Nonwovens
Drag goes as the square of slip, and slip collapses as the filament speeds up. Attenuation limits itself.
— x
Final velocity over extrusion velocity
This is a lumped balance at the end of the spinline, not a solution of the coupled momentum, energy and crystallisation equations that actually govern it: the real filament accelerates, cools and crystallises together, the drag coefficient varies along its length with local Reynolds number, and stress-induced crystallisation eventually arrests the draw entirely. Treat the stress figure as an order-of-magnitude check on whether the aspirator can plausibly deliver the draw-down being asked of it, not as a design value. Final velocity is derived from mass conservation and the target denier, which means it is the velocity the process MUST reach to make that denier rather than a prediction that it will; where the computed drag looks small against the stress required, the honest reading is that the denier is not achievable at that air setting. The skin friction coefficient is the least certain input and depends strongly on filament Reynolds number and on whether neighbouring filaments are shielding each other, which they are in any real spinneret. Nothing here treats filament-to-filament interaction, drag-induced whipping instability, or the quench that sets the crystalline structure and therefore the tenacity of the finished web.
Spunbond Spinline Draw-Down & Aerodynamic Drag — free, with the formula and a worked example, at Textile School.