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stokes-creeping-flow-draglisted

Use when you must compute the steady low-Reynolds-number viscous drag on a sphere in creeping flow, the Stokes solution for the slow motion of a sphere through a viscous fluid: evaluate the stokes streamfunction and the velocity field about the sphere, the surface pressure and wall-shear distributions with their high-pressure-facing-the-stream signature, the total stokes drag F = 6*pi*mu*a*U split one third pressure drag to two thirds friction drag, the drag coefficient Cd = 24/Re_D at the diameter Reynolds number, the Oseen correction factor 1 + (3/8)*Re_a on the radius-based Reynolds number, and the terminal settling velocity (2/9)*(rho_p - rho_f)*g*a^2/mu of a small dense sphere in still air. Produces the creeping-flow drag, the field values and the settling speed in SI units that anchor low-Reynolds-number body-drag estimates and viscous-flow checks. Trigger: stokes-creeping-flow-drag, creeping-flow, stokes-drag, stokes-streamfunction, oseen-correction, terminal-velocity.
ashfordeOU/aero-agent-skills · ★ 0 · AI & Automation · score 78
Install: claude install-skill ashfordeOU/aero-agent-skills
# Stokes Creeping-Flow Drag (aerodynamics/boundary-layer/stokes-creeping-flow-drag) Use when you must compute the steady creeping (Stokes, 1851) flow of a viscous fluid past a sphere at Reynolds number well below one: the slow-motion solution of the full Navier-Stokes equations with the inertia terms dropped, in the form Schlichting Boundary-Layer Theory section 4 presents it. This leaf implements the Stokes streamfunction and the velocity field about the sphere, the surface pressure and wall shear, the total drag F = 6*pi*mu*a*U with its exact one-third pressure (form) to two-thirds friction split, the drag coefficient Cd = 24/Re_D, the Oseen first-order drag correction and the terminal settling velocity, in pure Python stdlib, closed form, no iteration. It is the steady low-Reynolds-number member of the exact-viscous family, complementing the time-dependent plate Stokes layers of unsteady-laminar-stokes-layers, and it anchors low-Reynolds-number body-drag estimates for particle drift and droplet settling checks. It does not do time-dependent plate Stokes layers, high-Mach compressible sphere drag, flat-plate boundary layers or parachute descent balances: incompressible constant-property laminar flow only, uniform mu and nu, Reynolds numbers in the creeping range. ## Domain quick reference Spherical polar coordinates (r, theta) with theta measured from the downstream pole: the uniform stream U runs along +z toward theta = 0 and the windward stagnation point sits at theta