THE LAWS OF FLUID RESISTANCE. 



101 



illustrates these propositions, making allowance for the 

 frictional gradient. 



h k I e f g a b c (see Fig. 12) is a continuous series of 

 glass tubes, through which water is flowing from the 

 cistern n to the outlet m. The cistern is kept full to a 

 certain level. The tube from h to I is what I have called 

 an enlargement followed by a contraction (like Fig. 7) ; 

 from e to </, the diameter is the same throughout ; and 

 from a to b, the tube is a contraction followed by an 

 enlargement (like Fig. 6). Just as in Figs. 8, 9, 10, 11, 

 gauge-glasses are here fitted to the various tubes to show 

 the pressures of the water in them at various points. 



Let us first consider the parallel pipe e g. If the fluid 

 were frictionless, the diameter being uniform, the pressure 



would be uniform throughout, and the fluid would stand at 

 the same level in each of the three gauge-glasses. But, 

 owing to the friction, the water surfaces m the three glasses 

 do not come up to a level line, but forni 

 namely the frictional gradient. 



Now take the pipe a c. Here vhe sm&lleis^ jjfas^ilrs; 

 denoted by the water level at b', fs* in* one" middle &tr 5," 

 where the diameter is smallest, and the greatest pressure 

 denoted by the water levels at a', c', is at the two ends 

 a, c, where the diameter is greatest. And if the fluid 

 were frictionless, the pressure at the two ends, which have 

 the same diameter, would be the same, but with water 

 there is, as in the parallel pipe e g, a gradient or loss of 

 pressure due to the friction. 



