A cylindrical packed bed of height 1 m is filled with equal sized sphe...
Given information:
- Height of the cylindrical packed bed = 1 m
- Density of the particles = 1500 kg/m3
- Void fraction of the bed = 0.45
- Density of air = 1 kg/m3
- Acceleration due to gravity = 9.8 m/s2
Calculating the pressure drop:
The pressure drop across the bed at incipient fluidization can be calculated using the Ergun equation, which relates the pressure drop to the velocity of the fluid through the bed.
Ergun equation:
The Ergun equation is given by:
ΔP/L = 150 (1 - ε)^2 (ρu/ε^3) + 1.75 ρu^2 (1 - ε)/ε^3
Where:
- ΔP/L is the pressure drop per unit length of the bed
- ε is the void fraction of the bed
- ρu is the density of the fluid-solid mixture
Calculating the density of the fluid-solid mixture:
The density of the fluid-solid mixture can be calculated using the equation:
ρu = ε ρp + (1 - ε) ρf
Where:
- ρp is the density of the particles
- ρf is the density of the fluid
Substituting the given values into the equation:
ρu = 0.45 * 1500 + (1 - 0.45) * 1 = 1500 * 0.45 + 0.55 = 675 + 0.55 = 675.55 kg/m3
Calculating the pressure drop:
Substituting the values of ε and ρu into the Ergun equation:
ΔP/L = 150 (1 - 0.45)^2 (675.55/0.45^3) + 1.75 * 675.55^2 (1 - 0.45)/0.45^3
Simplifying the equation:
ΔP/L = 150 * 0.55^2 * 675.55/0.45^3 + 1.75 * 675.55^2 * 0.55/0.45^3
Calculating the pressure drop:
ΔP/L = 8079.61 Pa
Answer:
The pressure drop across the bed at incipient fluidization is 8079.61 Pa.