# Thread: Air entrainment in flowing product

1. jeffdixon Guest

## Air entrainment in flowing product

Hi all,

I'm working on a project to reduce the dust emissions for a truck loading hopper.
One of the first bits of science I'm trying to figure out is how much air is being entrained in the flow out of the hopper, and therefore subsequently the flowrate of air "blowback" when the product lands in the bottom of the bin.

I've found this thesis document which seems to do pretty well at calculating the entrainment. https://ro.uow.edu.au/theses/1816/
However in implementing the formula's I have had real trouble establishing what the boundary conditions should be.

To get the formula's to work I needed to assume the following boundary conditions:
- That the initial velocity of the air in the stream was the same as the particle velocity (makes sense)
- That the initial volumetric flow rate of entrained air is the volume of air making up the static bulk density (bulk density vs. particle density) - (this was my big assumption I am unsure of)

I then subtracted off the initial volume of air to establish the "entrained air".
The shape of the curve matches what is given in the thesis, so I am happy with that, but has anyone had experience with this that can offer a sanity check on the results?

I.e for the following conditions does 10m³/s (21,200 CFM) sound reasonable? This will be used for designing the shape and size of the bin, as well as potentially sizing a dust extraction system.
Flow rate - 84kg/s (430m³/hr @ 700kg/m³)
Hopper outlet - Ø800mm
Fall - 1m

Entrained Air.png

Thanks!

2. ## Up in the Air

Exigent flow from a Ø800mm nozzle falling through 1m drop will be very short lived & therefore not of concern.
No worries!

3. ## Ho Ho Ho

No replies then?
Ah well, another one bites the dust.
So to speak.
Seasons Greetings.

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