76 A MANUAL OF PHYSIOLOGY 



particles next this stationary layer rub on it, so to speak, and are 

 retarded, although not stopped altogether. The next layer rubs on 

 the comparatively slowly moving particles outside it, and is also 

 delayed, although not so much as that in contact with the immovable 

 layer on the walls of 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 over- 

 coming 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- 



FIG. 21. DIAGRAM TO ILLUSTRATE FLOW OF WATER ALONG A HORIZONTAL TUBE 

 CONNECTED WITH A RESERVOIR. 



section of the free end of the tube be joined to the centres oj: 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 2 , 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' 

 +^mv 2 , i.e., %mv 2 = 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 



