EXPERIMENTS ON THE PRESSURE OF GRAIN IN DEEP BINS. 326 

 PV -w-j^y-^d- r**'*/*) I 



- w R [ y - -~r] (approx.) (13) 



I 

 For example take a steel bin 10 ft. in diameter and 100 ft. deep; weight of wheat, 10-50 

 I). IM r cu. ft.; angle of friction of wheat on steel, / - 0.375; angle of repose of grain on grain, 

 i - tan 28 = 0.532 (M does not occur in formula (13) but may be used in calculating an approxi- 

 mate value of * = (i - sin 28)/(i + sin 28) = 0.37 which is a close approximation to k - 0.4 

 which will be used). Then the load carried by the side walls per lineal foot will be from (13) 



P V = 50 X 2.5 f 100 



* L 0.4 x 0.375 



10,416 lb. 



he total load on the entire bin walls will be 



P V X 31-416 = 327,635 lb. 

 'he total weight of wheat in the bin is 



5 X 78.5 X ioo = 392,700 lb. 

 and the total load carried by the bottom of the bin is 



392,700 - 327,635 = 65,065 lb. 



and the pressure on the bottom = V = 65,065/78.54 = 830 lb. per sq. ft. From formula (7) we 

 find that V = 830 lb. per sq. ft. 



EXPERIMENTS ON THE PRESSURE OF GRAIN IN DEEP BINS. The laws of pressure 

 of grain and similar materials are very different from the well known laws of fluid pressure. Dry 

 wheat and corn come very nearly filling the definition of a granular mass assumed by Rankine in 

 deducing his formulas for earth pressures. As stored in a bin the grain mass is limited by the 

 bin walls, and Rankine's retaining wall formulas are not directly applicable. 



If grain is allowed to run from a spout onto a floor it will heap up until the slope reaches a 

 certain angle, called the angle of repose of the grain, when the grain will slide down the surface 

 of the cone. If a hole be cut in the bottom of the side of a bin, the grain will flow out until the 

 opening is blocked by the outflowing grain. There is no tendency for the grain to spout up as 

 in the case of fluids. If grain be allowed to flow from an orifice it flows at a constant rate, which 

 is independent of the head and varies as the diameter of the orifice. 



Experiments by Willis Whited,* and by the author at the University of Illinois, with wheat 

 have shown that the flow from an orifice is independent of the head and varies as the cube of the 

 diameter of the orifice. This phenomenon can be explained as follows: The wheat grains in 

 the bin tend to form a dome which supports the weight above. The surface of this dome is 

 actually the surface of rupture. When the orifice is opened the grain flows out of the space below 

 the dome and the space is filled up by grains dropping from the top of the dome. As these grains 

 drop others take their place in the dome. Experiments with glass bins show that the grain from 

 the center of the bin is discharged first, this drops through the top of the dome, while the grain 

 in the lower part of the dome discharges last. 



The law of grain pressures has been studied experimentally by several engineers within 

 recent years. A brief resume of the most important experiments is given in the author's "The 

 Design of Walls, Bins and Grain Elevators," where after a careful study of all available experi- 

 ments the author reached the following conclusions: 



I. The pressure of grain on bin walls and bottoms follows a law (which for convenience will 

 be called the law of "semi-fluids"), which is entirely different from the law of the pressure of fluids. 



* Proc. Eng. Soc. of West. Penna., April, 1901. 



