116 



FLOW OF FLUIDS THROUGH TUBES. 



tube ; and (b.) from the quantity of fluid, q, which flows through the tube in 

 the unit of time. So that v = q : I Both values, q as well as I, can be accurately 

 measured. (The circumference of a round tube, whose diameter = d is 3'14.c?. 



Q 1 A 



The sectional area (lumen of the tube) is 1=^. d 2 .) 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, 



n*2 



in order to attain the velocity, v, In this case F = -^ (where y = the distance 

 traversed by a falling body in 1 sec. = 4-9 metre). 



A cylindrical vessel filled with water or, b, outflow tube, along which are 

 placed at intervals vertical tubes, 1, 2, 3, to estimate the pressure. 



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

 manometers at different parts of the tube (Fig. 39). 

 The propelling force at any part of the tube is 



or, 



(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, 7*. The outflow 

 rigid tube, a, b, has in connection with it a number of tubes placed vertically 

 1, 2, 3, constituting a piezometer. At the end of the tube, b, there is an opening 

 with a short tube fixed in it, from which the water issues to a constant 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 



h = F + D 1 ;-F + D 2 ;-F + D 3 . 



At the end of the tube, b, where D 4 = 0, h= + 0, i.e., h = 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 part where the fluid passes out of the cylinder into the tube towards the 

 end of the tube, b. The water in the pressure-cylinder, falling from the height, 7i, 

 only rises as high as F at 6. This diminution of the propelling power is due to the 



