118 CURRENTS THROUGH CAPILLARY TUBES. 



narrow parts. As a general rule, in tubes of unequal diameter the velocity of 

 the current is inversely proportional to the diameter of the corresponding section 

 of the tube; i.e., if the tube be cylindrical, it is inversely proportional to the square 

 of the diameter of the circular transverse section. In tubes of uniform diameter, the 

 propelling force of the moving fluid diminishes uniformly from point to point, but 

 in tubes of unequal calibre it does not diminish uniformly. As the resistance is 

 greater in narrow tubes, of course the propelling force must diminish more rapidly 

 in them than in wide tubes. Hence, withiu the wide parts of the tube the pressure 

 is greater than the sum of the resistances still to be overcome, while in the narrow 

 portions it is less than these. 



Tortuosities and Bending Of the Vessels add new resistance, and the fluid 

 presses more strongly on the convex side than on the concave side of the bend, 

 and there the resistance to the flow is greater than on the concave side. 



Division of a tube into two or more branches is a source of resistance, and 

 diminishes the propelling power. When a tube divides into two smaller tubes, of 

 course some of the particles of the fluid are retarded, while others are accelerated 

 on account of the unequal velocities of the different layers of the fluid. Many 

 particles which had the greatest velocity in the axial layer come to lie more towards 

 the side of the tube where they move more slowly ; and conversely many of those 

 lying in the outer layers reach the centre, where they move more rapidly. Hence, 

 some of the propelling force is used up in this process, and the pulling asunder of 

 the particles where the tube divides acts in a similar manner. If two tubes join 

 to form one tube, new resistance is thereby caused which must diminish the 

 propelling force. The sum of the mean velocities in both branches is independent 

 of the angle at which the division takes place (Jacobson). If a branch be opened 

 from a tube, the principal current is accelerated to a considerable extent, no 

 matter at what angle the branch may be given off. 



63. Currents through Capillary Tubes. 



Poiseuille proved experimentally, that the flow in the capillaries is subject to 

 special conditions 



(1.) The quantity of fluid which flows out of the same capillary tube is pro- 

 portional to the pressure. 



(2. ) The time necessary for a given quantity of fluid to flow out (with the like 

 pressure, diameter of tube and temperature), is proportional to the length of 

 the tubes. 



(3.) The product of the outflow (other things being equal) is as the fourth power 

 of the diameter. 



(4.) The velocity of the current is proportional to the pressure and to the square 

 of the diameter, and inversely proportional to the length of the tube. 



(5.) The resistance in the capillaries is proportional to the velocity of the current. 



64. Movement of Fluids and Wave-Motion in 



Elastic Tubes. 



(1.) When an uninterrupted uniform current flows through an elastic tube, it 

 follows exactly the same laws as if the tube had rigid walls. If the propelling 

 power increases or diminishes, the elastic tubes become wider or narrower, and 

 they behave, as far as the movement of the fluid is concerned, as wider or narrower 

 rigid tubes. 



