The Souders-Brown equation is a fundamental tool in chemical engineering used to calculate the maximum allowable vapor velocity in vertical vessels, such as distillation columns. This equation is crucial for designing and optimizing separation processes, ensuring efficient operation without liquid entrainment.

The Souders-Brown equation is expressed as:

\[ V = C\sqrt{\frac{\rho_L - \rho_V}{\rho_V}} \]

Where:

- \( V \) is the maximum allowable vapor velocity (m/s)
- \( C \) is the Souders-Brown coefficient (dimensionless)
- \( \rho_L \) is the liquid density (kg/m³)
- \( \rho_V \) is the vapor density (kg/m³)

Let's calculate the maximum allowable vapor velocity using the Souders-Brown equation:

- Given:
- Souders-Brown coefficient (\( C \)) = 0.1
- Liquid density (\( \rho_L \)) = 1000 kg/m³
- Vapor density (\( \rho_V \)) = 1.2 kg/m³

- Apply the Souders-Brown equation: \[ V = C\sqrt{\frac{\rho_L - \rho_V}{\rho_V}} \]
- Substitute the known values: \[ V = 0.1 \sqrt{\frac{1000 \text{ kg/m³} - 1.2 \text{ kg/m³}}{1.2 \text{ kg/m³}}} \]
- Simplify the expression under the square root: \[ V = 0.1 \sqrt{\frac{998.8 \text{ kg/m³}}{1.2 \text{ kg/m³}}} \]
- Calculate the final result: \[ V \approx 2.88 \text{ m/s} \]

Let's visualize the concept of vapor velocity in a distillation column:

This diagram illustrates:

- The distillation column with trays
- Upward vapor flow (blue arrows)
- Downward liquid flow (not shown, but occurs at column walls and through downcomers)
- The Souders-Brown equation helps determine the maximum vapor velocity to prevent liquid entrainment

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