Pneumatic transport - Pressure Drop Calculation (dilute phase)
How to calculate the pressure drop in a pneumatic conveying system ?
Do you have a question, a remark ? Please contact the author at admin@powderprocess.net| 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. Pressure drop in Horizontal pipe
Pressure
drop = Gas to Pipe friction + Solids to pipe friction + (gas
acceleration + particle acceleration) [1]
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. Pressure drop in Vertical pipe
Pressure drop = Gas to Pipe friction + Solids to pipe friction + static head of solids + static head of gas [1]
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. Pressure drop in 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 literature :
Pressure
drop = 7.5 m * (vertical pressure drop per unit of length) [1]
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 literature 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.
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Calculation models
Basic Model: Friction Pressure Drop Sizer
FOR EDUCATIONAL PURPOSES ONLY — NO WARANTY — NOT FOR DETAILED ENGINEERING OR SYSTEM MANUFACTURE1. Process Specifications
*Use the average line velocity: $u_{avg} = (u_{inlet} + u_{outlet}) / 2$. Velocity is not constant due to gas expansion.
2. Sizing Results (Simplified Estimates)
| Total Equivalent Length (L_eq): | - m |
| Gas-Only Pressure Drop (ΔP_gas): | - Pa (- mbar) |
| Solids-Additional Drop (ΔP_solids): | - Pa (- mbar) |
3. Total System Friction Loss
- Pa
equivalent to - mbar (- bar)
Selecting the Solids Friction Factor ($\lambda_s$)
In dilute phase pneumatic conveying, the solids-additional pressure drop is strongly governed by the **solids friction factor ($\lambda_s$)** [1]. Unlike the clean air friction factor ($\lambda_g$) which depends strictly on the pipe roughness and Reynolds number, the solids friction factor is semi-empirical [1, 2]. It is determined by particle-to-wall impact mechanics, particle-to-particle collision frequencies, and the saltation profile of the material [1, 3].
While precise values must be obtained through pilot plant trials or specific fluidization tests on your exact material batch, the table below provides standard representative engineering ranges for common industrial bulk solids:
| Material Class | Physical Characteristics | Typical $\lambda_s$ Range | Representative Examples |
|---|---|---|---|
| Fine & Light Powders | Very fine particles, smooth, non-abrasive, highly fluidizable | 0.001 – 0.003 | Wheat flour, starch, fine fly ash, talc, calcium carbonate |
| Standard Granules & Grains | Coarser, free-flowing, moderately cohesive, spherical or stable shapes | 0.003 – 0.005 | Sugar, wheat grains, plastic pellets (PE/PP), salt, urea granules |
| Coarse & Abrasive Solids | Very coarse, rough surfaces, highly abrasive, high density | 0.005 – 0.010 | Silica sand, cement, coal dust, alumina, iron ore fines |
Pneumatic Conveying References & Sources:
[1] Mills, D. (2004). Pneumatic Conveying Design Guide
(2nd ed.). Butterworth-Heinemann. (Chapter 5 provides
comprehensive charts on solids friction factors and air-only
piping resistance losses).
[2] Klinzing, G. E., et al. (2010). Pneumatic Conveying of
Solids: A Theoretical and Practical Approach. Springer.
(Detailed analysis of Weber's friction correlations and solids
impact mechanics).
[3] Rhodes, M. J. (2008). Introduction to Particle Technology
(2nd ed.). John Wiley & Sons. (Section on gas-solid flow
patterns and pressure drop approximations).
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Download Dilute Phase Sizing Excel Spreadsheet (Rhodes Method)
Get the professional dilute phase pressure drop calculation template offline. Verify line diameters, evaluate gas densities, and calculate system fan volume parameters using the established Rhodes Method.
Frequently Asked Questions (FAQ)
What are the main components of pressure drop in pneumatic conveying?
The total line pressure drop in dilute phase pneumatic conveying is the sum of gas-only pipe friction, solids-to-pipe friction, line elevation lifts (static head), and bend re-acceleration losses. Energy must also be expended at the pick-up nozzle to accelerate both the gas and stationary powder stream up to the system's operational terminal conveying velocity.
How does solids loading ratio affect conveying line pressure drop?
The solids loading ratio (Φ) directly multiplies the solids friction component, meaning higher solids loadings cause a linear increase in the additional solids pressure drop. While high loadings maximize conveying throughput per unit of gas, they demand substantially higher fan or blower pressure limits to prevent the horizontal lines from reaching saltation thresholds and plugging.
What is the equivalent length of a 90-degree bend in pneumatic piping?
In basic design calculations, a standard 90-degree pneumatic conveying bend is typically estimated to be equivalent to approximately 7.5 meters of straight vertical pipe. This empirical equivalent length represents the combined pressure losses from wall impact, friction, and the subsequent re-acceleration of the slowed particle stream back to gas velocity after exiting the elbow curvature.
[1] Principles of Powder Technology, M.J. Rhodes, 1990, page 151-153