# flowisentropic

Isentropic flow ratios

## Description

### Default Input Mode

example

[mach,T,P,rho,area] = flowisentropic(gamma,flow) returns an array that contains an isentropic flow Mach number 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) for the Mach input mode.

### Specify Input Mode

example

[mach,T,P,rho,area] = flowisentropic(___,mtype) uses any one of the isentropic flow types mtype. Specify mtype types after all other input arguments.

## Examples

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Calculate isentropic flow1

Calculate the isentropic flow relations for air (gamma = 1.4) for a design subsonic area ratio of 1.255.

[mach, T, P, rho, area] = flowisentropic(1.4, 1.255, 'sub')
mach = 0.5500
T = 0.9430
P = 0.8142
rho = 0.8634
area = 1.2550

Calculate isentropic flow2

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.

gamma = [1.3, 1.33, 1.4, 1.67];
[mach, T, P, rho, area] = flowisentropic(gamma, 0.5)
mach = 1×4

0.5000    0.5000    0.5000    0.5000

T = 1×4

0.9639    0.9604    0.9524    0.9227

P = 1×4

0.8525    0.8497    0.8430    0.8183

rho = 1×4

0.8845    0.8847    0.8852    0.8869

area = 1×4

1.3479    1.3454    1.3398    1.3201

Calculate isentropic flow3

Calculate the isentropic flow relations for a specific heat ratio of 1.4.

[mach, T, P, rho, area] = flowisentropic(1.4, (0.40:0.10:0.70)', 'temp')
mach = 4×1

2.7386
2.2361
1.8257
1.4639

T = 4×1

0.4000
0.5000
0.6000
0.7000

P = 4×1

0.0405
0.0884
0.1673
0.2870

rho = 4×1

0.1012
0.1768
0.2789
0.4100

area = 4×1

3.3018
2.0704
1.4674
1.1526

Calculate isentropic flow4

Calculate the isentropic flow relations for gases with provided specific heat ratio and density ratio combinations.

gamma = [1.3, 1.4];
rho = [0.13, 0.9];
[mach, T, P, rho, area] = flowisentropic(gamma, rho , 'dens')
mach = 1×2

2.3724    0.4639

T = 1×2

0.5422    0.9587

P = 1×2

0.0705    0.8629

rho = 1×2

0.1300    0.9000

area = 1×2

2.5769    1.4155

## Input Arguments

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Specific heat ratios, specified as an array or scalar of N specific heat ratios.

#### Dependencies

gamma must be a real, finite scalar greater than 1 for these input modes:

• Subsonic area ratio

• Supersonic area ratio

Data Types: double

One isentropic flow relation, specified as an array of real numerical values. This argument can be one of these types:

Isentropic Flow TypeDescription
Mach numbers

Mach numbers, specified as a scalar or array of N real numbers greater than or equal to 0. If flow and gamma are arrays, they must be the same size.

Use flow with the mtype value 'mach'. Because 'mach' is the default of mtype, mtype is optional when this array is the input mode.

Temperature ratios

Temperature ratios, specified as an array or scalar of real numbers:

• Greater than or equal to 0 (as the Mach number approaches infinity)

• Less than or equal to 1 (at Mach number equal 0)

If flow and gamma are both arrays, they must be the same size.

Use flow with mtype value 'temp'.

Pressure ratios

Pressure ratios, specified as an array or scalar of real numbers greater than or equal to 0.

• Greater than or equal to 0 (as the Mach number approaches infinity)

• Less than or equal to 1 (at Mach number equal 0)

If flow and gamma are both arrays, they must be the same size.

Use flow with mtype value 'pres'.

Density ratios

Density ratios, specified as an array or scalar of real numbers.

• Greater than or equal to 0 (as the Mach number approaches infinity)

• Less than or equal to 1 (at Mach number equal 0)

If flow and gamma are arrays, they must be the same size.

Use flow with mtype value 'dens'.

Area ratios

Area ratios, specified as a scalar real value greater than or equal to 1.

Use flow with mtype value 'sup'.

Data Types: double

Input mode of Fanno flow, specified as one of these values.

TypeDescription
'mach'Default Mach number. Indicates that the function is in Mach number input mode.
'temp'Indicates that the function is in temperature ratio input mode.
'pres' Indicates that the function is in pressure ratio input mode.
'dens'Indicates that the function is in density ratio input mode.
'sub'Indicates that the function is in subsonic area ratio input mode. The subsonic area ratio is defined as the local subsonic streamtube area over the reference streamtube area for sonic conditions.
'sup'Indicates that the function is in supersonic area ratio input mode. The supersonic area ratio is defined as the local supersonic streamtube area over the reference streamtube area for sonic conditions.

Data Types: double

## Output Arguments

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Mach numbers, returned as an array.

Temperature ratios, returned as an array.

Pressure ratios, returned as an array.

Density ratios, returned as an array.

Area ratios, returned as an array.

## Limitations

• This function assumes that variables vary only in one dimension. It also assumes that the main mechanism for the change of flow variables is the change of cross-sectional area of the flow stream tubes.

• If the temperature experiences large fluctuations, the perfect gas assumption might be invalid. If the stagnation temperature is above 1500 K, do not assume constant specific heats. In this case, the medium ceases to be a calorically perfect gas. Consider it a thermally perfect gas. For thermally perfect gas correction factors, see [2]. If the temperature is so high that molecules dissociate and ionize (static temperature 5000 K for air), you cannot assume a perfect gas.

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### Temperature Ratio

Calculated as local static temperature over the stagnation temperature.

### Pressure Ratio

Calculated as local static pressure over the stagnation pressure.

### Density Ratio

Calculated as local density over the stagnation density.

### Area Ration

Calculated as local stream tube area over the reference stream tube area for sonic conditions.

## Version History

Introduced in R2010a