### Pipe Diameter Follows Simple Equation

I cannot believe that RTL in fact is a term of physical relevance. In the end it is possibly only an outcome, determined by the many physical parameters of turbulent pipe flow. The right pipe diameter together with the necessary flow velocity are more important for the design of a conveying line. However, there is in fact something like a constant. In my thread "Data of Industrial Conveying Installations" (https://forum.bulk-online.com/showth...-Installations) the pipe diameters of many industrial installations for the conveying of fine-grained bulk solids follow more or less the simple equation**D** [mm] = 30 x Sqrt (_{s} [t/h])

This relation reminds of the material throughput, related to the pipe cross-section. ■

### Re: Solids Loading Ratio (Slr)

Dear Manfred,

The Solid Loading Ratio is a very important variable in pneumatic conveying, which cannot be ignored.

Simplified theory:

The internal gas energy, which is available for conveying is proportional to the GasMassFlow.

The lost energy in pneumatic conveying, consumed by the material is approx. proportional to

* MaterialMassflow * K * velocity^2 * Length / D (assuming this is the main pressure drop)

While the delivered energy equals the used energy:

GasMassFlow = * MaterialMassflow * K * velocity^2 * Length / D

or

MaterialMassflow/ GasMassFlow = SLR = 2 * D / (K * velocity^2 * Length)

K = material property (depending on SLR)

This (simplified) exercise shows:

-SLR decreases with increasing conveying length

-SLR decreases with increasing velocity (dilute phase)

-SLR decreases with increasing material loss factor

-SLR decreases with decreasing pipe diameter

D [mm] = 30 x Sqrt (s [t/h])

In this formula, the material throughput is considered independent from the conveying length.

As shown in the above generalized approach and as we all know, a longer conveying length dictates a lower SLR.

In reality, the physics of pneumatic conveying are much more complex then presented here and that complexity causes the shape of the Zenz diagram.

The statement that in pneumatic conveying the material throughput is only proportional to the square is pertinently not true.

Have a nice day

Teus ■

Teus

### Solids Loading Ratio

How to calculate the solids volume fraction if we know the solids loading ratio in pneumatic conveying systems. ■

### Re: Solids Loading Ratio (Slr)

Dear muhammadadnan,

The solids loading ratio is defined as:

SLR = (massflow material) / (massflow gas).

massflow gas = (massflow material) / (SLR)

massflow gas = Volume gas * density gas

Volume gas * density gas = (massflow material) / (SLR)

Volume gas = (massflow material) / (SLR * density gas)

massflow material = Volume material * density material

Volume gas = (Volume material * density material) / (SLR * density gas)

Easy. ■

Teus

### Slr And K Factor

@Mr. Manfred: " However, there is in fact something like a constant."

Agree with this statement. This is in the Barth&Siegel formulae as for critical SLR, there is a correlation with Fr^2 and a Clogging constant of the product.

Same eq but with a slight different form is from Rizk, assessing Clogging constant as a 1/10^x and a k power for the Froude number.

But the equation is not well balanced since there is no homogeneity left-right and results the Clogging Constant as dimensionless and having the same expression as SLR as kgofproduct/kgofair. And is not fair, one cannot have two variables with different names but with same units.

Correcting it by the Cross section area of the pipe, which at least for dilute phase takes into account for the ratio between the particle diameter and pipe diameter and the influence of deviation from the spherical form (that gives the floating speed as a domain rather than a fixed value), gives a physical meaning of this constant, expressed as kgofproduct/kgofair/cross section of the pipe (or as a specific load of the pipe - Mr. Manfred).

And this can be easily interpreted as permeability factor of the product revealed through Zenz diagram.

@Mr. Teus,

"- SLR decreases with increasing material loss factor"

My opinion is that increasing the material flow with air flow constant as kg/s (increasing SLR), will produce a higher compression of the air flow and therefore a velocity decrease of air flow (and by consequence, for the product).

Therefore, with all due respect, i think the reverse: SLR increases with increasing material loss factor, or material loss factor increases with SLR increase.

I assume the material loss factor is due to the slipping of the particles given by the relative velocity, which is actually increasing the theoretical SLR.

Also resulting from this assumption is that the K factor makes a correction of the theoretical SLR to the assessed real value.

Since the floating speed is a domain, it results that k is also a domain, and this is visible on a pipe operating at close to clogging regime.

Wish you all a nice new week,

Sincerely yours,

Tanase TANASE ■

### Re: Solids Loading Ratio (Slr)

Dear Mr Tanase,

For a moment I thought: How did I come to this conclusion?

Then I realized that I derived the equation under the assumption of constant energy.

And that assumption made SLR proportional to (2*D/(K*vel^2*L)

And the, as an equation believer, I concluded the 4 relation ships.

1)SLR must decrease at longer lengths. (sounds logic)

2)SLR must decrease at higher velocities. (sounds logic)

3)SLR must decrease at smaller diameters.

Sounds logic, as smaller diameters have a higher resistance due to the ratio L/D

4)SLR must decrease at a higher K-factor (different material)

Sounds logic as a higher K-factor requires a higher energy, which only can be compensated for by a lower SLR.

This kind of pneumatic conveying description approach is a good example, how complex the technology is.

Whatever parameter influence you want to understand and describe, many other parameters must be considered constant plus the necessity to make a variety of simplifications.

Easy to lose track of what you are doing.

Using thoroughly tested software, wherein all the bugs are removed over time, is an indispensable tool to do the pneumatic conveying calculations.

Although then, the calculation results confront the user with in return with the question; Why this outcome. This is not what I expected.

Many times I find a mistake in the input or an omission, but up till now I find the software to be correct. ■

Teus

### Re: Solids Loading Ratio (Slr)

3) SLR must decrease at smaller diameters.

Sounds logic, as smaller diameters have a higher resistance due to the ratio L/D**The above statement is debatable for fine powders i have tested very high SLR in very small dia pipes 10- 12 mmThe SLR can be achieved but the conveying pressure is higher due to L/D ratio. For small dia pipes the material needs tobe fed at very precise rate and ramping of rate at the start is most important. These kind of small bore systems are verycommon in gasification and small furnace injections.It can probably hold for granular powders only because of particle size : pipe X sectional area leading to mechanicalblocking of line. **

4) SLR must decrease at a higher K-factor (different material)

Sounds logic as a higher K-factor requires a higher energy, which only can be compensated for by a lower SLR.

**■**

*The above statement is not correct higher K-Factor will generate higher pressure drops but the SLR does not have*

to be reduced.to be reduced.

### Re: Solids Loading Ratio (Slr)

Dear Dr. Mantoo,

I understand that you agree with the first 2 conclusions, based on the equation SLR proportional to (2*D/(K*vel^2*L), which is based on constant energy.

The conclusions 3) and 4) are based on the same approximation equation.

3) SLR must decrease at smaller diameters.

Sounds logic, as smaller diameters have a higher resistance due to the ratio L/D

The above statement is debatable for fine powders I have tested very high SLR in very small dia pipes 10- 12 mm

The SLR can be achieved but the conveying pressure is higher due to L/D ratio. For small dia pipes the material needs to be fed at very precise rate and ramping of rate at the start is most important. These kind of small bore systems are very common in gasification and small furnace injections.

It can probably hold for granular powders only because of particle size : pipe X sectional area leading to mechanical

blocking of line.

I have no doubt that you tested very high SLR in very small diameter pipes 10-12mm.

I did a blast furnace injection system in the past.

But what is meant by the equation is; how the SLR needs to be changed when the diameter is decreased to keep the energy constant.

Your conclusion that the pressure must go up when the diameter I decreased is correct but does not comply with the condition of constant energy.

4) SLR must decrease at a higher K-factor (different material)

Sounds logic as a higher K-factor requires a higher energy, which only can be compensated for by a lower SLR.

The above statement is not correct higher K-Factor will generate higher pressure drops but the SLR does not have

to be reduced.

To comply with the condition of constant energy, the only option is to reduce the SLR.

I must admit that these kind of observations are academic and therefore it is better to do a proven computer calculation to bypass these mind blowing exercises. ■

Teus

### Re: Solids Loading Ratio (Slr)

Or you may say K factor is not a constant ! and is a function of pipe diameter and changes for smaller pipes.

The glass is always half full !

Have a nice day . ■

### Re: Solids Loading Ratio (Slr)

Dear Dr. Mantoo,

The equation is:

SLR proportional to (2*D/(K*vel^2*L) at constant energy

The term on the right are the variables, implying that, if the variables are not changed, the SLR does not have to be changed.

Sometimes, I have a problem to convey my thoughts and equations in a precise way and correct wordings.

Or you may say K factor is not a constant! and is a function of pipe diameter and changes for smaller pipes.

This is correct.

The equation is then rewritten as:

K proportional to (2*D/(SLR*vel^2*L) at constant energy

Up till now, it did not come to my mind of looking at the subject that way.

The conclusions must not change though.

Sometimes, I have a problem to convey my thoughts and equations in a precise way and correct wordings.

Because I am always trying to debunk my thoughts and equations and end up in confusion myself.

Reviews by other experts is hen required and this forum is a perfect platform for that.

Thank you for your input. Much appreciated. ■

Teus

## Solids Loading Ratio (SLR)

I received the following questionnaire through the private messages:

arunkumar.g2005Guest

Questionnaire

Hi Teus,

Have gone through your replies towards the various clarifications raised by the users. Based on the same i hope you will be the one who can help me in clarifying my questionnaires.

Please find below few of the related quires which needed to be clarified,

1)What are the factors affection solid loading ratio(SLR)? How its range being classified.

2)What will be the SLR for conveying coarse & fine fly ash?

3)Any graph is available between SLR vs pressure gradient

Kindly clarify the above. Please do the needful.

Dear arunkumar.g2005Guest,

I believe the sender is not registered and that might be the reason that I cannot reply through private messages.

Therefore, I use the forum to reply.

1)The factors affecting the solid loading ratio are basically the fly ash pneumatic conveying properties and the conveying pipeline. (horizontal, vertical and number of bends)

2)Needs to be calculated based on the items mentioned under 2)

3)Can be calculated for a specified fly ash, installation, pressure, airflow, altitude above sea level, temperature, etc.

If you want a preliminary design calculation, let me know the relevant data.

(and an e-mail address to reply to)

Have a nice day

Teus ■

Teus