64 THE MECHANISM OF THE CIRCULATION. 



BC, of which M and X are provided with bent nozzles, turned in the case of 

 M to face the direction of flow, in the case of X in the direction of flow ; S 

 is a stopcock, by means of which the fluid can be allowed to flow along BC 

 with different velocities. 



So long as S is kept closed, the level of the fluid in all the tubes is the 

 same as that in the vessel (A) ; but as soon as S is opened, the level falls in 

 all the tubes, and the fall is greater, the greater the distance along BC. This 

 gradual fall in pressure along BC is due to the loss through fluid resistance, 

 and as the amount of this loss is proportional to the length of tube traversed 

 (when the tube is uniform and the flow constant), it follows that the fall in 

 head in the tubes (D, E, F, and H) will be proportional to the length at which 

 each of these tubes is situate along BC, measured from the opening into the 

 reservoir (A), and will be represented by the line (XY). Since the fluid resist- 

 ance in a tube varies with the square of the velocity of the fluid, it follows 

 that the loss in head when the velocity is varied will be directly as the square 

 of the velocity. Hence, when the flow is made faster by opening more fully 

 the stopcock (S), the line of fall of pressure becomes more steeply inclined. 

 The tangent of the angle of slope of this line to the horizontal line (BC) is 

 called the "pressure gradient." The pressure gradient is from this evidently 

 equivalent to the fall in pressure per unit length. 



Besides this gradual fall, due to fluid resistance along BC, there is a 

 sudden drop in lateral pressure just at the beginning of BC, which is not due 

 to fluid resistance, but to a portion of the pressure due to the head in A being 

 used to give velocity to the fluid as it enters BC. The amount of head so 

 lost is called the "velocity head." Its value is easily calculated when the 

 velocity is known, for equating potential energy lost to kinetic energy gained, 



2 gh = v 2 , or h = — , where h is velocity head, v is velocity, and g accumula- 



tion due to gravity. 



The dependence of the velocity head on the velocity can be shown by 

 manipulating the tap (S). When the flow is made very slow, the pressure in 

 J) is nearly the same as that in A ; when the flow is increased, the level falls 

 in D, showing that the initial loss in pressure due to velocity has increased. 

 At the same time, the effect of the increased velocity on the pressure gradient 

 is shown by the increased steepness of the line (XY). That the loss in lateral 

 pressure due to velocity head persists all along the tube (BC) can be shown by 

 the tubes (M and X). In M the impact of the fluid against the mouth of the 

 tube raises the level in M above the height due to the lateral pressure alone at 

 that point by an amount (ab) equal to the velocity head. Similarly, in the 

 tube (X), the .suction of the fluid passing the bent end depresses the column 

 in X by an amount (ce) equal again to the velocity head. The lateral head 

 at any given point is often called the " effective head ; " and the loss in head 

 due to fluid resistance up to any point, the "resistance head." It is evident 

 that the sum of velocity head, resistance head, and effective head must equal 

 the total head, or reservoir head. 



In the arteries the velocity head is very small, because the velocity of flow 



is not great ; taking the velocity in the aorta as 32 cms. per second, the 



32 2 

 velocity head, h = ' " = § cm. of blood. 

 *j x y o l 



Poiseuille's law. — In tubes wherein the threads of fluid move in 



parallel lines, Poiseuille has laid down the law that the mean velocity is 



directly proportional to the sectional area of the tube and the pressure 



gradient. In other words, we can And the mean velocity by the product of 



three factors — sectional area, pressure gradient, and a constant coefficient (C), 



which depends on the viscosity or physico-chemical nature of the fluid in the 



conditions of experiment. This coefficient can be defined as that mean 



