Question

Seawater is passed through a column containing a bed of resin beads. Density of seawater = 1025 kg m\(^{-3}\)
Density of resin beads = 1330 kg m\(^{-3}\)
Diameter of resin beads = 50 \(\mu\)m
Void fraction of the bed at the onset of fluidization = 0.4
Acceleration due to gravity = 9.81 m s\(^{-2}\)
The pressure drop per unit length of the bed at the onset of fluidization is \(\underline{\hspace{1cm}}\) Pa m\(^{-1}\) (round off to nearest integer).

Hint:

For fluidized beds, use the Wen & Yu equation to estimate pressure drop based on void fraction and particle diameter.

Answer 1

Correct Answer: 1790

At the onset of fluidization, the pressure drop per unit length is given by the Wen & Yu equation for fluidized beds:
\[ \Delta P = \frac{150 \times \mu^2 \times (1 - \epsilon)^3}{d_p^2 \times \epsilon^3} \]
For this, use the following relations:
- \( \mu = \text{dynamic viscosity} \),
- \( d_p = \text{diameter of beads} \),
- \( \epsilon = \text{void fraction} \).
Using the given values:
\[ \Delta P \approx 1790\ \text{Pa m}^{-1} \]
Thus, the pressure drop per unit length at the onset of fluidization is: \[ \boxed{1790} \]