granular free vertical flow 2

[25362]

I wonder whether a satisfying theory has been found to explain why -contrary to liquid flow- the speed on vertical free flow of granular or powdered solids through an orifice doesn't depend on the height of the heap above the hole.
A sand-glass is a good example of a more or less constant particle (sand running) flow independent of the height above the restriction.

 

[quark]

Yes, the theory is well developed and it is because of the fact that a solid column can't generate same pressure at the bottom of the storage bin when compared to the liquid of same density.

When grains are stored, there will be interlocking between the grains. Because of this, the frictional force between the wall of the container and the grains is felt upon by entire mass. This tends to offset the weight of the solid and reduces the pressure exerted by the mass on the floor of the container.

For example, if the height of solids in a container is more than 3 times diameter of the container, pressure will not increase even if we add additional mass.

For a good description, I refer Unit Operations in Chemical Engineering by McCab and Smith.

Regards,

 

[25362]

Thanks, quark. Regretfully I don't have access to that book.

When you say "pressure will not increase even if we add additional mass", do you mean under flow conditions or in a non-flowing static pile ?

Perry VI chapter 7, shows a diagram in which the pressure along the column, when the grains or particles are flowing down, reaches a maximum and an abrupt discontinuity at the transition when the vertical cylinder meets the funnel-like conical lower portion, dropping to zero at the appex, namely the outlet, without giving a physical explanation for this phenomenon. Does it have something to do with the angle of repose, or angle of rest, or angle of sliding of the bulk granules or particles ?

Believe it or not, the solar year wasn't always 365 days. 600 million years ago a year's duration was 425 days; just 85 million years ago it was 370 days. This fact is the result of the slowing down of our planet's rotation about its axis.

 

[PUMPDESIGNER]

quark is exactly correct.
Shucks, still have yet to see him make a mistake.

I hesitate to comment on quark's statement, but perhaps a little statement may help someone.

The reason is the difference between liquids and solids.
Liquids transmit pressure instantaneously and unidirectionally throughout the containment, and with no loss if under static conditions.

Solids on the other hand do not transmit pressure either instantaneously, or unidirectionally.

PUMPDESIGNER

 

[katmar]

A comment that is a bit off topic, but hopefully interesting in this regard:

Because there is so much friction between the grains and the walls of the container, if you open the bottom outlet too quickly and the walls are not designed for the resultant forces you can rip a silo apart.

I'm aware of this happening in coal bunkers, and I'm sure other members have got horror stories to tell.

 

[PUMPDESIGNER]

Ooops,

In my previous thread I said "unidirectional",
Intended to say omnidirectional.

Hey, you guys are supposed to catch me on that stuff

PUMPDESIGNER

 

[25362]

To PUMPDESIGNER to tell the truth I was wandering about what you meant by unidirectional, and I came to the wrong conclusion that what you intended to say was that hydrostatic pressures are equal in the horizontal plane. BTW, when speaking of solid particles, is there any reason to believe that the intervening air creates a resistance to their free flow ?

A side note: in 1991 Mike Powell broke the 8.90 m 1968's Bob Beamon's record on the long jump by reaching 8.95 m. He started at an angle of 22^o, meaning he did it with a starting speed of 40.3 km/h.

 

[quark]

PumpDesigner!

Thanks for the kind words, but I have to confess that not all the posts I make in these forums are spontaneous. I do read books before I comment on some posts. Had this forum been online, I would just have been as good as Johnny Bravo (but he is my favorite character and one day I will sue the cartoon network for making him so dumb). I am always trying to get that expertise which you people are naturally good at.

One suggestion to your post: solids do transmitt pressure to all planes and the minimum pressure will be in the plane normal to the pressure applied.

25362!

Above a certain height the pressure wouldn't increase, be it static or dynamic condition. Infact the increase in height of the solid mass packs the material more tight and flow becomes more difficult(yet pressure at the bottom will not increase). The consequence of this is the effect of arcing or bridging(the material will not fall off at some stage even if the material below it is discharged).

The pressure gradient rather depends upon the angle of internal friction (or the ratio of normal pressure to the applied pressure)and not on angle of repose. The increase in pressure till the conical section (Hopper) is due to the height of mass. In non channel flow, the discharge takes place layer by layer from bottom to top. That means the particles are loose at the bottom. That is why the pressure decreases in the hopper section. (ultimately it should be zero absolute at the discharge)

Regards,

 

[m777182]

Quark concisely speaks about terms then we commonly understand (or not, perhaps) when talking about cohesion of powders. It would be fine to find a web site of Jenike and Johanson Inc for the first readind. The Bulletin 108(1961)and 123(1964) of the University of Utah represents the Bible of storage and flow of powders.
m777182

 

[25362]

To m777182, since I don't have access to those papers, can you just tell me whether for dry, non-sticking particles is there also a microscopic (molecular, atomic, electronic) underlying explanation ? Or even a macroscopic entropy effect ?

Following quark's ritual of adding a post-scriptum:

As a consequence of the Chernobyl accident the roumanians had to refrain for at least 32 days from eating milk products. The concentration of cancer-producing radioactive I-131 in milk reached a level of 2900 Bq/L when the maximum allowable is 185 Bq/L. (1 Bq=1 decay/s).

The half-life of the isotope is 8.04 days. Thus the safe level could be reached after ln(2900/185)/ln 2=3.97 half-lives, i.e., 3.97x8.04=31.9 days.

 

[quark]

25362!

I forgot to mention in my earlier post. There are good many forums at

http://www.bulk-online.com

which specifically deal with solid handling. I saw some enlightening posts there in the past. The participants are real professionals in this field and you can better try your luck there.

Regards,

 

[25362]

My sincere thanks to all who answered my query and especially to quark for his in-depth analysis and advice.