A submarine's periscope mast is a cylinder of diameter standing in a tidal current

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Instability, transition and turbulence

Fluid Dynamics, Ch Separation, wakes, jets and free shear flows

Problem

A submarine's periscope mast is a cylinder of diameter d=6.0 cmd = 6.0\,\mathrm{cm} standing in a tidal current. Its first bending mode has a natural frequency fn=8.0 Hzf_n = 8.0\,\mathrm{Hz}. The current speed at this location ranges from 0.3 m s−10.3\,\mathrm{m\,s^{-1}} to 2.0 m s−12.0\,\mathrm{m\,s^{-1}} under normal tidal conditions. Take the Strouhal number for vortex shedding from a cylinder as St=0.20St = 0.20. ((a)) Find the current speed at which the shedding frequency would match the mast's natural frequency (the lock-in condition). ((b)) Decide whether this speed falls within the normal tidal range, and state whether resonant excitation of the mast is expected under normal conditions.

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