# isentropic_units.py (Source)

```"""
Isentropic, adiabatic flow example - calculate area ratio vs. Mach number curve.
Uses the pint library to include customized units in the calculation.

Requires: Cantera >= 3.0.0, pint
Keywords: thermodynamics, compressible flow, units
"""

import cantera.with_units as ctu
import numpy as np

# This sets the default output format of the units to have 2 significant digits
# and the units are printed with a Unicode font. See:
ctu.units.default_format = ".2F~P"

def soundspeed(gas):
"""The speed of sound. Assumes an ideal gas."""

gamma = gas.cp / gas.cv
specific_gas_constant = ctu.units.molar_gas_constant / gas.mean_molecular_weight
return np.sqrt(gamma * specific_gas_constant * gas.T).to("m/s")

def isentropic(gas=None):
"""
In this example, the area ratio vs. Mach number curve is computed. If a gas
object is supplied, it will be used for the calculations, with the
stagnation state given by the input gas state. Otherwise, the calculations
will be done for a 10:1 hydrogen/nitrogen mixture with stagnation T0 = 1700.33
degrees Fahrenheit, P0 = 10 atm.
"""
if gas is None:
gas = ctu.Solution('gri30.yaml')
gas.TPX = 2160 * ctu.units.degR, 10.0 * ctu.units.atm, 'H2:1,N2:0.1'

# get the stagnation state parameters
s0 = gas.s
h0 = gas.h
p0 = gas.P

mdot = 1 * ctu.units.kg / ctu.units.s  # arbitrary
amin = 1.e14 * ctu.units.m**2

data = []

# compute values for a range of pressure ratios
p_range = np.logspace(-3, 0, 10) * p0
for p in p_range:

# set the state using (p,s0)
gas.SP = s0, p

v = np.sqrt(2.0*(h0 - gas.h)).to("m/s")     # h + V^2/2 = h0
area = mdot/(gas.density*v)    # rho*v*A = constant
amin = min(amin, area)
data.append([area, v/soundspeed(gas), gas.T, p/p0])

return data, amin

if __name__ == "__main__":
print(__doc__)
data, amin = isentropic()
label_string = "area ratio\tMach number\ttemperature\tpressure ratio"
output_string = "{0:.2E~P}\t{1}            {2}\t{3:.2E~P}"
print(label_string)
for row in data:
print(output_string.format(row[0] / amin, row[1], row[2], row[3]))
```