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This is an Advanced Physics Question. Please Answer Question no. (a), (b) and (c) Only. Thank you.

Problem B.2: Shock Wave This year's qualification round featured a spaceship escaping from a shock wave (Problem B). The crew survived and wants to study the shock wave in more detail. It can be assumed that the shock wave travels through a stationary flow of an ideal polytropic gas which is adiabatic on both sides of the shock. Properties in front and behind a shock are related through the three Rankine-Hugoniot jump conditions (mass, momentum, energy conservation): Pivž +P1 = P2v% +P2 + hị + h2 Pivi = P2V2 2 2 where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front (1) and behind (2) the shock respectively. Shock front v2, P2; P2; h2 V1, P1; P1, h1 (a) Explain briefly the following terms used in the text above: (i) stationary flow (ii) polytropic gas (iii) specific enthalpy (b) Show with the Rankine-Hugoniot conditions that the change in specific enthalpy is given by: P2 – P1 Ah = 1 1 + – P1 P2 The general form of Bernoulli's law is fulfilled on both sides of the shock separately: v2 + D + h = b 2 where d is the gravitational potential and b a constant. (c) Assuming that the gravitational potential is the same on both sides, determine how the con- stant b changes at the shock front. (d) Explain whether Bernoulli's law can be applied across shock fronts.
Transcribed Image Text:Problem B.2: Shock Wave This year's qualification round featured a spaceship escaping from a shock wave (Problem B). The crew survived and wants to study the shock wave in more detail. It can be assumed that the shock wave travels through a stationary flow of an ideal polytropic gas which is adiabatic on both sides of the shock. Properties in front and behind a shock are related through the three Rankine-Hugoniot jump conditions (mass, momentum, energy conservation): Pivž +P1 = P2v% +P2 + hị + h2 Pivi = P2V2 2 2 where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front (1) and behind (2) the shock respectively. Shock front v2, P2; P2; h2 V1, P1; P1, h1 (a) Explain briefly the following terms used in the text above: (i) stationary flow (ii) polytropic gas (iii) specific enthalpy (b) Show with the Rankine-Hugoniot conditions that the change in specific enthalpy is given by: P2 – P1 Ah = 1 1 + – P1 P2 The general form of Bernoulli's law is fulfilled on both sides of the shock separately: v2 + D + h = b 2 where d is the gravitational potential and b a constant. (c) Assuming that the gravitational potential is the same on both sides, determine how the con- stant b changes at the shock front. (d) Explain whether Bernoulli's law can be applied across shock fronts.
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