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Explore the mathematical analysis of steady, axisymmetric, fully developed flow through circular pipes using cylindrical coordinate systems in this 52-minute lecture. Derive the velocity profile, pressure gradient per unit length, and drag force on pipe walls by solving continuity and Navier-Stokes equations in cylindrical coordinates. Examine the relationship between friction factor and Reynolds number for laminar flow conditions up to Re ≈ 2000, and extend the analysis to flow through annular regions between concentric cylinders representing hollow pipes. Conclude with an introduction to Taylor-Couette flow between rotating coaxial cylinders and its importance in hydrodynamic stability studies.
