GATE 2026 BT – Question 65
A packed bed bioreactor with length 1 m and inside diameter 10 cm has liquid flowing at an interstitial velocity of 1 cm s$^{-1}$. Given a volumetric flow rate of 0.025 L s$^{-1}$, the void fraction of the packed bed is ______. (rounded off to two decimal places)
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Correct answer: 0.31 to 0.33
Explanation
The cross-sectional area is $\pi(5\text{ cm})^2 = 78.54$ cm$^2$. The superficial velocity is $\frac{25\ \text{cm}^3/\text{s}}{78.54\ \text{cm}^2} = 0.318$ cm/s. The interstitial velocity is the superficial velocity divided by the void fraction, so $\varepsilon = \frac{0.318}{1} = 0.32$.