GATE 2021 CH – Question 52
Seawater is passed through a column containing a bed of resin beads. Density of seawater = $1025\ \mathrm{kg\,m^{-3}}$; density of resin beads = $1330\ \mathrm{kg\,m^{-3}}$; diameter of resin beads = $50\ \mu\mathrm m$; void fraction of the bed at the onset of fluidization = 0.4; acceleration due to gravity = $9.81\ \mathrm{m\,s^{-2}}$. The pressure drop per unit length of the bed at the onset of fluidization is _____ Pa/m (round off to nearest integer).
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Correct answer: 1795
Explanation
At incipient fluidization, the drag force from the flowing fluid balances the buoyancy-corrected weight of the particles. For bed area A and height L,
$$\Delta P\,A=(\rho_s-\rho_f)(1-\varepsilon)ALg.$$
Thus
$$\frac{\Delta P}{L}=(1330-1025)(1-0.4)(9.81)=1795.23\ \mathrm{Pa/m}.$$
Rounded to the nearest integer, **1795 Pa/m**. Particle diameter is unnecessary for this force balance; it would be needed to calculate the minimum fluidization velocity.