Standard Equations

gas_dynamics.standard.standard.sonic_velocity(temperature=273.15, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the local speed of sound.

Notes

Given a ratio of specific heats, gas constant, and temperature this function returns the locoal speed of sound. Default fluid is air.

Parameters

  • gas (fluid) – A user defined fluid object. Default is air

  • temperature (float) – The temperature

Returns

The local speed of sound

Return type

float

Examples

>>> import gas_dynamics as gd
>>> gd.sonic_velocity(air, temperature=500)
448.2186966202994
>>> gd.sonic_velocity(gas=Argon, temperature=300)
gas_dynamics.standard.standard.stagnation_pressure(stagnation_pressure=None, mach=None, pressure=None, gas=<gas_dynamics.fluids.fluid object>, output=False) → float

Returns the stagnation pressure given pressure and Mach number.

Notes

Given a pressure, Mach number, and a ratio of specific heats return the stagnation pressure. Alternatively, provided two arguments the function will return the missing one. Default fluid is air.

Parameters

  • stagnation_pressure (float) – The stagnation pressure.

  • pressure (float) – The pressure.

  • mach (float) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

  • output (bool) – Print out a string to verify the output is the parameter desired

Returns

The stagnation pressure, static pressure, or mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> pt = gd.stagnation_pressure(pressure=10, mach=1)
>>> pt
18.92929158737854
>>> M = gd.stagnation_pressure(pressure=10, stagnation_pressure=pt)
>>> M
1.0
>>>
gas_dynamics.standard.standard.stagnation_temperature(temperature=None, stagnation_temperature=None, mach=None, gas=<gas_dynamics.fluids.fluid object>, output=False) → float

Returns the stagnation temperature given temperature and Mach number.

Notes

Given a temperature, Mach number, and a ratio of specific heats this function returns the stagnation temperature. Alternatively, provided two arguments the function will return the missing one. Default fluid is air.

Parameters

  • stagnation_temperature (float) – The stagnation temperature

  • temperature (float) – The temperature

  • mach (float) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

  • output (bool) – Print out a string to verify the output is the parameter desired

Returns

The stagnation temperature, temperature, or mach number

Return type

float

Examples

>>> Tt = gd.stagnation_temperature(temperature=300, mach=1)
>>> Tt
360.0
>>> M = gd.stagnation_temperature(temperature=300, stagnation_temperature=Tt)
>>> M
1.0
>>>
gas_dynamics.standard.standard.stagnation_density(density=None, stagnation_density=None, mach=None, gas=<gas_dynamics.fluids.fluid object>, output=False) → float

Returns the stagnation density given density and Mach number.

Notes

Given a density, Mach number, and a ratio of specific heats this function returns the stagnation density. Alternatively, provided two arguments the function will return the missing one. Default fluid is air.

Parameters

  • stagnation_density (float) – The stagnation density

  • density (float) – The density

  • mach (float) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

  • output (bool) – Print out a string to verify the output is the parameter desired

Returns

The stagnation temperature, temperature, or mach number

Return type

float

Examples

gas_dynamics.standard.standard.stagnation_pressure_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the pressure ratio of p / p_t

Notes

Given a Mach number and ratio of specific heats return the relation of pressure over stagnation pressure. Default fluid is air.

Parameters

  • mach (float) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The stagnation pressure ratio

Return type

float

Examples

>>> import gas_dynamics as gd
>>> p_pt = gd.stagnation_pressure_ratio(mach=3)
>>> p_pt
0.027223683703862817
>>>
gas_dynamics.standard.standard.stagnation_temperature_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the temperature ratio of T / T_t

Notes

Given a Mach number and ratio of specific heats return the relation of temperature over stagnation temperature. Default fluid is air.

Parameters

  • mach (float) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The stagnation temperature ratio

Return type

float

Examples

>>> import gas_dynamics as gd
>>> T_Tt = gd.stagnation_temperature_ratio(mach=1.5)
>>> T_Tt
0.6896551724137931
>>>
gas_dynamics.standard.standard.stagnation_density_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the density ratio rho / rho_t

Notes

Given a Mach number and ratio of specific heats, return the relation of density over stagnation density. Default fluid is air.

Parameters

  • mach (float) – The Mach #

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The stagnation density ratio

Return type

float

Examples

>>> import gas_dynamics as gd
>>> rho_rho_t = gd.stagnation_density_ratio(mach=1.5)
>>> rho_rho_t
0.39498444639115327
>>>
gas_dynamics.standard.standard.stagnation_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → list

Return stagnation pressure, temperature, density, and choked area ratio for a mach number

Notes

Given a mach number and the fluid, return the three stagnation ratios and the ratio of the area to the choked area. Default fluid is air.

Parameters

  • mach (float) – The mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The stagnation pressure, stagnation temperature, stagnation density ratio, and choked area ratio.

Return type

list

Examples

>>> import gas_dynamics as gd
gas_dynamics.standard.standard.stagnation_ratio_table(range=[0, 5], step=0.1, gas=<gas_dynamics.fluids.fluid object>) → str

Returns the isentropic flow tables in the given range.

Notes

Given a ratio of specific heats, print out the stagnation temperature ratio, stagnation pressure ratio, the area to choked area ratio, and the stagnation density ratio for every incremental Mach number.

Parameters

  • range (list) – The starting and ending Mach numbers in a list, ex: [0, 5]

  • step (float) – The step size between min and max mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The isentropic flow table

Return type

str

Examples

>>> import gas_dynamics as gd
>>> gd.stagnation_ratios(range=[0,2], step=.2, gas='nitrogen')
M: 0.000   |   P/Pt: 1.000    |    T/Tt: 1.000    |    A/A*: inf
M: 0.200   |   P/Pt: 0.972    |    T/Tt: 0.992    |    A/A*: 2.964
M: 0.400   |   P/Pt: 0.896    |    T/Tt: 0.969    |    A/A*: 1.590
M: 0.600   |   P/Pt: 0.784    |    T/Tt: 0.933    |    A/A*: 1.188
M: 0.800   |   P/Pt: 0.656    |    T/Tt: 0.887    |    A/A*: 1.038
M: 1.000   |   P/Pt: 0.528    |    T/Tt: 0.833    |    A/A*: 1.000
M: 1.200   |   P/Pt: 0.412    |    T/Tt: 0.776    |    A/A*: 1.030
M: 1.400   |   P/Pt: 0.314    |    T/Tt: 0.718    |    A/A*: 1.115
M: 1.600   |   P/Pt: 0.235    |    T/Tt: 0.661    |    A/A*: 1.250
M: 1.800   |   P/Pt: 0.174    |    T/Tt: 0.607    |    A/A*: 1.439
M: 2.000   |   P/Pt: 0.128    |    T/Tt: 0.556    |    A/A*: 1.688
>>>
gas_dynamics.standard.standard.mach_from_pressure_ratio(pressure_initial: float, pressure_final: float, mach_initial: float, entropy=0, gas=<gas_dynamics.fluids.fluid object>) → float

Return the Mach number given a Mach number and the local pressures

Notes

Given the local pressure in two regions and the Mach number in one, return the Mach number in the second region. Default arguments are for air and isentropic flow.

Parameters

  • pressure_initial (float) – Pressure in region 1

  • pressure_final (float) – Pressure in region 2

  • mach_initial (float) – Mach number in region 1

  • entropy (float) – Change in entropy, if any

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The Mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> M2 = gd.mach_from_pressure_ratio(pressure_initial=10, pressure_final=2, mach_initial=1)
>>> M2
2.1220079294384067
>>>
gas_dynamics.standard.standard.mach_from_temperature_ratio(temperature_initial: float, temperature_final: float, mach_initial: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the Mach number given a Mach number and two local temperatures

Notes

Given the local temperatures in two regions and the mach number in one, return the Mach number in the second region. Default fluid is air.

Parameters

  • temperature_initial (float) – Temperature in region 1

  • temperature_final (float) – Temperature in region 2

  • mach_final (float) – Mach number in region 1

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_final = gd.mach_from_temperature_ratio(temperature_initial=300, temperature_final=150, mach_final=1)
>>> mach_final
2.6457513110645907
>>>
gas_dynamics.standard.standard.pressure_from_mach_ratio(mach_initial: float, mach_final: float, pressure_initial: float, entropy=0, gas=<gas_dynamics.fluids.fluid object>) → float

Return the pressure given a pressure in one region and the two Mach numbers

Notes

Given the Mach numbers in two regions and the pressure in one, return the missing pressure from the second region. Default arguments are for air and isentropic flow.

Parameters

  • mach_initial (float) – Mach number in region 1

  • mach_final (float) – Mach number in region 2

  • pressure_initial (float) – Pressure in region 1

  • entropy (float) – Change in entropy, if any

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The local pressure

Return type

float

Examples

>>> import gas_dynamics as gd
>>> p_final = gd.pressure_from_mach_ratio(mach_initial=1, mach_final=2, pressure_initial=10)
>>> p_final
2.4192491286747444
>>>
gas_dynamics.standard.standard.temperature_from_mach_ratio(mach_initial: float, mach_final: float, temperature_initial: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the temperature given a temperature in one region and the two Mach numbers

Notes

Given the local Mach number in two regions and the temperature in one, return the missing temperature from the second region. Default fluid is air.

Parameters

  • mach_initial (float) – Mach number in region 1

  • mach_final (float) – Mach number in region 2

  • temperature_initial (float) – Temperature in region 1

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The local temperature

Return type

float

Examples

>>> import gas_dynamics as gd
>>> T_final = gd.temperature_from_mach_ratio(mach_initial=1, mach_final=2, temperature_final=297.15)
>>> T_final
198.10000000000002
>>>
gas_dynamics.standard.standard.entropy_produced(stagnation_pressure_initial: float, stagnation_pressure_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the change in specific entropy from the stagnation pressure ratio

Notes

Given two stagnation pressures and the fluid, determine the entropy produced per unit mass.

Parameters

  • stagnation_pressure_initial (float) – Stagnation pressure in region 1

  • stagnation_pressure_final (float) – Stagnation pressure in region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The specific entropy

Return type

float

Examples

>>> import gas_dynamics as gd
>>> gd.entropy_produced(pt_initial=10, pt_final=9, gas='air')
30.238467993796142 #J / kg K
>>>
gas_dynamics.standard.standard.mach_area_star_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the ratio of A / A* given the Mach number.

Notes

Given the Mach number and the ratio of specific heats, return the area ratio of the Mach number given to the area where Mach number is equal to 1. Default fluid is air.

Parameters

  • mach (float) – Mach Number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The ratio of area over choked area

Return type

float

Examples

>>> import gas_dynamics as gd
>>> A_Astar =gd.mach_area_ratio_choked(mach=3)
>>> A_Astar
4.23456790123457
>>>
gas_dynamics.standard.standard.mach_area_ratio(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>, entropy=0) → float

Return the area ratio given the two Mach numbers

Notes

Given two mach numbers, return the area ratio required to accelerate or deaccelerate the flow accordingly. Default fluid is air.

Parameters

  • mach_initial (float) – Mach number in region 1

  • mach_final (float) – Mach number in region 2

  • gas (fluid) – A user defined fluid object. Default is air

  • ds (float) – Entropy produced, if any

Returns

The area ratio

Return type

float

Examples

>>> import gas_dynamics as gd
>>> A2_A1 = gd.mach_area_ratio(mach_initial=1.5, mach_final=2.5)
>>> A2_A1
2.241789331255894   #area ratio
>>>
gas_dynamics.standard.standard.mach_from_area_ratio(area_ratio: float, gas=<gas_dynamics.fluids.fluid object>) → list

Return the possible mach numbers given a choked area ratio A / A*

Notes

Given a ratio of area over an area where Mach = 1, return the subsonic and supersonic Mach numbers for the change area.

Parameters

  • area_ratio (float) – The ratio of area over choked area

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The subsonic and supersonic mach numbers for the area ratio

Return type

list

Examples

>>> import gas_dynamics as gd
>>> gd.mach_from_area_ratio(2)
[0.30590383418910816, 2.197198121652187]
>>>
gas_dynamics.standard.standard.mass_flux_max(stagnation_pressure: float, stagnation_temperature: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the maximum flow rate per unit choked area

Notes

Given stagnation pressure, stagnation temperature, and the fluid, return the flow rate for a Mach number equal to 1. Default fluid is air.

Units:

J / kg-K and Pa return kg/m^2

kJ / kg-K and kPa returns kg/m^2

ft-lbf / lbm-R and psi returns lbm/in^2

Parameters

  • stagnation_pressure (float) – The stagnation pressure.

  • stagnation_temperature (float) – The stagnation temperature.

  • gas (fluid) – A user defined fluid object. Default is air

  • metric (bool) – Use metric or US standard.

Returns

The maximum mass flux

Return type

float

Examples

>>> mdot = 5 #kg/s
>>> mdot_per_area = gd.choked_mdot(1000000, 300) #units are in Pascals
>>> mdot_per_area
2333.558560606226
>>> throat_area = mdot / mdot_per_area
>>> throat_area             #units are in meters squared
0.0021426503214477164
>>>
#alternatively, we can use the english system; psi, rankine and
get lbm/s/in^2
>>> from gas_dynamics.fluids import air_us
>>> air_us.units
'Btu / lbm-R'
>>> flux = gd.mass_flux_max( stagnation_pressure=500, stagnation_temperature=500, gas=air_us)
>>> flux
2.097208828890205
>>>
gas_dynamics.standard.standard.mass_flux(mach: float, stagnation_pressure: float, stagnation_temperature: float, gas=<gas_dynamics.fluids.fluid object>) → float

Determine mass flow rate for a mach number up to 1

Notes

Given stagnation pressure, stagnation temperature, and the fluid, return the flow rate per unit area for the given Mach number. Default fluid is air.

Units:

J / kg-K and Pa return kg/s/m^2

kJ / kg-K and kPa returns kg/s/m^2

ft-lbf / lbm-R and psi returns lbm/s/in^2

Btu / lbm-R and psi returns lbm/s/in^2

Parameters

  • mach (float) – The mach number. Should not exceed 1

  • stagnation_pressure (float) – The stagnation pressure

  • stagnation_temperature (float) – The stagnation temperature

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The mass flux

Return type

float

Examples

>>> #metric, input units are Pa, K, output is kg/s/m^2
>>> flux = gd.mass_flux(mach=.8, stagnation_pressure=1e6, stagnation_temperature=500)
>>> flux
1741.3113452036841
>>> #us standard, input units are psi and Rankine, output units are lbm/s/in^2
>>> from gas_dynamics.fluids import air_us
>>> air_us.units
'Btu / lbm-R'
>>> flux = gd.mass_flux(mach=.8, stagnation_pressure=500, stagnation_temperature=500, gas=air_us)
>>> flux
2.01998480961849
>>>
gas_dynamics.standard.standard.plot_stagnation_ratios(range=[0.1, 5], step=0.01, gasses=[<gas_dynamics.fluids.fluid object>, <gas_dynamics.fluids.fluid object>, <gas_dynamics.fluids.fluid object>], dark=True)

Plot the isentropic stagnation relationships for different gasses

Notes

Plots Mach number vs T/T, P/Pt, A/A*, rho/rho_t, for a list of specific heat ratios.

Parameters

  • range (list) – The starting and ending Mach # in a list, ex: [.01,5]

  • step (float) – The increment between min and max

  • gasses (list) –

    A list of the user defined gas objects to be plotted

    ex: gasses = [air, methane, argon]

  • dark (bool) – Use a dark mode plot. Default true.

Examples

>>> import gas_dynamics as gd
>>> gd.plot_stagnation_ratios()
>>>