A straight horizontal lubricating-oil feed line of internal radius mm carries oil in…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity
Fluids and Continuum Physics, Ch The Navier-Stokes equations and exact viscous solutions
Problem
A straight horizontal lubricating-oil feed line of internal radius 12.0 mm carries oil in steady, smooth, layered flow, driven by a fixed pressure difference between its ends. After long service a deposit on the wall has reduced the internal radius to 10.0 mm. The length of the line, the oil viscosity and the pressure difference are unchanged, and the flow remains smooth, layered and fully developed, so the Hagen-Poiseuille law applies before and after.
((a)) By what factor does the volume flow rate change?
((b)) By what factor would the pressure difference have to be increased to restore the original flow rate through the narrowed line?