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Solvers

The solve() function is the main entry point for computing flow states.

solve

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from flow_state import solve

solve(
    *,
    mach: float | None = None,
    pres: float | tuple | None = None,
    temp: float | tuple | None = None,
    pres_stag: float | tuple | None = None,
    temp_stag: float | tuple | None = None,
    altitude: float | tuple | None = None,
    atm: str | Callable = "ussa76",
    re1: float | None = None,
    gas: PerfectGas | None = None,
) -> FlowState

Compute a flow state from the given parameters. The function examines which parameters are provided and dispatches to the appropriate calculation.

Parameters:

  • mach: Mach number
  • pres: Static pressure [Pa] or (value, "unit")
  • temp: Static temperature [K] or (value, "unit")
  • pres_stag: Stagnation pressure [Pa] or (value, "unit")
  • temp_stag: Stagnation temperature [K] or (value, "unit")
  • altitude: Altitude [m] or (value, "unit")
  • atm: Atmosphere model ("ussa76", "cira86", or callable)
  • re1: Unit Reynolds number [1/m]
  • gas: Gas model (default: air)

Returns: FlowState

Unit Support

Dimensional inputs can be specified with units:

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state = solve(mach=6, pres_stag=(140, "psi"), temp_stag=420)
state = solve(altitude=(30000, "ft"), mach=0.8)
state = solve(pres=101325, temp=(25, "C"), mach=2.0)

Supported units:

  • Pressure: Pa, psi, atm, bar, torr
  • Temperature: K, C, F, R (Rankine)
  • Length/altitude: m, ft, km, mi

Dispatch Logic

solve() examines the provided parameters and dispatches to the appropriate calculation:

Parameters Provided Calculation
mach, pres, temp From static conditions
mach, pres_stag, temp_stag From stagnation conditions
mach, altitude, atm Atmosphere lookup
mach, re1, temp From unit Reynolds + temperature
mach, re1, altitude From unit Reynolds + altitude

Examples

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from flow_state import solve

# From Mach, pressure, temperature
state = solve(mach=7.0, pres=1000.0, temp=200.0)

# From Mach and altitude
state = solve(mach=7.0, altitude=30_000, atm="ussa76")

# From Mach and unit Reynolds
state = solve(mach=6.0, re1=10e6, temp=300.0)

# From stagnation conditions
state = solve(mach=6.0, pres_stag=(140, "psi"), temp_stag=420)

Isentropic Relations

Low-level functions for isentropic flow calculations.

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from flow_state import isentropic

Temperature Ratio

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isentropic.temperature_ratio(mach: float, gamma: float = 1.4) -> float

Returns \(T_0 / T = 1 + \frac{\gamma - 1}{2} M^2\)

Pressure Ratio

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isentropic.pressure_ratio(mach: float, gamma: float = 1.4) -> float

Returns \(p_0 / p = \left(1 + \frac{\gamma - 1}{2} M^2\right)^{\gamma/(\gamma-1)}\)

Density Ratio

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isentropic.density_ratio(mach: float, gamma: float = 1.4) -> float

Returns \(\rho_0 / \rho = \left(1 + \frac{\gamma - 1}{2} M^2\right)^{1/(\gamma-1)}\)

Example

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from flow_state import isentropic

M = 7.0
gamma = 1.4

T0_over_T = isentropic.temperature_ratio(M, gamma)
p0_over_p = isentropic.pressure_ratio(M, gamma)
rho0_over_rho = isentropic.density_ratio(M, gamma)

print(f"T0/T = {T0_over_T:.2f}")   # 10.80
print(f"p0/p = {p0_over_p:.1f}")   # 4140.0