Is it easy to calculate the pressure that can be generated by the cold end of an extrusion system which is then available for the hotend?

I refer to this simple article

https://www.dummies.com/education/science/physics/how-to-calculate-force-based-on-pressure/

Which states : Pressure = Force/Area

Can you then work out - Pressure = What your extrusion system can lift (say 4 kg's before failing) / surface area of filament (A=π x 1.75 squared)

As with most things with physics I am probably missing something - any ideas.

For correctness, 1.75mm is the nominal diameter of the filament. 0.875mm is the radius of the filament. (Surface area then is about 2.405mm^2)

However, what you've calculated there is the amount of pressure that there will be in the nozzle if the nozzle is blocked to the point where it can no longer extrude. Any pressure above that point will be lost when the plastic flows out of the nozzle. However, if what you're interested in is the maximum that the system can exert, then in that case, you take the rated motor torque, (Nm) multiply by the radius of your extruder and any gear reduction that your extruder has (This ignored friction losses, but...) and you will get N of force, which you then divide by 2.405mm^2 in order to get pressure (N/mm^2) If your filament does not flow at this pressure, your extruder will stall.

Actual pressure in the melt chamber will be dependent on the viscosity of the melted filament, as to what makes it flow through the surface area of the nozzle, so you will have lower pressure in the melt chamber with a larger nozzle than you would with a smaller one, and greater pressure at lower temperature than at higher temperature.

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Comprehensive answer and sort of what I am after, thanks SupraGuy

One of the small issues we are having with 3D printing is that of part density - understandably there will always be small air gaps in printed models (normally not an problem and probably be an advantage as it would make parts marginally lighter and use marginally less material with no discernible loss of strength)

However I was just wondering how close to injection molded part.density could be achieved with 3d extrusion systems.

Also thanks for picking up the calculation error, math is not my strong suit - but I can lift heavy things.