Difficulty: Medium
Correct Answer: 25%
Explanation:
Introduction / Context:
Gas holdup (epsilon_g) is the volume fraction of gas in a gas–liquid dispersion at steady state. In tall columns and aerated reactors, holdup expands the dispersion height compared with the unaerated liquid height. This problem uses height expansion to estimate holdup quickly.
Given Data / Assumptions:
Concept / Approach:
For the same vessel cross-section, volume is proportional to height. Gas holdup equals gas volume divided by total dispersion volume. With heights: epsilon_g = (H_aerated − H_liquid) / H_aerated.
Step-by-Step Solution:
1) Compute the height difference: ΔH = 10 − 7.5 = 2.5 m.2) Divide by aerated height: epsilon_g = 2.5 / 10 = 0.25.3) Convert to percent: 0.25 * 100 = 25%.
Verification / Alternative check:
As a quick consistency check, if holdup were 0% there would be no expansion (heights equal); if holdup were 100% the liquid column would be all gas—impossible. A 25% expansion is realistic for vigorously aerated systems.
Why Other Options Are Wrong:
100% and 75% are far too high; 50% would require H_liquid to be half of H_aerated (5 m), not 7.5 m; 12.5% does not match the computed ratio.
Common Pitfalls:
Using H_liquid in the denominator or forgetting that holdup is based on total aerated volume, not the liquid-only height.
Final Answer:
25%
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