# 終端速度

2005年

## 摘要或動機

流體中之運動方程Fdrag = -k1V，無法符合實驗結果。我們的實驗結果顯示油中的自由落體的運動方程應該是Fdrag = -（k1V+ k2V2）。由不同材質的壓克力球（~1.18g/cm3）、玻璃珠（~2.47g/cm3）與水晶球（~2.66g/cm3）所獲得的終端速度（Vt）與球體半徑（a）的關係為a3(ρ-ρ')
= 0.00003（a Vt）2 + 0.00021（a Vt） + 0.00575，其中ρ與ρ'分別為球體密度與沙拉油密度（0.90 g/cm3）。

The motion of a sphere which is falling through a fluid is subject to the fluid
viscosity. In this study, we find out the relation between the radius of a sphere
and the terminal velocity. We used a digital camera to record the sphere's descent
in the oil. The three kinds of sphere we choose are acrylic（~1.18g/cm3）, glass （~2.47g/cm3）and
crystal （~2.66g/cm3）. Frame-by-frame analysis of the video footage yielded rough
estimates of the sphere's location within 1/30 seconds accuracy for statistically
consistent results. By measuring the location and time and analyzing them, we find
out the relation between the radius of a sphere and the terminal velocity. The expression
of the drag force,Fdrag = -k1V, is not cosistent with our results. The study indicates
the expression of the drag force should be Fdrag = -（k1V+
k2V2）. The expression
for the terminal velocities of the three kinds of sphere is of the form：a3(ρ-ρ')
= 0.00003（a Vt）2 + 0.00021（a Vt）+ 0.00575, where a is the radius, ρ is
the sphere
density and ρ' is the oil density（0.90 g/cm3）. In addition, if the radius is the
same, the terminal velocity of a denser sphere is higher and the time to approches
the terminal velocity is longer.

「為配合國家發展委員會「推動ODF-CNS15251為政府為文件標準格式實施計畫」，以及 提供使用者有文書軟體選擇的權利，本館檔案下載部分文件將公布ODF開放文件格式， 免費開源軟體可至LibreOffice 下載安裝使用，或依貴慣用的軟體開啟文件。」