Isentropic flow ratios
[
mach
, T
, P
, rho
, area
]
= flowisentropic(gamma
, flow
, mtype
)
[
returns
an array. This array contains an isentropic flow Mach number (mach
, T
, P
, rho
, area
]
= flowisentropic(gamma
, flow
, mtype
)mach
),
temperature ratio (T
), pressure ratio
(P
), density ratio (rho
),
and area ratio (area
). This function calculates
these arrays given a set of specific heat ratios (gamma
),
and any one of the isentropic flow types. You select the isentropic
flow with mtype
.
This function assumes that variables vary in one dimension only. It also assumes that the main mechanism for the change of flow variables is the change of crosssectional area of the flow stream tubes.
This function assumes that the environment is a perfect gas. In the following instances, the function cannot assume a perfect gas environment. If there is a large change in either temperature or pressure without a proportionally large change in the other, the function cannot assume a perfect gas environment. . If the stagnation temperature is above 1500 K, do not assume that constant specific heats. In this case, the medium ceases to be a calorically perfect gas. Consider it a thermally perfect gas. See 2 for thermally perfect gas correction factors. If the temperature is so high that molecules dissociate and ionize (static temperature 5000 K for air), you cannot assume a calorically or thermally perfect gas.

Array of  

Array of real numerical values for one of the isentropic flow relations. This argument can be one of the following:
 

Input mode for the isentropic flow in

All outputs are the same size as the array inputs. If there are no array inputs, all outputs are scalars.

Array of Mach numbers. 

Array of temperature ratios. The temperature ratio is the local static temperature over the stagnation temperature. 

Array of pressure ratios. The pressure ratio is the local static pressure over the stagnation pressure. 

Array of density ratios. The density ratio is the local density over the stagnation density. 

Array of area ratios. The area ratio is the local stream tube area over the reference stream tube area for sonic conditions. 
Calculate the isentropic flow relations for air (gamma
=
1.4) for a design subsonic area ratio of 1.255. This example returns
scalar values for mach
, T
, P
, rho
,
and area
.
[mach, T, P, rho, area] = flowisentropic(1.4, 1.255, 'sub')
Calculate the isentropic flow relations for gases with specific
heat ratios given in the following 1 x 4 row array for the Mach number
0.5. This example following returns a 1 x 4 row array for mach
, T
, P
, rho
,
and area
.
gamma = [1.3, 1.33, 1.4, 1.67]; [mach, T, P, rho, area] = flowisentropic(gamma, 0.5)
Calculate the isentropic flow relations for a specific heat
ratio of 1.4. Also calculate range of temperature ratios from 0.40
to 0.70 in increments of 0.10. This example returns a 4 x 1 column
array for mach
, T
, P
, rho
,
and area
.
[mach, T, P, rho, area] = flowisentropic(1.4, (0.40:0.10:0.70)', 'temp')
Calculate the isentropic flow relations for gases with provided
specific heat ratio and density ratio combinations. This example
returns a 1 x 2 array for mach
, T
, P
, rho
,
and area
each. The elements of each vector
correspond to the inputs elementwise.
gamma = [1.3, 1.4]; rho = [0.13, 0.9]; [mach, T, P, rho, area] = flowisentropic(gamma, rho , 'dens')
1. James, J. E. A., Gas Dynamics, Second Edition, Allyn and Bacon, Inc, Boston, 1984.
2. NACA Technical Report 1135, 1953, National Advisory Committee on Aeronautics, Ames Research Staff, Moffett Field, Calif. Pages 667–671.
flowfanno
 flownormalshock
 flowprandtlmeyer
 flowrayleigh