# Morton Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Morton number, abbreviated as Mo, a dimensionless number, is the shape of bubbles or drops moving in a surrounding fluid or continuous phase.

The motion of gas bubbles in boiling water was of particular relevance in the early 19th century, as it affects the water circulation in boilers of steamboats, steam engines, and pumps.  The Morton number was developed in the 1930's and is dependent only on the properties of the two fluids and is independant of the system the fluids are being used in.  Mechanical engineers focused on Morton's number to optimize the efficiency of steam systems.

As with all dimensionless numbers, it is important to ensure that the units of the various variables line up and cancel eachother out as the calculation is being performed.

## Morton Number formula

 $$\large{ Mo = \frac{ g \; \mu^4 \; \Delta \rho }{\rho^2 \; \sigma^3 } }$$

### Where:

 Units English Metric $$\large{ Mo }$$ = Morton number $$\large{dimensionless}$$ $$\large{ \Delta \rho }$$ = density differential in the phases $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ \rho }$$ (Greek symbol rho) = density of surrounding fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ \mu }$$ (Greek symbol mu) = dynamic viscosity of surrounding fluid $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$ $$\large{ g }$$ = gravitational acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$ $$\large{ \sigma }$$ (Greek symbol sigma) = surface tension coefficient $$\large{\frac{lbf}{ft}}$$ $$\large{\frac{N}{m}}$$

Tags: Equations for Fluid