For laminar flow between two plates of contact area separated by a gap and moving at…
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Quantities, units and the practice of measurement · Quantities, units and the practice of measurement
Measurement and Method, Ch What dimensions decide before you measure anything
Problem
For laminar flow between two plates of contact area A separated by a gap y and moving at relative speed v, Newton's law of viscosity gives the tangential force as F=ηA(v/y), where η is the dynamic viscosity.
((a)) Write dim(η) in terms of the base dimensions.
((b)) Stokes' law for the drag on a smooth sphere of radius r moving at speed v through a fluid of viscosity η is quoted as F=6πηrv. Check whether this is dimensionally homogeneous.