Imagine a pressure conveying system of which the capacity needs to be calculated.
Knowns are:
-Compressor volume.
-Begin velocity (=0)
-End pressure (f.i. a silo pressure=atmospheric)
Unknowns are:
-Compressor pressure
-Capacity
Mathematically the problem is now that we have 2 unknowns and 1 algorithm, which is, by definition, unsolvable.
To start such a calculation is by assuming one of the 2 unknowns is known (pressure drop).
Actually, the number of unknowns is mathematically reduced to one.
The second unknown (capacity) is guessed, and the calculation is executed.
The calculation results in a calculated pressure drop, which must comply with the assumed pressure drop.
Compressor pressure – calculated pressure drop = 0
The first calculation will (almost) never meet that requirement.
It the calculation results in a higher calculated pressure drop, then the requirement, the guessed capacity is too high, and the calculation must be repeated for a lower, guessed, capacity.
This, until the requirement, compressor pressure – calculated pressure drop = 0, is met.
Repeating calculations until a requirement is met is an iterative process.
Following this approach, the algorithm can be made now so complex that every variable can be calculated, from particle velocity to velocity loss in a bend chance of choking, condensation, etc.
The solid loss factor is only accounting for the real material friction and collision losses.
I am not aware of any other software that uses this approach.
Most calculation methods assume the influence of the presence of material in an air stream as an increase of the air only pressure drop plus additional pressures (elevation, filter, etc.).
The material solid los factor is here presented as K. (Where K should be a function of the SLR and the Reynold number)
All simplifications in this approach are accounted for in the factor K, thereby becoming a kind of fudge factor, ignoring f.i. the real material velocity along the pipe length, possible sedimentation, etc...
This approach reduces the accuracy and reliability of a pneumatic conveying calculation. ■
A pneumatic conveying calculation requires an iterative algorithm.
Imagine a pressure conveying system of which the capacity needs to be calculated.
Knowns are:
-Compressor volume.
-Begin velocity (=0)
-End pressure (f.i. a silo pressure=atmospheric)
Unknowns are:
-Compressor pressure
-Capacity
Mathematically the problem is now that we have 2 unknowns and 1 algorithm, which is, by definition, unsolvable.
To start such a calculation is by assuming one of the 2 unknowns is known (pressure drop).
Actually, the number of unknowns is mathematically reduced to one.
The second unknown (capacity) is guessed, and the calculation is executed.
The calculation results in a calculated pressure drop, which must comply with the assumed pressure drop.
Compressor pressure – calculated pressure drop = 0
The first calculation will (almost) never meet that requirement.
It the calculation results in a higher calculated pressure drop, then the requirement, the guessed capacity is too high, and the calculation must be repeated for a lower, guessed, capacity.
This, until the requirement, compressor pressure – calculated pressure drop = 0, is met.
Repeating calculations until a requirement is met is an iterative process.
Following this approach, the algorithm can be made now so complex that every variable can be calculated, from particle velocity to velocity loss in a bend chance of choking, condensation, etc.
The solid loss factor is only accounting for the real material friction and collision losses.
I am not aware of any other software that uses this approach.
Most calculation methods assume the influence of the presence of material in an air stream as an increase of the air only pressure drop plus additional pressures (elevation, filter, etc.).
In formula form:
Compressor pressure = (1+SLR*K)*1/2*air density*airvelocity^2*L/D
The material solid los factor is here presented as K. (Where K should be a function of the SLR and the Reynold number)
All simplifications in this approach are accounted for in the factor K, thereby becoming a kind of fudge factor, ignoring f.i. the real material velocity along the pipe length, possible sedimentation, etc...
This approach reduces the accuracy and reliability of a pneumatic conveying calculation. ■
Teus