Dear Ankita,

The Froude number is a dimensionless value that describes the relationship between inertial and gravitational forces and the length of a body moving through a medium or a medium moving along a body.

Fr = velocity/SQRT( g * L)

F.i. in shipbuilding, the wave patterns between model and real ship are comparable when the Fr-numbers for model and ship are equal.

In pneumatic conveying, there are some, who use(d) the Fr-number in calculations, but in my opinion with rather vague reasoning.

In my pneumatic conveying calculations, I do not use the Fr-number at all.

A much more important scale number is the Reynolds number.

The Re-number describes the influence of friction forces and is therefore an indicator for the existance and magnitude of turbulence in a flow.

In pneumatic conveying, the turbulence is responsible for keeping particles in suspension and for the chance on particle collisions.

The number of inter particle collisions increases with increasing turbulence and, because of this, the energy loss for product conveying increases also.

Please have a look at:

https://news.bulk-online.com/?p=65

Have a nice day

Teus ■

Dear Ankita,

As far as I can understand other papers, the authors did a lot of measurements on test installations and real installations and constructed regression lines and –formulas based on the respective Froude-numbers, as they believed it was the right choice.

I choose for the Reynold-number, as this number is a measure for the flow-turbulence.

The flow turbulence is a physical phenomenon that clearly plays a role in pneumatic conveying, as described in my previous reply.

Attached a derivation of the Reynolds number

All for now

Teus

Attachments

reynoldnumber_1 (PDF)

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Froude No. gives the relationship between pipe line diameter and conveying velocity. As pipe diameter increases, conveying velocity also increases.

For example, when using a stepped pipeline Froude No. is kept constant to determine the conveying velocity at each step.

Froude Number is also used for scaling-up lab test data (typically small diameter conveying lines) to commercial size pipelines.

Regards,

Amrit Agarwal

Consulting Engineer

Pneumatic Conveying Consulting

Email: polypcc@aol.com

Ph and Fax: 304 346 5125 ■

Originally Posted by Amrit Agarwal

Froude No. gives the relationship between pipe line diameter and conveying velocity. As pipe diameter increases, conveying velocity also increases.

For example, when using a stepped pipeline Froude No. is kept constant to determine the conveying velocity at each step.

Froude Number is also used for scaling-up lab test data (typically small diameter conveying lines) to commercial size pipelines.

Regards,

Amrit Agarwal

Consulting Engineer

Pneumatic Conveying Consulting

Email: polypcc@aol.com

Ph and Fax: 304 346 5125

Dear Mr Amrit

You explained the significane of Fr No. Now that is the conly area in pneumatic conveying where teh FR no plays the role . I mean originally the question raised by ANKITA (ie does the Fr NO plays a role in pressure drop ) . If yes , can we use Reno instead of Fr no as stated by Mr Teus . I think i raised a thrust point as the response against agaisnt teh same will eradicate the obvious confusion between application of Fr no and Re no . Both no does plays a imp role , but which is important one in pneumatic conveying system pressure gardient . Please clarify ■

Originally Posted by guddu

Dear Mr Amrit

You explained the significane of Fr No. Now that is the conly area in pneumatic conveying where teh FR no plays the role . I mean originally the question raised by ANKITA (ie does the Fr NO plays a role in pressure drop ) . If yes , can we use Reno instead of Fr no as stated by Mr Teus . I think i raised a thrust point as the response against agaisnt teh same will eradicate the obvious confusion between application of Fr no and Re no . Both no does plays a imp role , but which is important one in pneumatic conveying system pressure gardient . Please clarify

Dear Teus,

I like to know the significance of froud number for mixing of three powders in batch mixer

Explain ■

Dear Sudip Giri,

Whether a dimensionless number is useful in your mixing calculations, I do not know.

The Froude number is defined as:

Fr=(Inertia forces)/(gravity forces)=(mass*acceleration)/(mass*gravity)=(m*a)/(m*g)=a/g

Introducing a time T:

Fr(v⁄T)/gv/(g*T)

Where:

TL⁄v

Resulting in:

Frv/(g*T)v/(g*L⁄v)v^2/(g*L)

Redefining the Froude number as:

Frv/√(g*L)

In flow dynamics, the Fr-number is related to wave energy, existing at the boundary surface between 2 mediums of different density and vidcosity.

(F.i. a moving ship at the surface between water and air)

When submerged in a medium, the existence of waves is not possible, as there is no boundary with a second medium.

( A submerged submarine makes no waves at the water surface and therefore moves faster submerged than at the surface)

As this situation applies to a particle moving in a pipe, fully submerged in the conveying gas, waves cannot occur, causing the Fr-number becoming irrelevant.

Only friction forces can exist, which are governed by the Re-number.

In many publications, the Fr-number is used as a dimensionless variable to relate pneumatic conveying parameters to, which is to be considered as incorrect.

Reynolds number.

Defined as the ratio between mass force and viscous force.



Mass force:Fm=m*a(Newton)

Viscous force:Fv=*∂v/∂y*A(Stokes)

Definition:Fm/Fv =Re

Resulting in:

(*v*D)/=Re

The Reynolds number is related to turbulence and drag-factor.

You have to decide, based on your physical and mathematical description of the mixing process, which number is applicable.

Have a nice day ■

Originally Posted by sudipsudipgiri

href="showthread.php?p=88804#post88804" rel="nofollow">

Dear Teus,

I like to know the significance of froud number for mixing of three powders in batch mixer

Explain

This part of my badly tranlated script, availabel on bulk online, may show you some of the dificoulties which are connected with the physical description of moving bulks, including the influence of the Froude Number.

Regards, Manfred

Attachments

flowbehaviour (PDF)

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