Explanation: The Ergun Equation given as f = ΔP/L DP/ρϑS2 (∈3/1-∈) is fundamentally used to calculate the pressure drop in packed bed of given length and particle size, for a non-laminar flow regime.

Explanation: f= ΔP/L DP/ρϑS2(∈3/(1-∈)) is the Ergun equation for non-laminar flow regime, here DP is the Particle diameter or the pellet diameter and not the equivalent one.

Explanation: When we have very small particle size such as dp/di = 0.01, the flow regime more or less becomes laminar, hence the relation for laminar flow is Kozeny Carman equation.

Explanation: The Reynolds number for packed bed is defined as Re = \(\frac{\rho v_s D_P}{(1-\in)\mu} = \frac{990×2×0.003}{(1-0.14)×2.5×10^{-5}}\) = 2.76×105.

Now the Friction Factor is f=150/Re +1.75 = 150/2.76×105+1.75 = 1.751.

Explanation: The pressure drop per unit length of the bed is defined as \(\frac{∆P}{L} = \frac{-180μ}{S^2 D_P^2} (\frac{(1-∈)^2}{∈^3}) ϑ_S \)=\(-180×2.5\frac{\frac{10^{-5}}{0.6^2}}{0.003^2}×(\frac{(1-0.14)^2}{0.14^3})×2\) = -15625 Pa/m.

Explanation: Porosity = Vv/VT = (VT – Vp×N)/VT = \(\frac{\frac{\pi}{4}×0.03^2×0.1-100×\frac{4\pi}{3×8}×0.002^3}{\frac{\pi}{4}×0.03^2×0.1}\) = 0.994.

Explanation: Superficial velocity = Q/A = flow rate/cross section = \(\frac{5}{\frac{\pi}{4}×3^2}\)=0.7cm/s.

Explanation: The correct relation between the superficial velocity and the average velocity is given as ϑ=φu, whereϑ is the porosity of the bed. The average fluid velocity is the cumulative mean of the velocity of fluid through the voids which is difficult to measure.

Where V is the void volume, which is the volume excluding particles.

Explanation: The friction factor for a packed bed column for non laminar flow is given by the Ergun equation which can be represented as f = 150/Re+1.75.

∆P⁄L=[latex]\frac{f}{\frac{Dp}{\rho\vartheta_s^2}(\frac{\in^3}{1-\in})}\) = \(\frac{1.751}{\frac{0.003}{990×2*2}×\frac{0.14^3}{1-0.14}}\) = 724×106Pa.

Explanation: When we have fully packed bed, then the pressure drop experienced by the fluid is more for small particles as in that case the void space becomes very less because of the closed packed structure formed between the pellets.