THE CIRCULATION OF THE BLOOD 335 



power should be kept constant by permitting fluid to flow into the reservoir as 

 rapidly as it flows out of the horizontal tube.) 



The power or force which overcomes the resistance in the horizontal tube and 

 imparts velocity to the fluid is the downward pressure of the water in the reservoir, 

 represented by H. The amount of this power utilized in overcoming the resistance 

 is approximately determined by drawing a line from the outlet to the reservoir, 

 uniting the upper levels of the water in the vertical tubes. The height of the fluid 

 at the point at which the line intersects the reservoir, y, is a measure, therefore, 

 not only of the resistance but also an indication of the relative amount of the 

 downward pressure or the driving power used in overcoming it and is therefore 

 known as the resistance height and indicated by the letter, h. 



The amount of the pressure consumed in imparting the observed velocity is 

 determined by ascertaining the height from which a particle must fall in empty 

 space to acquire this velocity. This is obtained by dividing the square of the veloc- 

 ity by twice the accelerating force of gravity, 980 centimeters, as expressed in the 



v 2 



formula, ; the quotient is the height and is known as the -velocity height. Con- 

 versely if the moving fluid were discharged into empty space through an opening 

 in the tube at n, it would ascend an equal distance. If now this height is repre- 

 sented by F, and a line be drawn from it, parallel to the line of pressure until it 

 meets the reservoir at x, it will be seen what percentage, x y, or h' of the primary 

 propelling power is consumed in imparting the observed velocity. 



Of the total pressure a small portion is left over which is utilized in forcing into, 

 and overcoming the resistance offered by, the orifice of the horizontal tube. The 

 initial pressure in P therefore divides itself mainly into two portions; one, the larger 

 by far,&, is utilized in overcoming the resistance to the flow of the water; the other, 

 the smaller, h' in imparting velocity. 



Thus the two phenomena presented by the flow of a liquid through a tube with 

 rigid walls and of uniform diameter are velocity and pressure, of which the former 

 is the same for each cross-section, and the latter at any point directly proportional 

 to the resistance to be overcome. 



If, instead of a horizontal tube of uniform diameter, there be substituted a 

 tube the middle third of which is enlarged, the conditions will be similar to 

 the previous case until the fluid flows into the enlarged portion, when the velocity 

 will diminish, being inversely proportional to the area of the cross-section. The 

 resistance will be also diminished and therefore less of the pressure force or 

 driving power will be consumed than in the first section of the tube, and as a result, 

 the lateral pressure will fall less rapidly than in the first section. When the liquid 

 flows into the narrow or third section, the primary velocity returns. Though the 

 resistance again increases the amount to be overcome is small, and hence there is 

 a rapid and steady fall of pressure. 



On the contrary, if a tube be substituted the middle third of which is narrowed, 

 the conditions will be similar to the previous cases until the liquid flows into 

 the narrowed section, when at once the velocity increases and becomes inversely 

 proportional to the area of the cross-section ; the resistance being increased at the 

 same time, there will be a rapid consumption of the pressure force and a steep fall 

 of lateral pressure. On flowing into the third section, the velocity again diminishes 

 and the pressure falls though more slowly to the end of the tube. 



THE FLOW OF A LIQUID THROUGH A SERIES OF BRANCHING AND 

 AGAIN UNITING TUBES WITH RIGID WALLS UNDER A STEADILY 



ACTING PRESSURE 



In a system of this character, such as represented in Fig. 149, there must follow 

 as a result of the repeated branchings, a progressive increase in the total sectional 

 area of the collective tubes coincident with a progressive decrease in the sectional 



