查看“︁莫顿数”︁的源代码

'''莫顿数'''（{{lang-en|Morton number}}，簡稱'''Mo'''）是[[流體力學]]的[[無因次量]]，和[[厄特沃什数]]一起描述氣泡或是水滴在流體或是連續相（c）中移動時的外形<ref>{{citation |first1=R. |last1=Clift |first2=J. R. |last2=Grace |first3=M. E. |last3=Weber |title=Bubbles Drops and Particles |location=New York |publisher=Academic Press |year=1978 |isbn=978-0-12-176950-5 }}</ref>。莫頓數得名自美國數學家{{link-en|Rose Morton|Rose Morton}}，他和W. L. Haberman在1953年一起描述此物理量<ref>{{citation|first1=W. L.|last1=Haberman|first2=R. K.|last2=Morton|title=An experimental investigation of the drag and shape of air bubbles rising in various liquids|url=https://archive.org/details/experimentalinve00habe|series=Report 802|publisher=Navy Department: The David W. Taylor Model Basin|year=1953}}</ref><ref>{{cite journal | last1 = Pfister | first1 = Michael | last2 = Hager | first2 = Willi H. | date = May 2014 | doi = 10.1061/(asce)hy.1943-7900.0000870 | issue = 5 | journal = Journal of Hydraulic Engineering | page = 02514001 | title = History and significance of the Morton number in hydraulic engineering | volume = 140 | url = http://infoscience.epfl.ch/record/198760/files/2014_971_Pfister_Hager_history_and_significance_Morton_number_in_hydraulic_engineering.pdf | access-date = 2024-09-22 | archive-date = 2016-10-02 | archive-url = https://web.archive.org/web/20161002104140/https://infoscience.epfl.ch/record/198760/files/2014_971_Pfister_Hager_history_and_significance_Morton_number_in_hydraulic_engineering.pdf | dead-url = no }}</ref>。

莫顿数定義為：
: <math>\mathrm{Mo} = \frac{g \mu_c^4 \, \Delta \rho}{\rho_c^2 \sigma^3}, </math>

其中：
:''g''為重力加速度
:<math>\mu_c</math>為周圍流體的[[黏度]]
:<math>\rho_c</math>為周圍流體的[[密度]]
:<math> \Delta \rho</math>為兩相的密度差
:<math>\sigma</math>為[[表面張力]]係數

針對內部密度小到可以忽略的氣泡，莫顿数可以簡化如下： 

:<math>\mathrm{Mo} = \frac{g\mu_c^4}{\rho_c \sigma^3}.</math>

莫頓數可以視為是流體粘滯力和表面張力之間的比例。

莫頓數只和氣泡內部以及氣泡外流體的材料特性有關，和氣泡的大小無關，由於氣泡的大小會隨時間而變化，使用莫頓數可以消除這部分的影響。

莫顿数可以用[[韋伯數]]、[[福祿數]]和[[雷諾數]]定義：

:<math>\mathrm{Mo} = \frac{\mathrm{We}^3}{\mathrm{Fr}\, \mathrm{Re}^4}.</math>

上述的福祿數定義如下：

:<math>\mathrm{Fr} = \frac{V^2}{g d}</math>

其中
:''V''為參考速度
:''d''為泡泡或水滴的[[等效球直徑]]
==相關條目==
*[[毛細數]]
==參考資料==
*{{cite book |first=R. |last=Clift |first2=J. R. |last2=Grace |first3=M. E. |last3=Weber |title=Bubbles Drops and Particles |url=https://archive.org/details/bubblesdropspart0000clif |location=New York |publisher=Academic Press |year=1978 |isbn=0-12-176950-X }}
{{reflist}}
{{NonDimFluMech}}
[[Category:流體力學中的無因次量]]
[[Category:流体动力学]]