FYKOS Year 30 Series 5 Problem 2 — spheres in viscous fluids · FYKOS 30 #30.5.2

Physics · mechanics · electromagnetism

Problem

When solving problems involving drag in air or in general a fluid, we use Newton's resistance equation F=12CρSv2 ,F=\frac{1}{2}C\rho Sv^2\,, where CisCis the drag coefficient of the object in the direction of motion, ρisρis the density of the fluid, SisSis the cross-section area and visvis the velocity of the object. This is usually quite accurate for turbulent flow. We are interested in a sphere, for which C=0.50C=0.50. In the case of laminar flow, we usually use Stokes' law F=6πηrv ,F = 6 \pi \eta r v\,, where ηisηis the dynamic viscosity of the fluid and risris the radius of the sphere. Is there a velocity for which the two resistance forces are equal for the same sphere?. How will this velocity depend on the radius of the sphere?

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