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Air flows from a large reservoir in which the pressure and temperature are 1 MPa and 30°C, respectively, through a convergent–divergent nozzle and into a constant area duct. The ratio of the nozzle exit area to its throat area is 3.0 and the length– diameter ratio of the duct is 15. Assuming that the flow in the nozzle is isentropic, that the flow in the duct is adiabatic, and that the average friction factor is 0.005, find the back-pressure for a normal shock to appear at the exit to the duct.

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sahir9397

Answer:

The solution is attached in the attachment.

Answer:

The back pressure for a normal shock to appear at the exit to the duct is  375.959 kPa  

Explanation:

Here we have

A₁/A* = 3 =   [tex]\frac{(1+0.2Ma^2_1)^3}{1.728Ma_1}}[/tex]  Which gives

Mₐ₁ = 2.637

P₀₁ =[tex]P_1(1+0.2(2.637}^2)^{3.5}[/tex] = 1 MPa

∴ P₁ = 47298.69 Pa

P₂/P₁ shock = [tex]\frac{2.8(2.637)^2-0.4 }{2.4}[/tex]   = 7.949

∴ P₂ = 47298.69 Pa× 7.949 =  375959.457 Pa          

Therefore, for a normal shock to appear at the exit to the duct we have the back pressure [tex]p_b[/tex] =  375959.457 Pa  = 375.959 kPa      

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