a a ee T eens SPS PRESSURE OF GRANULAR SUBSTANCES IN LONG TUBES STN aN AE Gia sRoteie: Dar i ] a2 2S Ss 3 f= SS pp adtae | —_ 2 men. LIBRARY Michigan State Unrversity ~Bee 2a. we Senior Mechanical Thesis on "PRESSURE OF GRANULAR SUBSTANCLS IN LONG Tubks." F. V. Warren, WaT. Class of '98. liichigan Agricultural College, Acricultural College, iach. TWESIS PRESSURE OF GRANULAR SuBSTANCES IN LONG TUBES. The question of the presc:ures exerted by cranular substances, esnecially grain and coal, is one of freat im portance to the engincer, as it should be the basis of com putation in Cesicning crain elevators, and the coal bins which must necessarily fori. & pert of every large storn plant. The frecuent failure of these structures has ied to a rreat deal of sdeaulation as to the nrobable pressures, put to very little of actual experiment. Consequently, there is very little engineering literature upon the strains in such structures that is of practical value to the engineer. The failure of a large coal bin at Paterson, N. J., in the year of 1897 led to numerous Aiscussions in the Engrinecr- ing News by engineers all over the country, and it was with & view to try to discover something in regard to some of the theories suggested by them that these experinents were scor- ducted. The results obtaincd related particularly to the yressures exerted on the potton and on the sides. ? If grain, or any granular substance, be poured ina stream in one place it will Yvorm A /C acone. Suppose this process be continued in a grain bin until the bave of the cone just reaches the lower edge of the vertical wails. Tho entire weight of the sub- stance is held by the bottom, and no pressure whatever is exerted on the sides. Suppose the process to be continue?,; the substanec will continue to form in the shave of @ cone 104049 and G& pressure mst necessarily be exerted on thro sides. Consequently, a portion of the weirht will be taken off the bottom. The experinents tried were to determine, if possibic, how tucn of this veight wes held by friction on the csices, and if there was any heighth at which the addition of maticz on the top brought no additional weifht on the bottom. The experiments vere tried with the following apparatus A tube sixteen fcet long, savere in section and six inches on each cide, was constructed of pine lwaber. This was rigidly supported in a vertical position, with the lover end about eiseht inehes from tie floor. The tube was supvorted by a frame, to which vere bolted several pulleys running a drill; consequontly, it vas cubjected to 2 sligh nearly the same corditions as are usually founc in an cleva- tor. Over the lover er.d of the tube vas placed @& box about 10 by 12 inches, resting on a pair of scales, anc the scales Cclevated so that the inside of the bottom of the box ras about two inches from the lover end of the tube. Under these conditions, ensugh or the material to be tested was soured in to seal the vottom of the tube, and the weirnht on the seales noted. Known amounts of srain were then poured in at the top, and the reading noted each time on the scales below. Had there been no friction on sidcs, or if the entire weight had been held by the botton, since there was no connection between tne scales and the vertical tube, the weight on the seales below vould have been equal to the weight of gfrain put in at the top. The dirfercree betveen the two is the enount eld by the sides, ena it was fcund in every case that after a certain ceonortionate heirrt the ac@ition of more material at the top brought no aiciticenal wolgnt on the botton. The first ocirpstance tried vas oats, anc the result was not very satisfactory, beeause the size of tne tube Was evidently too small for a rrain having so great e friction. The weight of the box enw the grain necessary to seal the end of the tube was 7.é rounds, and roilovines vas the experi- ment. The experiment was verified, fivine same results on second and third trials, Grain put in at the ton. Total veight on botton, ad including the 7.6 =: é 8.88 i 8.6 7 2.25 5.4 10 9.7 10 9.7 Totel 58.50 9.7 Final The experiments with wheat were as follows, and perhaps are trore satisfactory than those with oats, because of the less friction. Amount necessary to seal the bottom of tne tube 11.5 15s. Grain at Top Total weight on botton. O 11.5 12 16 10 17 20 18 The tube was raised slightly and it was 14 10 15.5 10 13.5 4 © 14 Oo on }—4 oO =) Cc) @ Ien Total 72 rinal 1 O) On Experiment 2 with wheat. Grain at Top Weight at vottom. 0 10 neeessary to seal bottom of tibe 13 15 13 16 13 16.5 13 17 13 17 TOtal 65 Final 17 In the next experinent vith wheat the amount put in eacn time wes mace :udl smueller., This would tend to produce more of a layer effe2t; reduce the conv formed and more weight would come on the bottom. The exveriment verified this fact. Wt. or Grain at Top Total weight on bottom. 0 10 necessary to seal bottom of tube 4.5 12.5 Zeb 14 “5 L5 tf 16.5 4.5 16.5 4.5 L7 4.0 L725 4.5 17.5 £20 18 4.5 18 4.5 LS 4.5 vane) 4.5 A906 & of 20.5 TOtal 8S Final £0.5 i | Ta rs ‘ a-% ; Accitional welght broucht no inerease on vottor 44 doe @ EXD Piisent 4 °WLth wheat. VWeicht of crain at top Welght on bottom 0 10 4.6 ed ALLE 14.5 4.5 14.5 & eG 16.5 4.5 18.5 4.5 17. C1 4.5 18.5 4.5 19 40 19 4.5 19 4.5 £0.58 4.5 £0.56 te 20.5 =o 20.5 Total 86 rinal 29.6 Veilght at ton Totel on vottom 0.95 8.6 TOtal 38.6 Final 9.7 In cach case the pressure on the bottom, et the time when additional veirht at the top brought no inecreasc of pressure on the bottom, was about onc:—thirdc of the reight . of the material already in the tube, It would seem that, after the tube was filled, a jar would sottle the rrain ene bring increased weight on the bottom, but expcriment did not pear out this sunposition, as a jar of the tube made no difference, sceming to incieate that the grain actec like a continuously drive vederc, and the increase from the jer probably being borne vy the sides. As an ireidence of the preseure on the walls, a ceseription in the Ergeincerire liews for Jan. 27tr., 1888, tells of an elevator in which the bins 80 £t. high having its sides so compressed that the walls were one foot lower when filled with grain than when eérptv. The same issue contains some interesting discussions of experiments in regard to pressure of stored rreain. In thosc experiments in no case did the vressiure on the bottom excecd seven and one-nalf pounds. The fact that in our expcrinents the pressure vent as high as 20 1/2 is probably accounted for by tov Lfaet that in their experinents the tube uscd was 4 in. square, and in ours 86 in. square. Another very intcresting feature of the experinents deserlbed in Engineering News is tre following formula: P= ACDW=4].08 A. D. VW. P= cDW =1.08 DW in whnien P is A pressure in pounds on the bottom, A is arca of bottom in c .] ' 2D square feet, uv. the dianeter of inscribed sirele, ¢C a con- stant foun? to be 1.928 anil the weignt of a cubic foct of wheat. Or, expressed in words, the maximum pressure that can come wpoen the potton of a bin of wheat is equal to the Te vweirnt of a orism of wheat with a base equal to the bottom of the bin, and altitude equal to the diameter of the in- seribed cirele. "e think the pressure on the sides,anc the engle at which it is exerted, will depend largely on the angle or repose of the substance. I%t trould be interesting to cdisecover tne »oint of maximmm orecsure on the side, and @ fev opserva- tions indicate that it is 1/3 of tho distance from the botion, but observations are too few to lead to a definite conclusion. Interesting articles relating to this vroblen may be found in Engineering Hews of Jan. 27th., 1893, Nov. 4th., 1897, March 3rd., 1898, font. £38rd., 1897, June 19th. and POtN., 1836, Van Nostrand Selence Series (Wo. 3, Eenjemin Baker's book on Actual Lateral Pressure of Tavthworke, Annals ces Ponts ct Cheussess April, 1887, Report of Britisn Association ror the Advancement of Science 1882 and from the cxperiments of cn Englishman by the name of Roberts. + df THN