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2. Consider isentropic flow of a perfect gas in a variable area channel (convergent divergent channel). Starting from the equations of state, the first and second law of thermodynamics, equation of continuity, and the equation of conservation of energy, (a) Show that $$ \frac{\delta A}{A} = \frac{1 - M^2}{M^2(\gamma - 1)} \frac{\delta T}{T} = \frac{1 - M^2}{\gamma M^2} \frac{\delta p}{p} $$ Here the quantities $$ \delta A, \delta T $$ and $$ \delta p $$ represent changes in area, A, temperature, T, and pressure, p. (30 Points) (b) For subsonic flow, $$ M < 1 $$ with $$ \gamma = 1.4 $$, does the temperature and pressure increase or decrease with increasing area. (5 Points) (c) For supersonic flow, $$ M > 1 $$ with $$ \gamma = 1.4 $$, does the temperature and pressure increase or decrease with increasing area. (5 Points)

Name: 2 consider isentropic flow of a perfect gas in a variable area channel convergent divergent channel starting from the equations of state the first and second law of thermodynamics equation o 62366
Uploaded: 2022-08-25T13:53:25-08:00
Duration: 2 min 49 s
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Description: 2 consider isentropic flow of a perfect gas in a variable area channel convergent divergent channel starting from the equations of state the first and second law of thermodynamics equation o 62366

          2. Consider isentropic flow of a perfect gas in a variable area channel (convergent divergent channel). Starting from the equations of state, the first and second law of thermodynamics, equation of continuity, and the equation of conservation of energy,

(a) Show that
$$ \frac{\delta A}{A} = \frac{1 - M^2}{M^2(\gamma - 1)} \frac{\delta T}{T} = \frac{1 - M^2}{\gamma M^2} \frac{\delta p}{p} $$
Here the quantities $$ \delta A, \delta T $$ and $$ \delta p $$ represent changes in area, A, temperature, T, and pressure, p. (30 Points)

(b) For subsonic flow, $$ M < 1 $$ with $$ \gamma = 1.4 $$, does the temperature and pressure increase or decrease with increasing area. (5 Points)

(c) For supersonic flow, $$ M > 1 $$ with $$ \gamma = 1.4 $$, does the temperature and pressure increase or decrease with increasing area. (5 Points)

2 consider isentropic flow of a perfect gas in a variable area channel convergent divergent channel starting from the equations of state the first and second law of thermodynamics equation o 62366

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