[ f_n = \frac\lambda^22\pi L^2 \sqrt\fracEIm ]
(simplified uniform beam): ( I = \frac\pi (d_root^4 - d_bore^4)64 ) (assume bore dia 6 mm → 0.006 m) ( I ≈ 8.9 × 10^-8 , m^4 ) ( m_metal = \rho_m × \textcross-sectional area ≈ 8000 × 7.85e-4 = 6.28 , kg/m ) ( m_added = 1000 × 4.91e-4 = 0.49 , kg/m ) ( m_total = 6.77 , kg/m ) thermowell wake frequency calculation
determines the vortex shedding frequency and compares it to the thermowell’s natural frequency to ensure safe operation. 2. Governing Physics 2.1 Strouhal Number (St) The dimensionless Strouhal number relates vortex shedding frequency to flow velocity and thermowell diameter: [ f_n = \frac\lambda^22\pi L^2 \sqrt\fracEIm ] (simplified