Air ( , ) enters a pipe of diameter at with stagnation temperature

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

Signal Speeds in Fluids, Ch Flow through nozzles: area change, choking and thrust

Problem

Air (γ=1.4\gamma=1.4, cp=1005 J kg−1 K−1c_p=1005\,\mathrm{J\,kg^{-1}\,K^{-1}}) enters a pipe of diameter D=5.0 cmD=5.0\,\mathrm{cm} at M1=0.40M_1=0.40 with stagnation temperature T01=300 KT_{01}=300\,\mathrm K. The wall has 4fF=0.0204f_{\mathrm F}=0.020, and no heat passes through it. ((a)) Find the length of pipe after which this flow would choke. ((b)) The pipe is in fact 3.0 m3.0\,\mathrm m long. Find the Mach number at its outlet. ((c)) The same inlet flow is instead sent through a frictionless duct of the same area and heated. Find the stagnation temperature at which it chokes and the heat added per unit mass. ((d)) From the Rayleigh relation, say what cooling a length of that frictionless duct does to the Mach number of the subsonic flow, and so whether cooling brings the flow towards choking or away from it.

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