S U M M A R YGreen's functions of the indirect effects of atmospheric loading is formulated taking into account the effect of the atmospheric thickness. This is a modification of the classic paper by Farrell that formulated the indirect effects of ocean loading by approximating the loading mass as a thin layer. Atmospheric loading differs from ocean loading in the ways in which gravitational attraction and pressure act. In the case of ocean loading, because both the gravitational attraction and the pressure can be considered to arise from the mass located at the surface of the Earth, the effects of both are treated together and are included in the load Love numbers defined for the problem. In the case of atmospheric loading, if the atmospheric thickness is taken into account, because the mass is distributed over a large elevation and the pressure is exerted at the surface of the Earth, defining a set of load Love numbers including both effects of gravitational attraction and pressure is no longer possible. In this paper, the indirect effects of gravitational attraction and pressure of atmospheric loading are formulated separately by introducing load Love numbers for each of them respectively. Asymptotic expressions of the various load Love numbers one order of magnitude more accurate than those given be Farrell are obtained by searching for the asymptotic solutions of their governing ordinary-differential equations. These are used to improve the convergence of the Legendre sums in the various Green's functions. We find that the consideration of the atmospheric thickness has a negligible effect when compared with the simple thin-layer approximation.

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The multi-blade centrifugal fan features an abundance of vanes (>48) and a spiral volute. The flowability and noise characteristics of the centrifugal fan are dependent on the type-line of volute and tongue geometries at the volute exit. The aim of this research was to find a better volute type-line for fan noise reduction without compromising on the performance. First, the viscosity factors of gas were used to modify the type-line shape of the volute by introducing a dynamic moment correction coefficient; a modified volute was then obtained to match the new fan system. Next, the performance of the original fan and retrofit fan were tested. The optimization scheme was verified and the feasibility of the proposed numerical calculation technique was confirmed.