Final answer:
To find the maximum back pressure that will allow the duct to be choked, we can use the Isentropic Flow Relations. The maximum back pressure occurs when the flow is choked. Using the given information, we can calculate the maximum back pressure to be approximately 30.07 psia.
Step-by-step explanation:
To find the maximum back pressure that will allow the duct to be choked, we can use the Isentropic Flow Relations. For choked flow in a duct, the Mach number at the throat is 1.
The maximum back pressure occurs when the flow is choked.
Using the given information, we can use the Mach number equation to calculate the maximum back pressure:
Mach number equation:
Mach number at the throat, M₁ = √(2/(γ-1) * ((P₀ / P₁)^((γ-1)/γ) - 1))
Where, γ is the specific heat ratio, P₀ is the upstream pressure, and P₁ is the back pressure.
Since the Mach number at the throat is 1, we can substitute M₁ = 1 into the equation and solve for P₁.
In this case, γ for air is approximately 1.4. Substituting the given values, we get:
P₁ = P₀ / ((2/(γ-1) + 1)^((γ/(γ-1))))
Now we can calculate P₁ using the given values of P₀ = 100 psia and γ = 1.4:
P₁ = 100 / ((2/(1.4-1) + 1)^((1.4/(1.4-1))))
P₁ ≈ 30.07 psia