May 12, 1898J 



NATURE 



35 



general mass of the stream. This not only occurs with 

 obstacles placed in a flowing stream, but in pipes as in 

 Fig. 3. At the International Congress of Naval Archi- 

 tects held at the Imperial Institute last July, this mode 

 of representing the flow of water was brought forward 

 for the first time. It was then suggested that, in this 

 clear border line the water was flowing in layers with 

 parallel motion, while in the main body of the stream the 

 flow was taking place with sinuous, or broken-up motion, 

 and that the change of critical velocity occurred at the 

 darker border between the two. This dark border is 

 always more intense the higher the velocity of the flow, 

 the width of the border becoming correspondingly 

 reduced. 



m>- 



I'iG. I. — Cle.ir water (thick sheet). 



Fig. 2. — Soapy w.itL-i (thick ■.hut). 



As a good many important results turn upon this 

 point, the subject has been pursued since that time by 

 making a variety of experiments with bodies of varying 

 degrees of roughness of surface, and with passages 

 of various forms. One experiment, however, may be 

 considered as a crucial test, which is to reduce the 

 width of the channel itself, till it actually corresponds 

 with the dimensions of the clear border. This has been 

 done with the result indicated in Fig. 4, when what may 

 be called the air method of making the flow visible 

 entirely fails, the clear border line disappearing and the 

 air passing through, not steadily as before, but spas- 

 modically, while the clear border line of separation 



Fig. 4. — Passage still further reduced, showing failure of air method. 



entirely disappears. One further step is now obvious, 

 and that is to obtain, if possible, a sheet of water as thin 

 as the border line itself, and examine its behaviour. The 

 result of doing this has been brought forward in a paper 

 read a few weeks ago at the meeting of the Naval 

 Architects in London, when it was shown that in such a 

 thin sheet oi water stream line motion exists, thus 

 indicating the absence of sinuous motion and the ex- 

 istence of the motion of parallel flow alone. Under 

 these conditions, while it is impossible to make the 

 motion of water visible, as before, by means of air, 

 colour can be used, and colour bands, corresponding 



NO. 1489, VOL. 58] 



to the stream lines of the mathematician, can be ob- 

 tained. Figs 5 and 6 indicate a comparison of these two 

 methods to a semi-cylinder. Fig. 5. which is a case of a 

 thick sheet, is an eddying mass of water all round, but is 

 widest, of course, behind where the largest mass of 

 slowly moving water exists. This case is particularly 

 mteresting, since it is a case for which the stream lines 

 have been worked out on hydro-dynamical principles, 



^ > 



Fig. 5. — Semi-cylinder in thick sheet. 



Fig. 6 — Sem-cylinder in thin sheet 

 (test case). 



and it is found, by carefully working out a test case, 

 that for all practical purposes the results of the stream 

 lines experimentally produced, agree with those theoret- 

 cally obtained. As is well known the lines of flow for 

 leat and electricity can be determined mathematically in 

 the same way as those for a perfectly incompressible and 

 frictionless fluid. Hence further verifications can be 



obtained by comparing the theoretical lines of force which 

 have been worked out for electrical and magnetic 

 problems. Fig. 7 is a case of the flow of water through a 

 hole (called in hydro-mechanics a "sink"), and which 

 corresponds to the flow of electricity from an electrified 

 body into one of the wires of a wire grating (see Clerk- 

 iMaxwell's " Magnetism and Electricity," Fig. xiii.. Art. 



Fig. 8. — Inclined plate in thin sheet. 



203, Vol. i. ; third edition). A still more remarkable 

 verification is that shown in Fig. 8, which is the case of 

 water flowing past a plate inclined at 45 degrees. The 

 central stream line has been predicted by Prof. Lamb to 

 be a hyperbola, which dividing on the plate would flow 

 round it and re-form on the other side, flowing away 

 exactly as shown in Fig. 8, which figure can be compared 

 with the illustration given in the treatise of Prof. Lamb. 



