100 MOTION OF A LIQUID IN TWO WMKNSloNs. |rll.uv IV 



DitWUtti'H'HtHtit AfottOIMT. 



73. We have, in the preceding pages, had several instance* of 



the tlow of a liquid round a sharp projecting edge, and it appeared 

 in oaeh case that the voloeiix ihoio \\as intinite. This is indeed a 

 necessary consequence of the assumed irrot at tonal character of the 

 motion, whether tho lluid ho incompressible or not, as may be 

 seen by considering the configuration oi the oquipotontial surfaei-; 

 (which meet the boundary at right angles) in the immediate 

 neighbourhood, 



Tho occurrence of infinite values of the velocity may be 

 avoided by supposing the edge to be --lightly rounded, but oven 

 then tho velocity near tho edge will much exceed that which 



i ms at a distance great in compan-.on with the radius of 

 curvature, 



In order that the motion of a tluid may conform to such 

 conditious.it is nocossan th.u the pressure at a distance should 

 greatly exceed that at the edge. This excess of pressure ia 

 demanded by tho iitwftW of tho tluid, which cannot bo guided 

 round *v sharp curve, in opposition to centrifugal force, except by 

 a distribution of pressure increasing with a very rapid gradient 

 outward* 



Hence unless the pressure at a distance be very great, the 



maintenance of the motion in question would require .\ ucgamc 

 pressure it the corner. Mich as thuds under ordinary conditions 

 are unable t o sust .un 



To put the matter in aa definite a form aa possible, let wa 

 imagine the following case* Let us suppose that a straight tube, 



whoso length i-- !.-u:y compared \\ith the diameter, is ti\ed in the 

 middle of a laiy.c closed \essel tilled with frictiouless liquid, and 

 that (hi-, tube contains. at .1 distance from tho ends, a sliding 

 pin,;, or piston. /'.which van be moved in ain required manner by 

 o. :,<.-. I";-., :';.:/,,.. > : :-.. u.i'.'.s of 



the tube is supposed to be small in comparison with tho diameter; 

 and the * . . : .--. tv> be \ >tV. so that there ai\> 



r.o -.l-.a-n .i:. : ; . Lot us further suppv^se that at some point of tlio 

 walls of the vessel therx' is a lateral tube, with a piston ( t >. b\ 

 n\etvns of which the pressure in the interior can bo wyusU>d at will 



