Fanno Flow

pygasflow.fanno.get_ratios_from_mach(M, gamma)

Compute all fanno ratios given the Mach number.

Parameters

Marray_like

Mach number

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

prsarray_like

Critical Pressure Ratio \(\frac{P}{P^{*}}\)

drsarray_like

Critical Density Ratio \(\frac{\rho}{\rho^{*}}\)

trsarray_like

Critical Temperature Ratio \(\frac{T}{T^{*}}\)

tprsarray_like

Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\)

ursarray_like

Critical Velocity Ratio \(\frac{U}{U^{*}}\)

fpsarray_like

Critical Friction Parameter \(\frac{4 f L^{*}}{D}\)

epsarray_like

Critical Entropy Ratio \(\frac{s^{*} - s}{R}\)

pygasflow.fanno.critical_temperature_ratio(M, gamma=1.4)

Compute the Fanno’s Critical Temperature Ratio \(\frac{T}{T^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Temperature Ratio \(\frac{T}{T^{*}}\).

pygasflow.fanno.critical_pressure_ratio(M, gamma=1.4)

Compute the Fanno’s Critical Pressure Ratio \(\frac{P}{P^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Pressure Ratio \(\frac{P}{P^{*}}\).

pygasflow.fanno.critical_density_ratio(M, gamma=1.4)

Compute the Fanno’s Critical Density Ratio \(\frac{\rho}{\rho^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Density Ratio \(\frac{\rho}{\rho^{*}}\).

pygasflow.fanno.critical_total_pressure_ratio(M, gamma=1.4)

Compute the Fanno’s Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\).

pygasflow.fanno.critical_velocity_ratio(M, gamma=1.4)

Compute the Fanno’s Critical Velocity Ratio \(\frac{U}{U^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Velocity Ratio \(\frac{U}{U^{*}}\).

pygasflow.fanno.critical_friction_parameter(M, gamma=1.4)

Compute the Fanno’s Critical Friction Parameter \(\frac{4 f L^{*}}{D}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Friction Parameter \(\frac{4 f L^{*}}{D}\).

pygasflow.fanno.critical_entropy_parameter(M, gamma=1.4)

Compute the Fanno’s Critical Entropy Parameter \(\frac{s^{*} - s}{R}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Entropy Parameter \(\frac{s^{*} - s}{R}\).

pygasflow.fanno.m_from_critical_temperature_ratio(ratio, gamma=1.4)

Compute the Mach number given Fanno’s Critical Temperature Ratio \(\frac{T}{T^{*}}\).

Parameters

ratioarray_like

Fanno’s Critical Temperature Ratio \(\frac{T}{T^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(0 < \frac{T}{T^{*}} < \left.\frac{T}{T^{*}}\right|_{M=0, \, \gamma}\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.fanno.m_from_critical_pressure_ratio(ratio, gamma=1.4)

Compute the Mach number given Fanno’s Critical Pressure Ratio \(\frac{P}{P^{*}}\).

Parameters

ratioarray_like

Fanno’s Critical Pressure Ratio \(\frac{P}{P^{*}}\). If float, list, tuple is given as input, a conversion will be attempted.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.fanno.m_from_critical_density_ratio(ratio, gamma=1.4)

Compute the Mach number given Fanno’s Critical Density Ratio \(\frac{\rho}{\rho^{*}}\).

Parameters

ratioarray_like

Fanno’s Critical Density Ratio \(\frac{\rho}{\rho^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be: \(\frac{\rho}{\rho^{*}} > \sqrt{\frac{\gamma - 1}{\gamma + 1}}\)

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.fanno.m_from_critical_total_pressure_ratio(ratio, flag='sub', gamma=1.4)

Compute the Mach number given Fanno’s Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\).

Parameters

ratioarray_like

Fanno’s Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(\frac{P_{0}}{P_{0}^{*}}\) > 1.

flagstring, optional

Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.fanno.m_from_critical_velocity_ratio(ratio, gamma=1.4)

Compute the Mach number given Fanno’s Critical Velocity Ratio \(\frac{U}{U^{*}}\).

Parameters

ratioarray_like

Fanno’s Critical Velocity Ratio \(\frac{U}{U^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(0 \le \frac{U}{U^{*}} < \sqrt{\frac{\gamma + 1}{\gamma - 1}}\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.fanno.m_from_critical_friction(fp, flag='sub', gamma=1.4)

Compute the Mach number given Fanno’s Critical Friction Parameter \(\frac{4 f L^{*}}{D}\).

Parameters

fparray_like

Fanno’s Critical Friction Parameter \(\frac{4 f L^{*}}{D}\). If float, list, tuple is given as input, a conversion will be attempted. If flag=”sub”, it must be \(\frac{4 f L^{*}}{D} \ge 0\). Else, \(0 \le \frac{4 f L^{*}}{D} \le \frac{\left(\gamma + 1\right) \log{\frac{\gamma + 1}{\gamma - 1}} - 2}{2 \gamma}\)

flagstring, optional

Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.fanno.m_from_critical_entropy(ep, flag='sub', gamma=1.4)

Compute the Mach number given Fanno’s Critical Entropy Parameter \(\frac{s^{*} - s}{R}\).

Parameters

eparray_like

Fanno’s Critical Entropy Parameter \(\frac{s^{*} - s}{R}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(\frac{s^{*} - s}{R} \ge 0\).

flagstring, optional

Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.