72 A MANUAL OF PHYSIOLOGY 



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 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 



FIG. 17. DIAGRAM TO ILLUSTRATE FLOW OF WATER ALONG A HORIZONTAL 



TUBE CONNECTED WITH A RESERVOIR. 



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 %mz> 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' + Jwz> 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 , 

 t.e., ^mv <1 = 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 



