126 



PROPELLING FORCE, VELOCITY AND LATERAL PRESSURE. 



F (which effects the velocity of escape) and the height of the resistance D 

 (which overcomes any resistance that may be present) : hence h = F -f- D. 



PROPELLING FORCE, VELOCITY AND LATERAL PRESSURE. 



If a fluid passes through a tube (which it completely fills) , the first thing to 

 determine is the propelling force h with which the current flows at different points 

 in the tube. The degree of the propelling force depends on two factors: 



1. The velocity of the current, v; 



2. The pressure (resistance-height) to which the fluid is subjected at different 

 points in the tube, D. 



1. The velocity of the current v is determined: (a) from the lumen of the 

 tube 1, and (6) from the quantity of fluid q, that passes through the tube in a 

 given unit of time. Then v = q : 1. Both values, q as well as 1, can be deter- 

 mined directly by measurement. The circumference of a circular tube, the diameter 



of which is d, is 3.14 X d. The cross-section (the lumen of the tube) is 1 = - - X d 2 . 

 After the value of v has been determined in this way, the so-called velocity- 

 height F (of hydraulic engineers) can be estimated from v; that is, the height 

 from which a body would have to fall in a vacuum in order to acquire the velocity 



of v. This is F = (in which g indicates the distance through which the body 



falls in one second, or 4.9 meters). 



2. The pressure D (resistance-height) is measured directly at various points 

 in the tube by inserting manometer- tubes (Fig. 38). 



The propelling force at any selected point in the tube will thus be: 



For experimental investigation the large cylindrical pressure- vessel (Fig. 38, A) 

 may be used, within which by a suitable arrangement water can be maintained 

 at a constant level h. The rigid tube a b, passing off from the bottom of the 



vessel, and of uniform size, is 

 provided with a number of 

 vertical tubes (i, 2, 3) consti- 

 tuting a piezometer, for the 

 measurement of the pressure; 

 at the extremity b the tube is 

 provided with an opening di- 

 rected upward. From the lat- 

 ter the water, providing the 

 level at h remains the same, 

 will be thrown to a constant 

 height, and this distance is 

 equivalent to F, the velocity- 

 height. As the pressure D lt 

 D 2< D 3 in the manometric tubes 



1,2,3 can be read off directly, 



III * " ' ' 



FIG. 38. A Pressure-vessel, A, with Outflow Tube, a b, and Manom- 

 eters, Di,D 2 D 3 , Inserted at Different Points. 



it follows that the propelling 

 force of the water at the posi- 

 tion of the tubes I, II, III is 

 respectively h = F -f D t ; F + 

 D 2 ; F + D 3 . 



At the extremity of the tube (at b) where D t =o,h = F + o, hence h = 

 F. Within the pressure- vessel itself, it is the constant force h .that influences 

 the movement of the fluid. 



It is, therefore, at once apparent that the propelling force of the water 

 has become progressively smaller from the point where the fluid enters the 

 tube from the pressure- vessel to the end of the tube b. The water in the 

 pressure-vessel falling from h rises at b only to the height F. This diminution 

 in the propelling force is due to the resistances encountered by the current in the 

 tube, which neutralize a part of the kinetic energy (that is, convert it into heat). 

 As, when the water has reached b, the motor power h in the vessel has been re- 

 duced to F, the difference having been neutralized by the resistances, the sum of 

 these resistances must be D = h - F, from which it follows that h = F -}- D, 



