9Q 



VELOCITY OF THE CURRENT. RESISTANCE. 



absent ; but in every physical experiment such resistance exists. Hence, the propelling force, 

 h, has not only to cause the efflux of the fluid, but has also to overcome resistance. Ihese two 

 forces may be expressed by the heights of two columns of water placed over each other, viz., by 

 the height of the column of water causing the outflow, F, and the height of the column, D, 

 which overcomes the resistance opposed to the outflow of the fluid. So that 



A = F + D. 

 6 2- VELOCITY OF THE CURRENT. RESISTANCE. In the case of a fluid flowing through 

 a tube', which it fills completely, we have to consider the propelling force, 7i causing the fluid 

 to flow through the various sections of the tube. The amount of the propelling force depends 



UP (1) On the velocity of the current, v ; (2) on the pressure (amount of resistance) to which the 

 fluid is subjected at the various parts of the tube, D. 



(1) The velocity of the current, v, is estimated (a) from the lumen, I, of the tube ; and (b). 

 from the quantity of fluid, q, which flows through the tube in the unit of time. So that v = q:l. 

 Both values, q as well as I, can be accurately measured. (The circumference of a circular tube, 



whose diameter *<Z is S'U.d. The sectional area (lumen of the tube) is I- 



3-14 



dr). Having in 



this way determined v, from it we may calculate the height of the column of fluid, F, which 

 will give this velocity, i.e., the height from which a body must fall in vacuo, in order to attain 



the velocity v. In this case F-j- (where g = the distance traversed by a falling body in 1 sec. 



= 4 "9 metre). 



(2) The pressure, D (amount of resistance), is measured directly by placing manometers at 

 different parts of the tube (fig. 67). 



The propeUing force at any part of the tube is 7i = F + D ; or, /* = + D (Bonders). This 



is proved experimentally by taking a tall cylindrical vessel, A, of sufficient size, which is 

 kept filled with water at a constant level, h. The rigid outflow tube, ab, has in connection with 

 it a number of tubes placed vertically, 1, 2, 3, constituting a piezometer. At the end of the 



h 



Id 



* .... ! 



D 

 A 



-0. 



fi 



J I 



Fig. 66. 

 Cylindrical vessel filled with water, h, 

 height of the column of fluid ; D, height 

 required to overcome the resistance ; 

 F, height causing the efflux. 



a I IT HE 



Fig. 67. 

 A cylindrical vessel filled with water, ab, 

 outflow tube, along which are placed at 

 intervals vertical tubes, 1, 2, 3, to estimate 

 the pressure. 



tube, b, there is an opening with a short tube fixed in it, from which the water issues to a con- 

 stant height, provided the level of h is kept constant. The height to which it rises depends on 

 the height of the column of fluid causing the velocity, F. As the pressure in the manometric 

 tubes, D 1 , D 2 , D 3 , can be read off directly, the propelling force of the water at the sections of 

 the tubes, I, II, III, is- 



7i = F + D 1 ; F + D 2 ; F + D 3 . 

 At the end of the tube, b, where D 4 =0, 7i=F + 0, i.e., 7i = F. In the cylinder itself it is the 

 constant pressure, h, which causes the movement of the fluid. It is clear that the propelling 

 force of the water gradually diminishes as we pass from the inflow towards the outflow of the 

 tube, b. The water in the pressure-cylinder, falling from the height, h, only rises as high as F 

 at b. This diminution of the propelling power is due to the presence of resistances, which oppose 

 the current in the tube, i.e., part of the energy is transformed into heat. As the propelling 

 force at b is represented only by F, while in the vessel it is h, the difference must be due to the 

 sum of the resistances, D = h - F ; hence it follows that A= F + D. 



