To find the turbine exit pressure, we can use the principles of thermodynamics and the adiabatic process. The specific entropy of the air entering the turbine is given by the isentropic relation. Using the relation between pressure and specific volume, we can solve for P2 and find the turbine exit pressure.
To find the turbine exit pressure, we can use the principles of thermodynamics and the adiabatic process. Since the turbine and nozzle are reversible and adiabatic, we can assume that the entropy remains constant. The specific entropy of the air entering the turbine is given by the isentropic relation:
s2 = s1
Using the relation between pressure and specific volume, we can write:
P2/(v2^γ) = P1/(v1^γ)
Where γ is the ratio of specific heats, which is approximately 1.4 for air. We can rearrange this equation to solve for P2:
P2 = P1 * (v2/v1)^γ
The specific volume v2 at the turbine exit can be found using the ideal gas law:
P2 * v2 = R * T2
Where R is the specific gas constant for air and T2 is the temperature at the turbine exit. Rearranging this equation, we can solve for v2:
v2 = (R * T2) / P2
Substituting this expression for v2 back into the equation for P2, we obtain:
P2 = P1 * [(R * T2) / (P2 * v1)]^γ
This equation is nonlinear, but we can solve it using an iterative numerical method. We can start with an initial guess for P2, and using the known values of P1, T2, v1, γ, and R, we can update the guess until we converge to a solution that satisfies the equation. This will give us the turbine exit pressure that corresponds to the desired nozzle exit velocity of 800 m/s.