54 HYDRAULICS AND ITS APPLICATIONS 



When the velocities are decreased between each pair of experiments, it 

 is found that the plotted points follow the straight line C B D to its 

 intersection D with D O, indicating that eddies once initiated do not die 

 out until the velocity is reduced to that corresponding to D. The velocity 

 at D, which is less than that at A, is termed the lower or true critical 

 velocity. 



For velocities between D and A the motion, if steady, is unstable, 

 and any initial disturbance will produce eddy motion which will not 

 die out. 



A consideration of the part of the log /?, log v, curve between A and B, 

 shows that here the value of n is greater than before A or after B, and 

 that with motion of this intermittently unsteady or unstable type the 

 increased resistance accompanying an increase in velocity is greater than 

 even when the motion is altogether sinuous. This would appear to be 

 due to the fact that within this range of velocities eddies are being 

 initiated in the tube, and the loss of head in the tube is due, not only to 

 the actual resistance to motion, but also to the absorption of energy in 

 eddy formation. After B is passed the eddies fill the whole length of 

 tube, and the loss of head is then simply due to resistance to motion 

 through the tube, i.e., to the maintenance, as opposed to the initiation, 

 of eddy motion. 1 



As a result of his experiments, Eeynolds concluded that the critical 

 velocity is inversely proportional to the diameter d of the pipe, and is 

 given by the formula 



1 P 



Vc= -b'd' 

 where b is a numerical constant. 



-P a rc g -+ , and therefore depends on the temperature of the 

 water. 



If t = temperature in degrees centigrade, then for water the value of 

 P is given by 



P= 



1 + '03368 t + -000221 t 2 ' 



1 Messrs. H. T. Barnes and E. G. Coker, " Proc. Koy. Soc.," vol. 74, determined the 

 critical velocity by allowing water to flow through the given tube, which was jacketed 

 with \vateratahighertemperature. A delicate thermometer indicated the temperature of 

 the discharge water at exit. So long as the motion is steady, the transmission of heat through 

 the water takes place entirely by conduction and is extremely slow, so that the thermometer 

 gives a steady reading practically identical with that in the supply tank. Immediately the 

 critical velocity is attained, however, the temperature of discharge increases rapidly and the 

 change from Mr-adv t. unsteady motion is manifested by a sudden jump of the mercury 

 thiead of the thermometer. 



