Air flows through a packed bed of a powdery material of 2 cm depth at a superficial gas
velocity of 1 cm/s. A manometer connected to the unit registers a pressure drop of 2 cm of
water. The bed has a porosity of 0.6. If Burke - Plummer equation is valid for the range of
study, estimate the particle diameter size of the powder.
Data:
Par = 1.23 kg/m', poate = 1000 kg/m', g = 9.8 m/s” and O. = 1.
a) D = 4.06 x 10 m
b) D = 5.06x10 m
c) D = 6.06x10 m
d) D. = 8.06x10m
Answer
А A
B
D
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Answers
Explanation:
Mass flow rate of Air = 60 kg/min = 1 kg/sec
Density of Air (r) = 0.001156 gm/cc = 1.156 kg/m3
Viscosity of Air (m) = 0.0182 cP = 0.0182 x 10-3 kg/(m.sec)
Bed porosity (e) = 0.38
Diameter of bed (D)= 125 cm = 1.25 m
Length of bed (L) = 250 cm = 2.5 m
Dia of particles (Dp)= 1.25 cm = 0.0125 m
Sphericity (F s) = 1 (sphere)
Formulae:
NRePM = DpVor/(m (1 - e) )
For laminar flow (i.e. NRePM < 10) pressure drop is given by Blake-Kozeny equation.
For turbulent flow (i.e. NRePM > 1000) pressure drop is given by Burke-Plummer equation.
For intermediate flows pressure drop is given by Ergun equation
Superficial velocity Vo = Volumetric flow rate/ cross-sectional area of bed
Calculations:
Volumetric flow rate = mass flow rate / density = 1 / 1.156 = 0.865 m3/sec
Superficial velocity Vo = 0.865 / ( (p/4) D2 ) = 0.865 / ( (p/4) 1.252 ) = 0.705 m/sec
NRePM = 0.0125 x 0.705 x 1.156 / (0.0182 x 10-3 x ( 1- 0.38 ) ) = 903
We shall use Ergun equation to find the pressure drop.
i.e. Dp x 0.0125 x 0.383 / ( 2.5 x 1.156 x 0.7052 x ( 1 - 0.38 ) ) = 150 / 903 + 1.75
Dp x 7.702 x 10-4 = 1.92
Dp = 1.92 / 7.702 x 10-4 = 2492.92 N/m2
Answer:
Your answer is 2492.92 N/m2