F Flow conditions An important parameter for calculating the minimum discharge opening width of a arch or knot is the critical open yield strength Æ’ cc . The solution to Æ’ cc is to represent the flow factor Æ’ æµåŠ¨ on the flow function FF, the intersection CC is Æ’. e.g. Johnson (JRJohanson) measurement and calculation of 10% aqueous iron ore is 11 is shown in FIG.
(2) Unloading port of mine silo (1) Size of unloading port to avoid arching:
Where B a ———unloading port width (unloading port length L a >2.5Ba), m;
D a ———Drawing port diameter, m;
D p ———average particle size, m;
ƒ cc ———critical open yield strength, Pa;
γ———the bulk density of the material, kg/m 3 ;
g———gravitational acceleration, g=9.81m/s 2 .[next]
(2) Avoid the size of the discharge port of the knot:
Where D p ——— discharge port diameter (or diagonal length), m;
K—the knot factor, as shown in Figure 12;
Other symbols are the same as before.
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(3) Funnel discharge (production volume): Johnson pointed out that only under the condition of blocking the silo, when the material size is larger than 250 microns, the discharge of the funnel is:
Where Q v ———discharge amount, m 3 /h;
B———Discharge port width, m;
L———the length of the discharge port, m;
D———Dropping port diameter, m;
θ ch ———Half angle of the flow channel, (°);
g———gravitational acceleration, g=9.81m/s 2 ;
Æ’ Æ’ --- critical flow factors (for arching);
ƒ ƒ•a ——— Actual flow factor (for a defined discharge port):
ƒ a •a =σ 1 /ƒ cc =σ 1 /σ y (11)
σ 1 =γBgƒ ƒ (12)
{Example 1} 10% water-containing coarse iron ore, the fluidity is shown in Fig. 11. Find the size of the discharge port of the tapered steel bucket. Solution steps:
(1) For the smallest overall silo height to obtain the maximum overall flow capacity, the new steel hopper bucket half angle does not exceed 20 ° (Figure 8).
(2) Determine the half angle of the bucket θ 1 = 10 °; by testing the internal friction angle of the material δ ' = 46 °, the friction angle with the wall ф ' = 25 °.
(3) The effective internal friction angle δ of the material that must be assumed at the beginning of the design of the bucket. It can be seen from Fig. 11a that δ is between 55° and 70°, assuming δ=60°.
(4) It can be found from Fig. 10a that when ф'=25° and δ=60°, ƒ ƒ =1.08.
(5) Draw ƒ ƒ =1.08 line on Figure 11c. The intersection of this line and the flow function FF curve is the critical point, so that the critical open yield strength (stress) can be obtained, ƒ cc =9kPa, compaction stress σ 1 = 10 kPa; corresponding σ 1 = 10 kPa, δ = 60 ° (assuming δ = 60 °).
(6) According to δ=60°, then ƒ ƒ =1.06, then draw ƒ ƒ =1.06 line on Fig. 11c, get σ 1 =9kPa, ƒ cc =8.5kPa, and get δ=67°. Then we can determine δ = 60°, ƒ cc = 8.5 kPa, γ = 2120 kg/m 3 .
(7) Avoid the minimum discharge opening width of the (conical bucket) arching according to the formula:
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A pure molybdenum rod is a cylindrical bar made entirely of molybdenum, a chemical element with the symbol Mo and atomic number 42. Molybdenum is a refractory metal known for its high melting point, excellent thermal conductivity, and resistance to corrosion. Pure molybdenum rods are commonly used in various applications, including the manufacturing of electrodes, heating elements, and high-temperature furnaces. They are also utilized in the aerospace, defense, and medical industries due to their exceptional mechanical and thermal properties.
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