181 



1. The increase of sectional area. The velocity is inversely pro- 

 portional to the whole sectional area of the branches. 



2. The increase of resistance, due to the great extent of surface 

 contact between the moving fluid and the fluid that wets the walls 

 of the tubes. The resistance is proportional to the surface area, 

 nearly proportional to the square of the velocity, and inversely pro- 

 portional to the sectional area. The formula used by engineers for 

 what they call "skin fraction" is R = S0 2 , where R = resistance ; 

 k, a constant; S, surface area; v, velocity. 



If water flows from a head of pressure through a tube on which 

 stand a number of vertical side tubes, it is found that, according to 



D E 



H 



n 



, 86. SCHEMA TO SHOW EFFECT OF INTRODUCING RESISTANCE. 



the degree that the outflow from the tube is obstructed, so will the 

 water rise in the side tubes ; the nearer the side tube to the head of 

 pressure, the higher the fluid rises in it (Fig. 86). 



This is because water flowing through a tube from a constant head 

 of pressure encounters a resistance occasioned by the friction of the 

 moving water particles against each other and against the stationary 

 layer that wets the wall of the tube. Part of the potential energy of 

 the head of pressure is spent in endowing the fluid with kinetic energy, 

 part in overcoming this resistance. The 'latter and greater part is 

 rubbed down into heat. The narrower the tube is made, the greater 

 the friction, until finally the flow ceases, the total energy being then 

 insufficient to overcome the resistance. 



This is well exemplified by the modified schema (Fig. 86). W is a, 

 bottle containing coloured water connected to the rigid tube X, on which 



