328 H. A. Baker — Loose Arenaceous Sediments. 



The flow of a liquid tlirougli a tube is either of the steady, 

 irrotational type, in which the liquid is moving in cylindrical layers 

 coaxial with the axis of the tube, and the layer of liquid against 

 the wall of the tube is at rest, or of the rotational, eddying type, 

 in' which the velocity of the current is more or less uniform over 

 a large part of the cross section of the tube. To obtain the first 

 type of flow certain preliminary precautions must be taken, but in 

 the case of the current of water passing through an elutriator these 

 precautions are ignored, so that we have to deal with the case of 

 eddying flow. The tube wall has an important retarding effect 

 upon the current, and the ratio of the circumference of a tube to its 

 cross section varies inversely as the diameter. Osborne Reynolds 

 has stated that the critical mean velocity at which the steady type 

 of flow breaks up and is replaced by eddying flow varies inversely 

 as the diameter of the tube. Hence, with so narrow a tube as the 

 smaller tube of a Crook elutriator there is a much stronger tendency 

 for the flow to approximate to the steady, irrotational type than 

 in the case of a fairly wide tube. For the steady, irrotational type 

 of flow the formula 



V = — . [a — r) applies 



Tra 



where v = velocity at a point distant r from axis of tube, 



Q = volume passing a cross section of the tube in unit time 



(or outflowing from jet in unit time), 

 a = radius of tube. 



In the centre of the tube r — o, consequently 



V = — -3 



Q 



and since — ^ is the average velocity of the current, as calculated 



from the outflow from the jet, it follows that, in the centre of the 

 tube the velocity of the current is twice as fast as the calculated 

 average. Therefore, in the smaller tube of a Crook elutriator, 

 although the conditions requisite for steady, irrotational flow are 

 not completely realized, the velocity of the current in the centre 

 of the tube is approaching double the value of the mean speed for 

 which the apparatus has been adjusted. Hence much material 

 will be washed off which should be retained within the tube, and 

 a mechanical analysis, effected by means of a Crook elutriator, will 

 always give too low a percentage weight for the sand grade, and too 

 high a percentage weight for the silt grade. The seriousness of the 

 error involved is seen at once from the following comparative 

 results, which are selected from a number of tests made by the 

 writer : — 



