In the previous paper, we had devied the following equation
P=1-e^-K·E
where P is probability of fracture, E, energy of impact and K, constant.
In the present paper, the effect of repeated impact on P has been studied and the following results were obtained
P=1-e^-K·n·E (E≥E_C)
P=P_∞(E){1-e^-K·n·E} (E<E_C)
where P_∞(E) is final value of probability of fracture when energy of impact is E, n, number of impact and E_C, critical energy of impact.

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In air-solid two-phase flow quite different mass flow rate, pipe diameter and air velocity are used and the sort of solid to be conveyed is in limitless variety. The relationship between these factors in horizontal and vertical flow has been shown in linear diagram. Moreover the coefficient of pressure drop due to acceleration of solid particles in horizontal and vertical flow have been obtained as a function of mass flow ratio and settling velocity.

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The analyses of Jenike and Walters are discussed in order to apply to structural design for mass-flow hoppers.
In the case of static conditions, Walters' analysis is not practical except very steep hoppers. On the assumption that no material yield takes place except on the hopper walls, that is, the Mohr stress circle touches the wall yield locus, Walters' analysis however applies to mass-flow hoppers in agreement with the experimental results.
In the case of dynamic conditions, with respect to the normal wall stress only, no significant difference is found in the values estimated from Jenike's and Walters' analysis respectively. The estimated normal wall stresses agree with the experimental results for granular materials and powders used.
The minimum dimension of the hopper outlet determined by means of Jenike's criterion is compared favourably with the experimental results. The flow-factor of the mass-flow hopper, however, is estimated on the basis of the static major stress, which is considered to be the largest in lower part of the hopper, since the powder develops a strength according to the stress. On the other hand, the failure function of the powder is measured using our own direct shear tester in which the powder specimen is sheared under restriction.

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