# Given a viscosity is it possible to calculate required pressure for desired output?

The following rheology question relates to predicting the flow of polymer-based non-newtonian fluids extrusion processes. In this case, applied to 3D printing.

I'm trying to calculate the pressure required to produce the desired output based on my current system (pictured). I'm working under the assumption that it can be described in the same way as an MFI test.

Specifically, is it possible to calculate the Melt Flow Index (MFI) of a polymer under different test conditions (dimensions)?

The MFI test is defined by the following:

• piston radius (change to match my system)
• nozzle radius (change to match my system)
• nozzle length (change to match my system)
• test load (change to match desired output)

Using either the pre-existing MFI rating or the viscosity (or shear rate and shear stress) is it possible for me to define the test load in order to achieve output (gr/min)?

This paper seems to prove this is possible but I've not yet been able to condense it into a single/understandable equation.

Melt Rheology of Polymer Blends from Melt Flow Index (bottom of page 222, 223, 224)

I know that pressure = force / piston cross-sectional area

• Welcome to 3D Printing! Sep 6 '18 at 20:03
• Uhm.. would you please elaborate how this is related to 3D printing? because as it is, this more looks like a question for engineering or physics. Sep 6 '18 at 20:29
• It's a calculation that underlies polymer-based extrusion 3D printing. I considered both and settled on this channel given that it requires knowledge of rheology and the process itself. Sep 6 '18 at 20:37
• please add this to the question primer and explain this significance - and welcome to the stack! Sep 6 '18 at 20:44

The answer hews close to the famous cliche "In theory, theory and practice are the same. In practice, they are not." That is to say, yes, there is a nonlinear but repeatable relationship between viscosity and pressure and feed rate. However, it's strongly dependent on temperature, and further the apparent viscosity is a function of the pressure (think oobleck).

In the end, it depends mostly on whether a couple percent variation matters to the final product. (and if it did, nearly all hobbyist extrusion printers would fail)

• Can you put a figure to the variation found in most FDM extrusion printers? Sep 12 '18 at 14:40