Propulsion Assignment - Mathematica code for Isentropic flow equation – I. Surya Prabhas 21103100
ClearAll["Global`*"]
(* Define variables *)
γ = 1.4; (* specific heat ratio for air *)
M = 0.5; (* Mach number *)
ρ0 = 1.225; (* freestream density, kg/m^3 *)
p0 = 101325; (* freestream pressure, Pa *)
T0 = 288.15; (* freestream temperature, K *)
A = 1; (* cross-sectional area, m^2 *)
R = 287.058; (* gas constant for air, J/(kg*K) *)
(* Calculate derived quantities *)
a0 = Sqrt[γ*R*T0]; (* freestream speed of sound, m/s *)
V0 = M*a0; (* freestream velocity, m/s *)
ρV0 = ρ0*V0; (* mass flow rate per unit area, kg/(m^2*s) *)
p = p0*(1 + (γ-1)/2*M^2)^(γ/(γ-1)); (* pressure as a function of Mach number *)
T = T0/(1 + (γ-1)/2*M^2); (* temperature as a function of Mach number *)
ρ = ρ0*(1 + (γ-1)/2*M^2)^(-1/(γ-1)); (* density as a function of Mach number *)
V = M*Sqrt[γ*R*T]; (* velocity as a function of Mach number *)
Astar = A*(1/M)*((2/(γ+1))*(1 + (γ-1)/2*M^2))^((γ+1)/(2*(γ-1))); (* sonic area, m^2 *)
Machstar = Sqrt(((γ-1)/(2*γ))*(A/Astar)^2 + 1)^(-1/2); (* Mach number at sonic conditions *)
(* Print results *)
Print["Isentropic flow properties for a perfect gas:"]
Print["Mach number: ", M]
Print["Pressure: ", p, " Pa"]
Print["Temperature: ", T, " K"]
Print["Density: ", ρ, " kg/m^3"]
Print["Velocity: ", V, " m/s"]
Print["Sonic area: ", Astar, " m^2"]
Print["Mach number at sonic conditions: ", Machstar]