Galileo number, abbreviated as Ga, a dimensionless number, also called Galilei number, used in fluid dynamics that compares gravitational forces to viscous forces in a flow system. It’s particularly relevant in situations where gravity drives the motion of a fluid, think of sediment settling, bubbles rising, or flow in packed beds, without the complicating effects of inertia dominating the picture. It’s less common than some other numbers like Reynolds or Grashof, but it pops up in specific contexts like multiphase flows or low-speed viscous regimes.
Galileo Number Interpretation
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High Galileo Number (Ga >> 1) - Gravitational forces dominate over viscous forces. The fluid or object moves freely under gravity’s influence, with viscosity playing a minor role. This happens with large scales, dense fluids, or low viscosity (a heavy particle sinking fast in water).
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Low Galileo Number (Ga << 1) - Viscous forces dominate over gravitational forces. Motion is heavily damped by viscosity, and gravity struggles to drive significant flow. This occurs with small scales, high viscosity, or low density (a tiny particle creeping through honey).
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Intermediate Ga - A transitional regime where both forces matter. The outcome depends on the specifics, motion might start but be noticeably slowed by viscosity.
The Galileo number is particularly important in areas such as fluid mechanics, chemical engineering, and geophysics, where it helps engineers and scientists understand and predict the behavior of fluid flows under different conditions.
Galileo number formula |
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| \( Ga \;=\; \dfrac{ g \cdot l_c^3 \cdot \mu^2 }{ \rho^2 }\) | ||
| Symbol | English | Metric |
| \( Ga \) = Galileo Number | \(dimensionless\) | \(dimensionless\) |
| \( g \) = Gravitational Acceleration | \(ft \;/\; sec^2\) | \(m \;/\; s^2\) |
| \( l_c \) = Characteristic Length | \(ft\) | \(m\) |
| \( \mu \) (Greek symbol mu) = Fluid Viscosity | \(lbf - sec \;/\; ft^2\) | \( Pa - s \) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
