• International Journal of Fluid Machinery and Systems
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• v.8 no.2
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• pp.94-101
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• 2015

To investigate the influence of blade profiles on cavitation behavior in impeller of centrifugal pump, a centrifugal pump with five different blade profiles impellers are studied numerically. The impellers with five different blade profiles (single arc, double arcs, triple arcs, logarithmic spiral and linear-variable angle spiral) were designed by the in-house hydraulic design code using geometric parameters of IS 150-125-125 centrifugal pump. The experiments of the centrifugal pump have been conducted to verify numerical simulation model. The numerical results show that the blade profile lines has a weak effect on cavitation inception near blade inlet edge position, however it has the key effect on the development of sheet cavitation in impeller, and also influences the distribution of sheet cavitation in impeller channels. A slight changing of blade setting angle will induce significant difference of cavitation in impeller. The sharp changing of impeller blade setting angle causes obvious cavitation region separation near the impeller inlet close to blade suction surface and much more flow loss. The centrifugal pump with blade profile of setting angle gently changing (logarithmic spiral) has the super cavitation performance, which means smaller critical cavitation number and lower vapor cavity volume fraction at the same conditions.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.13-17
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• 1987

Let S denote the class of nivalent functions normalized so that f(0)=f'(0)-1=0 in vertical bar z vertical bar <1. Let $S_{\alpha}$$^{*}$, -.pi./2<.alpha.<.pi./2, denote the subclass of S that satisfies Re $e^{i{\alpha}}$zf'(z)/f(z).geq.0 in vertical bar z vertical bar <1; then f is called .alpha.-spiral-like and the case .alpha.=0 is the class of normalized starlike functions [6, pp.52]. Let T denote the class of functions f normalized as above and satisfying Im z[Im f(z)]..geq.0 in vertical bar z vertical bar <1; then f is called typically real and T contains those functions of S whose coefficients are real [6, pp.55]. Also, in view of [6, pp.231], let B(.lambda.) be the class of function normalized as above and map vertical bar z vertical bar <1 onto the complement of an arc with radial angle .lambda.(0<.lambda.<.pi./2). The radial angle is meant to be the angle between the tangent and radial vectors to the arc. This note includes a sharp version for Corollary 1 of [2] when f.mem. $S_{\alpha}$$^{*}$ as well as a logarithmic coefficient estimate.nt estimate.

• Geotechnical Engineering
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• v.4 no.4
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• pp.39-50
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• 1988

Until now, most probabilistic approaches to the slope stability analysis have been accomplished on the arc failure surface without load. In this study, the relationships between the probability of failure and the safety factor are investigated when the shape of failure is logarithmic spiral on the homogeneous slope with ground water level, the probability distributions of the load and the strength parameter of soil being assumed as normal distribution, log-normal distribution and beta distribution. The results obtained are as follows; 1. For the same safety factor, the design of slope is more reasonable by using the probability of failure than by the safety factor because the probability of failure is increased as the coefficient of variation is increased. 2, The safety factor is more reasonably determined by the coefficient of variation of the strength parameter than by the field condition when the safety factor is applied to design of slope.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.2
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• pp.425-433
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• 2019

In this study, a simple method of calculating the passive earth pressure coefficient, which is based on the limit equilibrium method, was proposed and the calculated earth pressure coefficients were compared with those of several researchers. The angle of the linear failure surface, which is combined with the logarithmic spiral arc, to the failure surfaces of the passive zone was derived and the whole passive thrust acting on the Rankine passive zone was considered in the proposed method instead of considering the horizontal component of passive thrust. The variations of the passive earth pressure coefficients of the proposed method showed the same tendency as that of the Coulomb's passive earth pressure coefficients with an inclined angle of backfill and internal friction angle. The magnitude of passive earth pressure coefficients of the proposed method were smaller than those of the Coulomb in almost all cases. A comparison of the passive earth pressure coefficients with the wall friction angle revealed the passive earth pressure coefficients of the proposed method to be smaller than those of the Coulomb and the differences between the two values increased with increasing internal friction angle and wall friction angle. A comparison of the passive earth pressure coefficients of the proposed method with those of the existing researchers for the considered internal friction angles of $25^{\circ}$, $30^{\circ}$, $35^{\circ}$, and $40^{\circ}$ and three wall friction angles revealed the maximum percentage differences for the Kerisel and Absi method, Soubra method, Lancellotta method, $Ant\tilde{a}o$ et al. method, Kame method, and Reddy et al. method to be 4.8%, 3.8%, 31.1%, 4.0%, 20.6%, and 12.8% respectively. The passive earth pressure coefficient and existing pressures were similar in all cases.

• Journal of the Korean Geotechnical Society
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• v.15 no.4
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• pp.167-173
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• 1999

In this paper the failure behavior of the reinforced earth retaining wall structures according to the deformed types of the face was studied by model test using carbon rods. In model test the behavior of the face for the model of the reinforced earth wall was divided into three cases : the displacement of the top part(case 1), the lateral displacement(case 2) and the displacement of the lower part (case 3). The photographic method was applied to examine the failure line of the deformed wall with the naked eye. The failure line shows a parabolic shape for case 1, a large circular arc for case 2 and a logarithmic spiral for case 3 in the experimental results. The design failure line for the coherent gravity structure hypothesis was most similar to the failure line for the case of the lower part displacement.