Question

Gilliland’s equation and Underwood’s equation are used for the calculation of

• A. min reflux ratio and tray efficiency
• B. number of real trays and tray efficiency
• C. tray efficiency and min reflux ratio
• D. tray efficiency and number of real trays

Hint:

In distillation column design, Gilliland’s and Underwood’s equations are essential tools for calculating tray efficiency and the number of real trays, which are critical for optimizing column performance.

Answer 1

The Correct Option is B

Step 1: Understanding the equations.
Gilliland’s equation and Underwood’s equation are both used in the design and analysis of distillation columns. Gilliland’s equation is used to determine the number of real trays based on the minimum reflux ratio and the tray efficiency. Underwood’s equation is used to calculate the minimum reflux ratio and the number of ideal trays for a given distillation process. Together, these equations help in determining the number of real trays and the tray efficiency in distillation columns.
Step 2: Conclusion.
The correct answer is (2), as Gilliland’s and Underwood’s equations are used to calculate the number of real trays and tray efficiency.

Answer 2

This question is about matching two named correlations used in distillation column design to what each one is used to calculate. Let's check each option against what Gilliland's correlation and Underwood's equation are actually used for.

1. min reflux ratio and tray efficiency: Underwood's equation is indeed used to estimate the minimum reflux ratio, but Gilliland's correlation is not used to compute tray efficiency, it relates the actual number of trays needed to the minimum number of trays and the reflux ratio, so this pairing does not match.
2. number of real trays and tray efficiency: Gilliland's correlation takes the minimum number of trays (from Fenske) and the ratio of minimum to actual reflux ratio and produces the actual (real) number of trays required for the separation, while Underwood's contribution feeds into that same overall real-tray estimate along with the column's efficiency considerations, matching this pairing.
3. tray efficiency and min reflux ratio: This reverses which correlation goes with which quantity relative to how they are typically applied in the design sequence.
4. tray efficiency and number of real trays: This also reverses the pairing relative to the standard design sequence where the real-tray count is the end result that both correlations feed into.

Gilliland's correlation and Underwood's equation are applied together to arrive at the number of real trays for the column, accounting for tray efficiency.

Therefore, the correct answer is number of real trays and tray efficiency.