MOTION OF VISCOUS FLUIDS 



45 



Osborne Keynolds, by his method of colour bands, 1 to prove conclusively 

 that the motion in a mass of water may be of two kinds ; to make clear 

 the simplicity of the one, and the complexity of the other ; and to 

 demonstrate the reasons for, and the laws governing each kind of 

 motion. 



The conclusions to be drawn from Professor Eeynolds's experiments are 

 as follows : firstly, we may have a continuous steady motion of the 

 particles, in which the motion at a fixed point always remains constant ; 

 and secondly, we may have unsteady or eddy motion, when the motion at 

 any fixed point varies according to no definite law. This is due to the 

 formation of eddies or vortices in the fluid. 



Introducing the idea of stream lines, i.e., of imaginary lines in the fluid, 

 such that at any point the direction of motion is tangential to the line, it 



FIG. 22. 



follows that in steady motion these stream lines become fixed, and this type 

 of motion is therefore known as stream line motion. Certain properties of 

 these stream lines are of interest. They must always have a continuous 

 curvature, except where the motion is zero, since to cause an infinite change 

 of curvature, an infinite force acting perpendicular to the direction of curva- 

 ture would be necessary. It follows that in steady motion a fluid will always 

 move in a curve round any sharp corner, and that the stream lines will be 

 tangential to any such boundaries, as indicated in Fig. 22 a and b, in 

 which the general form of the stream lines for steady flow out of two 

 forms of orifice are shown. With a very viscous fluid, an approximation 

 to this infinite force may be introduced by the effect of cohesion, and the 

 radius of curvature may then become very small. This has been clearly 



1 For a full account of this method of investigating the two manners of motion of water 

 see a paper by Osborne Reynolds, " Phil. Trans. Royal Society," 1883, 



