MOTION OF VISCOUS FLUIDS 57 



leeded to settle this point and also to determine how, with the same 

 T alues of 6 but with different inlet and outlet diameters, the critical velocity 

 iepends on the latter factor. 



ART. 19. MOTION OF A FLUID. 



The motion of any particle of fluid acted upon by external forces and 

 y its own weight may be considered from two points of view. In the 

 irst, by equating the work done on the mass to the increase of energy in 

 he potential, pressure, and kinetic form, together with the loss by 

 dissipation, as by internal friction, which converts mechanical energy 

 nto heat, we get an expression for the velocity in terms of the applied 

 brces. With steady motion of a non-viscous fluid this method is always 

 ipplicable. 



Where a mass of fluid has unsteady sinuous motion, however, the 

 impossibility of determining the kinetic energy possessed by its eddies in 

 rirtue of their rotation renders the application of the energy equation 

 mpossible, and it becomes necessary to consider the motion from the 

 x>int of view of the production of momentum, since the momentum 

 of the fluid forming a vortex is unaltered by its motion of rotation. 



With unsteady motion, .moreover, of a viscous fluid, the magnitude and 

 direction of the forces including those due to viscosity acting at any 

 ^articular point become indeterminate, so that the molecular motion at 

 he point is then indeterminate, and the general equations of motion 

 become in general impossible of application. Even in the case of the 

 steady motion of a viscous fluid, these, when stated in terms of the 

 viscosity, become so unwieldy that, except in one or two particular cases, 



., those of steady flow between parallel plates or through a circular 

 pipe, they are unfitted for application to the solution of any practical 

 problem, although where so applicable the solution becomes perfectly 

 accurate. 



A simplification of these equations may be obtained by neglecting the 

 effect of viscosity i.e., assuming the liquid to be a perfect fluid and it 

 s in this form that they are usually stated. Evidently the solution of 

 any such equation can only be made to apply to the results of any given 

 problem by the introduction of some constant obtained by experiment 

 which itself has the effect of modifying the solution so as to take into 

 account the effect of viscosity, and it is to this extent that hydraulics is to 

 be considered an experimental science. If it were possible in every case 

 to apply the equations of motion in full, the science would become exact. 



