Welcome to # Pneumatic transport - Pressure Drop Calculation

## Dilute Phase

Section summary
1. Introduction
2. Pressure drop in horizontal pipes
3. Pressure drop in vertical pipes
4. Pressure drop in bends
5. Total pressure drop in pipes
6. Models

## 1. Introduction

Calculating the pressure drop in a pneumatic conveying line is not easy, some correlations exist but may not be very precise, with most of the knowledge staying at process suppliers. Experience is still the best way to design reliably a pneumatic conveying system. However, it may be interesting, for a better understanding of the physical phenomena involved in pneumatic conveying, to express in principle which are the different physical terms that are contributing to the pressure drop in pipes.

As the forces involved are different in horizontal pipes, vertical pipes and bends, each case is explained below. The total pressure drop of the line is the sum of each of these pressure drops.

The explanations below are mainly applicable to dilute phase conveying.

## 2. Horizontal pipe

Pressure drop = Gas to Pipe friction + Solids to pipe friction + (gas acceleration + particle acceleration) 

Gas to pipe friction : as for any fluid flow, the gas flowing in the pipe to transport the solids has a friction with the conveying pipe, it is necessary to take it into account.

Solids to pipe friction : the gas is interacting with the pipe but so do the solids particles which are hitting the pipe wall, being dragged against the wall...etc... contributing to the pressure drop

Gas acceleration + particle acceleration : in most of the case, the bulk solids conveyed are introduced in a straight horizontal section. It is necessary at the pick-up point to spend energy to accelerate the gas and the particles, which contributes to the pressure drop. Note that it is necessary to do so after a bend as well, please refer below for reference.

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## 3. Vertical pipe

Pressure drop = Gas to Pipe friction + Solids to pipe friction + static head of solids + static head of gas 

Gas to pipe friction : as for any fluid flow, the gas flowing in the pipe to transport the solids has a friction with the conveying pipe, it is necessary to take it into account.

Solids to pipe friction : the gas is interacting with the pipe but so do the solids particles which are hitting the pipe wall, being dragged against the wall...etc... contributing to the pressure drop

Static head of solids + static head of gas : when going vertically, the flow of gas and powder must overcome the weight of solids and gas in the vertical pipe.

## 4. Bends

It is particularly difficult to model the actual pressure drop in a bend for pneumatic conveying. One must account for the regular friction of gas and solids but also for some re-acceleration after the bend. The simplest method is to assume that the bend is equivalent to a certain length of straight pipe. For a rough evaluation but not for a detail design, the following value for 90 degrees bend can be found in the litterature :

Pressure drop = 7.5 m * (vertical pressure drop per unit of length) 

## 5. Total pressure drop in pipe

Total pressure drop = Pressure drop horizontal + Pressure drop vertical + Pressure drop bends

## 6. Models

The equations above just explain qualitatively what are the physical phenomena that create pressure drop in a pneumatic conveying line but for actual calculation, a model needs to be used. They are usually of 2 different types :

- Detailed models that are attempting to physically describe each of the terms above

- Experienced based models that are proposing equations or abascus to represent behavior observed

None of these models found in the litterature are actually very precise and should therefore be used with caution, and never for detail design. For detail design, pilot plant trials are necessary and / or the help of an established engineering company, which has most of the case adapted its own models from the one publicly known, must be asked.

Shortcut Calculation

Published calculation models

Sources
 Principles of Powder Technology, M.J. Rhodes, 1990, page 151-153