A converging nozzle with throat area is fed with air ( , ) from a reservoir at ,

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

A converging nozzle with throat area 3.0 cm23.0\,\mathrm{cm^2} is fed with air (γ=1.4\gamma = 1.4, R=287.05 J kg−1 K−1R = 287.05\,\mathrm{J\,kg^{-1}\,K^{-1}}) from a reservoir at p0=5.0 barp_0 = 5.0\,\mathrm{bar}, T0=300 KT_0 = 300\,\mathrm{K}, into ambient air at 1.0 bar1.0\,\mathrm{bar}. Someone works it out as follows: "since pb/p0=1.0/5.0=0.20<0.528p_{\rm b}/p_0 = 1.0/5.0 = 0.20 < 0.528, the nozzle is choked. For a choked nozzle the gas leaves at the back pressure, so pe=1.0 barp_{\rm e} = 1.0\,\mathrm{bar}. Using pe/p0=0.20p_{\rm e}/p_0 = 0.20 in the isentropic relation (1+0.2M2)−3.5=pe/p0(1+0.2M^2)^{-3.5} = p_{\rm e}/p_0 then gives the exit Mach number." ((a)) Carry out the last step of this working and show that it gives an impossible result for a purely converging duct. ((b)) Find the error, state the correct exit pressure, and use it to find the correct choked mass flow.

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