8 4 



THE CIRCULATION OF THE BLOOD AND LYMPH 



the tube. In this way it comes about that every particle of the liquid 

 is hindered by its friction against others those in the axis of the tube 

 least, those near the periphery most and part of the energy of position 

 of the water in the reservoir is used up in overcoming this resistance, 

 only the remainder being transformed into the visible kinetic energy 

 of the liquid escaping from the open end of the tube. 



If vertical tubes be inserted at different points of the horizontal 

 tube, it will be found that the water stands at continually decreasing 

 heights as we pass away from the reservoir towards the open end of 

 the tube. The height of the liquid in any of the vertical tubes indicates 

 the lateral pressure at the point at which it is inserted; in other words, 

 the excess of potential energy, or energy of position, which at that 

 point the liquid possesses as compared with the water at the free end, 

 where the pressure is zero. If the centre of the cross-section of the 

 free end of the tube be joined to the centres of all the menisci, it will 

 be found that the line is a straight line. The lateral pressure at any 

 point of the tube is therefore proportional to its distance from the free 

 end. Since the same quantity of water must pass through each cross- 

 section of the horizontal tube in a given time as flows out at the open 

 end, the kinetic energy of the liquid at every cross-section must be 



constant and equal to %mv 2 , 

 where v is the mean velocity 

 (the quantity which escapes in 

 unit of time divided by the 

 cross-section) of the water at 

 the free end. 



Just inside the orifice the 

 total energy of a mass m of 

 water is mgh; just beyond it 

 at the first vertical tube, mgh' 

 + \mv z , where h' is the lateral 

 pressure. On the assumption 

 that between the inside of the 

 orifice and the first tube no 

 energy has been transformed 

 into heat (an assumption 

 the more nearly correct the 

 smaller the distance between 



it and the inside of the orifice is made), we have mgh = mgh' + 1 mv 2 , 

 i.e., lmv* = mg(h-h'}. In other words, the portion of the energy of 

 position of the water in the reservoir which is transformed into the 

 kinetic energy of the water flowing along the horizontal tube is measured 

 by the difference between the height of the level of the reservoir and 

 the lateral pressure at the beginning of the horizontal tube that is, 

 the height at which the straight line joining the menisci of the vertical 

 tubes intersects the column of water in the reservoir. Let H represent 

 the height corresponding to that part of the energy of position which 

 is transformed into the kinetic energy of the flowing water. H is easily 

 calculated when the mean velocity of efflux is known. For v= *j2gH 

 by Torricelli's theorem (since none of the energy corresponding to H 



is supposed to be used up in overcoming friction), or H- v -. At the 



second tube the lateral pressure is only h". The sum of the visible 

 kinetic and potential energy here is therefore Imv^+mgh". A quantity 

 of energy mg(h - h") must have been transformed into heat owing to 

 the resistance caused by fluid friction in the portion of the horizontal 



Fig. 26. Diagram to illustrate Flow of 

 Water along a Horizontal Tube connected 

 with a Reservoir. 



