Morton number, abbreviated as Mo, a dimensionless number, is the shape of bubbles or drops moving in a surrounding fluid or continuous phase, based on the balance of gravitational, viscous, and surface tension forces. It is used in fluid dynamics, particularly in the study of multiphase flow. The Morton number characterizes the balance between viscous, surface tension, and gravitational forces in a system.
Morton Number formula |
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\( Mo \;=\; \dfrac{ g \cdot \mu^4 \cdot \Delta \rho }{ \rho^2 \cdot \sigma^3 }\) \( \mu \;=\; \sqrt[4] { \dfrac{ Mo \cdot \rho^2 \cdot \sigma^3 }{ g \cdot \Delta \rho } }\) \( \Delta \rho \;=\; \dfrac{ Mo \cdot \rho^2 \cdot \sigma^3 }{ g \cdot \mu^4 }\) \( \rho \;=\; \sqrt{ \dfrac{ g \cdot \mu^4 \cdot \Delta \rho }{ Mo \cdot \sigma^3 } }\) \( \sigma \;=\; \sqrt[3] { \dfrac{ g \cdot \mu^4 \cdot \Delta \rho }{ Mo \cdot \rho^2 } }\) |
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| Symbol | English | Metric |
| \( Mo \) = Morton number | \(dimensionless\) | \(dimensionless\) |
| \( g \) = Gravitational Acceleration | \(ft\;/\;sec^2\) | \(m\;/\;s^2\) |
| \( \mu \) (Greek symbol mu) = Dynamic Viscosity of Surrounding Fluid | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
| \( \Delta \rho \) = Density Differential in the phases | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( \rho \) (Greek symbol rho) = Density of Surrounding Fluid | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( \sigma \) (Greek symbol sigma) = Surface Tension Coefficient | \(lbf\;/\;ft\) | \(N\;/\;m\) |
