在現今科技中，為了金屬噴粉以及計算流體力學發展，得知高溫金屬液之物性變得十分重要，但大多量測高溫金屬液體之設備，除了價格高昂之外，且至多僅能同時量測兩種物性，因此本文使用排液容器法(Draining vessel method)的方法學，其優勢為一次量測三種物性，且裝置較簡易價格較低廉，再配合適當的演算法，同時量測出密度、黏度以及表面張力，此方法不論是冷流場抑或是高溫金屬液都可以進行量測。本實驗以錫液為主，系統設計以傳統高溫爐為雛形，將底部開有小孔之圓柱形不鏽鋼乾鍋放置高溫爐內部進行加溫，並在上方通一塞子孔道，以及在下方通一排液孔道，使預測物性之流體能流出此容器，不同的流體物性會有不同的流動特性，本文使用描述內部流動特性之修正伯努力方程式來收集其液面變化之高度頭與質量通量的數據，並結合數值方法配合敏感度分析使用適當的高度頭範圍，並使理論高度頭與實驗高度頭誤差平方和最小化，以得到最佳物性解。本研究使用此數值方法量測錫液，比較一次迴歸與三階段迴歸之收斂結果，發現密度與黏度的量測能有效提升準確性。

To impure the results of metal injection molding and the accuracy of computational fluid dynamics, it is important to know the physical properties of high-temperature metal liquids. Most of the measuring instruments can only measure one or two physical properties at the same time. Recently a method called Draining Vessel Method has been developed to simultaneously measure density, viscosity and surface tension. This method can be applied to both a cold flow field and a high temperature metal liquid. In this thesis, the physical properties of tin liquid were measured using the draining vessel method. The experimental system was set up with a furnace to build the prototype. A cylindrical stainless steel container with a small hole at the bottom is placed inside the furnace for heating, and a plug hole is opened at the furnace upper side, and a drain hole is opened at the furnace bottom. The fluid can flow from the container to the load cell. Different fluid properties result in different inject. The modified Bernoulli equations describing flow characteristics to collect two data of elevation height head and mass flux. Combined with numerical methods and sensitivity analysis. The fluid’s density, viscosity and surface tension were computed iteratively through minimizing the difference between the theoretical and experimental elevation heads. In this study, this numerical method was used to measure the tin liquid, and the convergence results of the primary regression and the three-stage regression were compared. It was found that the measurement of density and viscosity can effectively improve the accuracy.

Brooks, R. F., Dinsdale, A. T., & Quested, P. N. (2005). The measurement of viscosity of alloys—a review of methods, data and models. Measurement science and technology, 16(2), 354-362.
Crawley, A. F. (1974). Densities of liquid metals and alloys. International Metallurgical Reviews, 19(1), 32-48.
Gancarz, T., Gąsior, W., & Henein, H. (2014). The discharge crucible method for making measurements of the physical properties of melts: an overview. International Journal of Thermophysics, 35(9-10), 1725-1748.
Gancarz, T., Moser, Z., Gąsior, W., Pstruś, J., & Henein, H. (2011). A comparison of surface tension, viscosity, and density of Sn and Sn–Ag alloys using different measurement techniques. International Journal of Thermophysics, 32(6), 1210-1233.
Gaskell, D. R., McLean, A., & Ward, R. G. (1969). Density and structures of ternary silicate melts. Transactions of the Faraday Society, 65, 1498-1508.
Girault, H. H. J., Schiffrin, D. J., & Smith, B. D. V. (1984). The measurement of interfacial tension of pendant drops using a video image profile digitizer. Journal of colloid and interface science, 101(1), 257-266.
Herschel, W. H. (1917). Determination of absolute viscosity by short-tube viscosimeters. Govt. Print. Off..
Keene, B. J. (1993). Review of data for the surface tension of pure metals. International Materials Reviews, 38(4), 157-192.
Lagarias, J. C., Reeds, J. A., Wright, M. H., & Wright, P. E. (1998). Convergence properties of the Nelder--Mead simplex method in low dimensions. SIAM Journal on optimization, 9(1), 112-147.
Pstruś, J., Fima, P., & Gąsior, W. (2011). Surface tension, density, and thermal expansion of (Bi-Ag) eut-Zn alloys. Journal of electronic materials, 40(12), 2465-2469.
Roach, S. J., & Henein, H. (2003). A dynamic approach to determining the surface tension of a fluid. Canadian metallurgical quarterly, 42(2), 175-186.
Roach, S. J., & Henein, H. (2005). A new method to dynamically measure the surface tension, viscosity, and density of melts. Metallurgical and Materials Transactions B, 36(5), 667-676.
Roach, S. J., & Henein, H. (2012). Physical properties of AZ91D measured using the draining crucible method: Effect of SF 6. International Journal of Thermophysics, 33(3), 484-494.
Self, M. W., & Ripken, J. F. (1955). Steady-state cavity studies in a free-jet water tunnel.
Thresh, H. R., Crawley, A. F., & White, D. W. G. (1968). The densities of liquid tin, lead, and tin-lead alloys. TRANS MET SOC AIME, 242(5), 819-822.
Weast, R. C., Astle, M. J., & Beyer, W. H. (1988). CRC handbook of chemistry and physics (Vol. 69). Boca Raton, FL: CRC press.
莊宗翰. (2019). 以排液容器法量測流體的密度、黏度以及表面張力. 國立中央大學碩士論文.
顏芷珊. (2019). 以計算流體力學結合排液容器法量測錫液之密度、黏度與表面張力係數. 國立中央大學碩士論文.