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GATE 2023 CH – Question 20

Fluid Mechanics and Mechanical Operations · Settling, centrifuges, cyclones, thickening, filtration, agitation and mixing · 1 mark · Multiple choice

For a packed-bed comprising of uniform-sized spherical particles of diameter $D_p$, the pressure drop across the bed is given by the Kozeny-Carman equation when the particle Reynolds number ($Re_p$) < 1. Under this condition, minimum fluidization velocity is proportional to $D_p^n$. Which one of the following is the CORRECT value of exponent $n$ ?

  1. 2
  2. −1
  3. −2
  4. 1

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Correct answer: (A) 2

Explanation

In the Kozeny-Carman (laminar) range the pressure drop per unit height is $\frac{\Delta P}{L} \propto \frac{\mu u}{D_p^2}$. At minimum fluidisation $\frac{\Delta P}{L}$ is fixed by the weight of the bed, which does not depend on $D_p$. So $u_{mf} \propto D_p^2$ and $n = 2$.