Density of Air (ρ) = 6.8 kg/m³

Viscosity of Air (μ) = 0.025 cP = 0.025 x 10^-3 kg/(m.sec)

Bed porosity (ϵ) = 0.44

Length of bed (L) = 3.5 m

Dia of particles (D_p)= 6 mm = 0.006 m

Sphericity (φ_s) = 6 v_p / (D_pS_p)

v_p = volume of particle = D_p³ (for cube)

S_p = surface area of particle = 6 x D_p² (for cube)

NRe_PM = D_pV_oρ/(μ(1 - ϵ))

For laminar flow (i.e. NRe_PM < 10) pressure drop is given by Blake-Kozeny equation.

\(\displaystyle \frac{\Delta p \phi_s^2D_p^2\varepsilon^3}{LV_o\mu(1-\varepsilon)^2} = 150 \)

For turbulent flow (i.e. NRe_PM > 1000) pressure drop is given by Burke-Plummer equation.

\(\displaystyle \frac{\Delta p \phi_sD_p\varepsilon^3}{L\rho V_o^2(1-\varepsilon)} = 1.75 \)

For intermediate flows pressure drop is given by Ergun equation

\(\displaystyle \frac{\Delta p \phi_sD_p\varepsilon^3}{L\rho V_o^2(1-\varepsilon)} = \frac{150\mu(1-\varepsilon)}{\phi_sD_pV_o\rho} + 1.75 \)

Superficial velocity V_o = Volumetric flow rate/ cross-sectional area of bed

Superficial velocity V_o = mass flow rate per unit area / density = 0.139 / 6.8 = 0.0204 m/sec

(φ_s) = 6 v_p / (D_pS_p) = 6 x 0.006³ / (0.006 x 6 x 0.006²) = 1

NRe_PM= 0.006 x 0.0204 x 6.8 / (0.025 x 10^-3 x (1-0.44)) = 59.45

We shall use Ergun equation to find the pressure drop.

\(\displaystyle \frac{\Delta p \phi_sD_p\varepsilon^3}{L\rho V_o^2(1-\varepsilon)} = \frac{150\mu(1-\varepsilon)}{\phi_sD_pV_o\rho} + 1.75 \)

i.e. Δp x 0.006 x 0.44³ / ( 3.5 x 6.8 x 0.0204² x ( 1 - 0.44 ) ) = 150 / 59.45 + 1.75

Δp x 0.0712= 4.273

Δp = 4.273 / 0.0712 = 60 N/m²

Last Modified on: 01-May-2024

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