Interpretation: The pressure drop through packed tubes is to be calculated for the different conditions of the pellets.
Concept introduction: The pressure drop through the packed tubes is calculated by the Ergun equation which is a combination of the Kozeny-Carman equation and Burke-Plummer equation.
The Kozeny-Carman equation is applicable for the particles in a bed whose Reynold’s number is less than 1. It is given as,
In the above formula, the notations used are,
The Burke Plummer equation is applicable for the particles in a bed whose Reynold’s number is more than 1000. It is given as,
The density of air can be given as,
In the equation (3), notations used are,
P is the pressure at which air enters
M is the molecular weight of air
R is the Universal Gas constant
T is the temperature at which air enters
Combining equation (1) and equation (2) we get Ergun equation.
Answer to Problem 7.1P
The pressure drop for diameter of pellets 0.003 m is 18465.6 Pa and when the diameter of pellet is increased to 0.004 m, the pressure drop is reduced by 5667.1 Pa or 30.7%.
Explanation of Solution
The data given for the air density calculation is,
Substitute this data in equation (3),
Now other data given to calculate pressure drop is,
For air at the given temperature, the viscosity from appendix is,
Substitute all the required data from above in equation (4),
When diameter is increased from 0.003 m to 0.004 m, the increase in diameter is 1.33 times the original so pressure drop will reduce by the same factor as all conditions are identical as previous conditions.
Thus,
The reduction in pressure is the difference between equation (5) and equation (6).
Reduction in pressure = 18465.6 Pa − 12798.5 Pa = 5667.1 Pa
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Chapter 7 Solutions
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