Question:

The porosity of a fluidized bed increased from 0.5 to 0.75. If the initial bed of height was 10 cm, the final bed height is:

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Solids volume constant: (1 - \(\epsilon\))H = constant.
Higher porosity = higher bed height.
  • 16 cm
  • 20 cm
  • 18 cm
  • 14 cm
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The Correct Option is B

Solution and Explanation

Step 1: Understanding the Concept:
Porosity is the void fraction in a bed.
The bed height changes with porosity.

Step 2: Key Formula or Approach:

Volume of solids is constant: (1 - \(\epsilon_1\)) \(\times\) H\(_1\) = (1 - \(\epsilon_2\)) \(\times\) H\(_2\).

Step 3: Detailed Explanation:

\(\epsilon_1\) = 0.5, \(\epsilon_2\) = 0.75, H\(_1\) = 10 cm.
(1 - 0.5) \(\times\) 10 = (1 - 0.75) \(\times\) H\(_2\).
0.5 \(\times\) 10 = 0.25 \(\times\) H\(_2\).
5 = 0.25 H\(_2\).
H\(_2\) = 5 0.25 = 20 cm.
Thus, the final bed height is 20 cm.

Step 4: Final Answer:

The final bed height is 20 cm.
Hence, the correct option is (B).
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