Chap. XX.] FLOW OF LIQUIDS THROUGH TUBES. 21 3 



velocity of efflux at b, however, is less than this, be- 

 cause much of that pressure has been lost in over- 

 coming the resistance due to friction. The total re- 

 sistance to be encountered would be measured by the 

 height of the column of liquid that would be sup- 

 ported at the point by the pressure along the hori- 

 zontal tube, and this height is OP, the level at which 

 the dotted line joining the surfaces of the liquid in 

 the piezometers strikes the reservoir. Thus, of the 

 total effective force HO of the head of water in the 

 reservoir, the total charge of the reservoir, as it is 

 called, the portion PO is required to overcome the 

 resistance encountered in the horizontal tube. There 

 remains only the portion HP to determine the velocity 

 of efflux at the outlet b. Suppose the end 6 of the 

 tube to be blocked, and an opening directed upwards 

 made instead, the water would issue from the tube ab 

 in an upward jet, and the height of that upward jet 

 would be a measure of the velocity of efflux ; that is, 

 the velocity which a body would acquire in falling 

 from rest through that distance is the velocity of dis- 

 charge. The height of the upward jet is the same 

 as the height HP. The velocitv of flow is uniform 



^j t/ 



(constant) throughout the whole length of the tube. 

 To sum up : 



(1) The rate of discharge is equal to the total 

 charge of the reservoir less the force required to over- 

 come the resistance. 



(2) The resistance is directly proportional to the 

 length of the tube. 



(3) Further, the resistance increases with the speed 

 of the stream. Since the resistance is due to the 

 friction of the molecules of the liquid at the centre of 

 the stream with the molecules outside of thern> which 

 are retarded more and more as they are nearer to 

 contact with the sides of the tube, it is evident when 

 there is no movement there is no friction, and as the 



