Section summary |
---|

1. introduction |

2. Rhodes |

3. Air only
pressure drop method |

4. Universal conveying method |

5. Modified Zenz-Othmer method |

There are not many design models for
pressure dense phase published in the literature. The knowledge
mainly remains with systems vendors. The author has found 4
detailed methods in books or articles, which are presented in this
page.

Some explanations on each models is
given and an Excel Calculation Sheet is proposed for 3 of the
pressure drop calculation methods. *These files are given
without guarantee and the user should keep a critical eye on the
results and revert to reputable companies for detail design*.

Note some of the methods are iterative.
It is necessary to make some assumptions perform iteration to
confirm them by calculation.

**Commercial companies and consulting
firms have indeed their own models or have modified the methods
presented in this page to make them more accurate. They also
have large database of materials conveyed that are helpful to
calibrate the models.**

This method has been published in *Principles
of Powder Technology, M.J. Rhodes et al., Wiley, 1990*. It is
a rigorous method in its approach which is to breakdown the
pressure drop in multiple components, allowing to calculate them
one by one.

The following link gives access to an
Excel file performing the calculations according to this method -
no guarantee is given, one should use this file as a 1st
approximation and consult a reputable company for detail design :
Link

The file is showing an example given in
the solutions to the problems of the books and that can be found
in the site of the editor (Link).
There are minor differences in the calculations results.

Contrary to the method proposed by
Rhodes, this method is mainly empirical and relies 1st on the
calculation of the pressure drop of the conveying flowing alone
(air ONLY). From this pressure drop, a correlation is applied to
estimate the pressure drop when materials is transported. This
calculation procedure for calculating the pressure drop in dilute
phase conveying is given in *Pneumatic Conveying Design Guide,
Mills, 2004, Elsevier*.

The following link gives access to an Excel file performing the calculations according to this method - no guarantee is given, one should use this file as a 1st approximation and consult a reputable company for detail design : Link

The file is showing the example used in
the book of Mills, page 411 onwards.

This method is also empirical and
relies on abacus built from experimental data on a 53 mm bore
line. To be used, the characteristics of the industrial line
foreseen must therefore be scaled down to define what is specific
pressure drop foreseen as a function of the air flowrate and
product flowrate. From the specific pressure drop, the calculation
of equivalent length of the industrial line for horizontal,
vertical and bends allow to calculate the expected pressure drop.

This design method is given in *Pneumatic
Conveying Design Guide, Mills, 2004, Elsevier*. To be noted
that this method is also valid for dense phase conveying.

The method is not given here but the reader can refer to the book mentionned.

This method is similar to the one presented by Rhodes (see above) as it breaks down the pressure drop in several components that are representing the physical phenomena experienced by the fluid and the solids and which are leading to pressure drop. It is modified from the original method of Zenz-Othmer as the friction due to the solid has been simplified and represented by a single coefficient K called friction multiplier. This factor must be calculated from experimental data for every product transported.

This makes the method very interesting
in order to adjust the model to a particular component thanks to
the K friction multiplier. However, it means that the method
cannot be used a priori, while the methods presented above can.

The following link gives access to an Excel file performing the calculations according to this method - no guarantee is given, one should use this file as a 1st approximation and consult a reputable company for detail design : Link

The file shows the example given in the
article from Agarwal, the reader will not there is a slight
difference in the results of the article and the calculation file
probably due to slightly different inputs. The
note can be found on internet.
Please refer to the article for more details on the inputs
required.

When almost no data are available on the product to transport, a shortcut calculation method can be used to have an idea of the pressure drop of a line. Note that it is not at all an accurate methodology and should therefore not be used for the design of industrial installation.