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A TEXTBOOK OF PHYSIOLOGY 



at a constant pressure, if the diameter be constant, is directly pro- 

 portional to the length of the tube. 



3. That with the same head of pressure the time spent in the 

 outflow of a certain volume of fluid through equally long tubes is 

 inversely proportional to the fourth power of the diameter. 



The Flow in a Tube of Varying Diameter. Since fluid is incom- 

 pressible, an equal amount must flow in the unit of time through 

 every section of the tube, and thus the velocity in any part of a tube 

 which varies in diameter stands in inverse proportion to the sectional 

 area. In such a tube the pressure gradient is steepest in the narrowest 

 section, for there the velocity and the friction is greatest. In two 

 sections of equal diameter the pressure gradient is the same. Where 

 a wide section follows upon a narrower, the lateral pressure may either 



FIG. 85. SCHEMA TO SHOW THE VELOCITY AND RESISTANCE HEADS. 

 B, Pressure bottle ; A, tube with piezometers; E F, Pitot tubes. 



sink, remain unaltered, or even rise.. How this can be so is seen by 

 the following considerations: At any point of the tube the whole 

 pressure head (H) equals the sum of the velocity head (h 1 ) and the 

 resistance head (h 2 ). Now H decreases uniformly along the tube, 

 and since, where the tube widens, the velocity becomes less, and H 1 

 suddenly diminishes, it follows that k 2 increases, and it is conceivable 

 that h 1 in the wide section may become higher than h 2 in the narrow 

 section. In other words, since more of .H is spent in maintaining 

 the velocity in the. narrow section, the lateral pressure may be lower 

 here than in the succeeding wide section. 



The Flow in Branching Tubes. When a tube branches into a number 

 of smaller branches, and these connect again into one tube, we have 

 two opposing factors to consider: 



