A fine capillary tube carries a steady laminar (Hagen-Poiseuille) flow driven by a…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity
Fluid Dynamics, Ch The stress tensor completed: constitutive law and fluid properties
Problem
A fine capillary tube carries a steady laminar (Hagen-Poiseuille) flow driven by a fixed applied pressure difference Δp, small compared with the absolute pressure in the tube. The tube radius a and length L are unchanged throughout, and the water is kept under enough pressure that it stays liquid at 100∘C. Two experiments are run in turn, one with air and one with water filling the tube, first at 20∘C and then with the whole tube heated to 100∘C, the same Δp applied each time. Someone argues: "Heating always makes a fluid thinner and runnier, so both the air flow rate and the water flow rate must increase when the tube is heated."
((a)) Using μair=1.81×10−5Pas at 20∘C and μair=2.17×10−5Pas at 100∘C, and μwater=1.00×10−3Pas at 20∘C and μwater=0.282×10−3Pas at 100∘C, find the ratio Q100/Q20 of flow rate after heating to flow rate before heating, for air and for water separately.
((b)) State whether the claim above is correct for each fluid, and explain in one or two sentences, in terms of how momentum is carried in a gas and in a liquid, why heating has opposite effects on the two viscosities.