from it — instead of ttt — . 



9 v\g 



Hagenbach tested his method of correction by applying it 

 to a set of very rough experiments of his own, made at 

 slightly varying temperatures, and in which, as it appears, the 

 liquid was allowed to issue into the air, so that there was a 

 capillary back-pressure of varying magnitude. The reduced 

 results which he obtained agreed verv badly when the cor- 



