A single high-speed photograph of an explosion in air of density shows the blast-wave…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Oblique shocks, expansion fans and blast waves

Problem

A single high-speed photograph of an explosion in air of density ρ1=1.2 kg m−3\rho_1=1.2\,\mathrm{kg\,m^{-3}} shows the blast-wave shock front at radius R=200 mR=200\,\mathrm{m} at time t=40 mst=40\,\mathrm{ms} after detonation. Use the strong-shock similarity result R=ξ0(Et2/ρ1)1/5R=\xi_0(Et^2/\rho_1)^{1/5} with the quoted constant ξ0=1.033\xi_0=1.033 for γ=1.4\gamma=1.4, and take the sound speed of the undisturbed air as c1=343 m s−1c_1=343\,\mathrm{m\,s^{-1}}. ((a)) Estimate the energy EE released, in joules. ((b)) Find the shock speed UU at this instant, and check that the strong-shock assumption (U≫c1U\gg c_1) is reasonable.

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