CH. viii BLOOD-STEEAM : MOVEMENT IN VESSELS 233 



of hydrodynamics, which are intimately connected with haemo- 

 dynamics. 



(a) Let us take the simplest case of a fluid contained in a vessel 

 having an outlet in its base. As soon as this is opened, the 

 resistance offered to the hydrostatic pressure over the outlet 

 vanishes, and the fluid pours out through the opening. Accord- 

 ing to Torricelli's theorem (1643), the velocity (v) with which a fluid 

 escapes is (apart from the resistance it encounters) exactly equal 

 to that which a body would acquire in falling free through the 

 height of the column of fluid to the orifice. It is therefore in- 

 dependent of the nature of the fluid, and depends on the pressure, 

 i.e. on the height (H) of the column of fluid, and is proportional 

 to the square root of this height, i.e. it increases as 1, 2, or 3, when 

 the increment of height is as 1, 4, 9. If the acceleration due to 

 gravity at each second (which = 9'8 in.) is represented as g, we 

 have : 



(5) When a rigid horizontal tube is joined to the orifice of the 

 same vessel (in which a column of fluid is maintained at equal 

 height and constant diameter throughout its length) the velocity 

 of outflow, and therefore the amount of fluid escaping from the 

 end of that tube, will be less than in the previous case, because a 

 portion of the available hydrostatic pressure will be applied to 

 overcoming the new resistance which the fluid encounters in its 

 passage through the tube, and cannot therefore add to the velocity 

 of the escaping fluid. 



The resistances are represented by the internal friction between 

 the molecules of fluid, which are forced, partly by the adhesion of 

 the external layer of fluid to the walls of the tube, partly by 

 viscosity (see p. 151), to glide one over the other. As we have seen 

 elsewhere (p. 189) the velocity of the single-current threads, into 

 which we may consider the cylinder of fluid driven through the 

 tube to be broken up, increases from the periphery to the axis of 

 the cylinder, where it is maximal. The mean velocity corresponds 

 with half the maximal velocity observed in the axis. 



Since liquids are incompressible, i.e. can neither be compressed 

 nor the reverse in their passage through tubes, it follows that 

 their average velocity must be equal at every section of the same, 

 also that the amount passing every section in the unit of time 

 must be equal. 



Owing to internal friction the fluid exerts a lateral pressure on 

 the walls of the tube, which can be measured by fixing manometer 

 tubes, or piezometers, perpendicular to the axis (Fig. 88). The 

 height to which the fluid ascends in the piezometers decreases 

 regularly from that in the tube nearest the orifice by which it 

 enters to that nearest the outflow, so that the highest points of 



