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:''For Morton number in number theory, see [[Morton number (number theory)]].''

In [[fluid dynamics]], the '''Morton number''' ('''Mo''') is a [[dimensionless number]] used together with the [[Eötvös number]] to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase, ''c''.  The Morton number is defined as

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

where ''g'' is the acceleration of gravity, <math>\mu_c</math> is the [[viscosity]] of the surrounding fluid, <math>\rho_c</math> the [[density]] of the surrounding fluid, <math> \Delta \rho</math> the difference in density of the phases, and <math>\sigma</math> is the [[surface tension]] coefficient.  For the case of a bubble with a negligible inner density the Morton number can be simplified to 

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

The Morton number can also be expressed by using a combination of the [[Weber number]], [[Froude number]] and [[Reynolds number]],

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

The Froude number in the above expression is defined as

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

where ''V'' is a reference velocity and ''d'' is the [[Equivalent spherical diameter|equivalent diameter]] of the drop or bubble.

==References==
*{{cite book |first=R. |last=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=0-12-176950-X }}

{{NonDimFluMech}}
[[Category:Dimensionless numbers]]
[[Category:Fluid dynamics]]