1. A fixed-geometry supersonic inlet starts at a Mach number of 3. After starting, the cruise Mach number is 2, and the operatin
g shock is positioned at a location where the area is 10% larger than the throat. a) Assuming the flow is ideal except for shock losses, find the inlet stagnation pressure ratio poz/poa during cruise. b) During cruise, the Mach number at the exit of the diffuser M, is required to be 0.3. Determine the ratio of the areas at the diffuser exit to that at the inlet (find A/A), and the static pressure ratio pz/p.
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Answer:
The answer to the question is
The heat transferred in the process is -274.645 kJ
Explanation:
To solve the question, we list out the variables thus
R-134a = Tetrafluoroethane
Intitial Temperaturte t₁ = 100 °C
Initial pressure = 3.5 bar = 350 kPa
For closed system we have m₁ = m₂ = m
ΔU = m×(u₂ - u₁) = ₁Q₂ -₁W₂
For constant pressure process we have
Work done = W = = P×ΔV = P × (V₂ - V₁) = P×m×(v₂ - v₁)
From the tables we have
State 1 we have h₁ = (490.48 +489.52)/2 = 490 kJ/kg
State 2 gives h₂ = 206.75 + 0.75 × 194.57= 352.6775 kJ/kg
Therefore Q₁₂ = m×(u₂ - u₁) + W₁₂ = m × (u₂ - u₁) + P×m×(v₂ - v₁)
= m×(h₂ - h₁) = 2.0 kg × (352.6775 kJ/kg - 490 kJ/kg) =-274.645 kJ