Fanno line flow relations
Calculate the Fanno line flow relations for air
gamma = 1.4) for subsonic Fanno parameter 1.2. This example
returns scalar values for
[mach,T,P,rho,velocity,P0,fanno] = flowfanno(1.4,1.2,'fannosub')
mach = 0.4849 T = 1.1461 P = 2.2080 rho = 1.9265 velocity = 0.5191 P0 = 1.3699 fanno = 1.2000
Calculate the Fanno line 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 yields
a 1 x 4 row array for
gamma = [1.3,1.33,1.4,1.67]; [mach,T, P,rho,velocity,P0,fanno] = flowfanno(gamma,0.5)
mach = 0.5000 0.5000 0.5000 0.5000 T = 1.1084 1.1188 1.1429 1.2318 P = 2.1056 2.1155 2.1381 2.2198 rho = 1.8997 1.8908 1.8708 1.8020 velocity = 0.5264 0.5289 0.5345 0.5549 P0 = 1.3479 1.3454 1.3398 1.3201 fanno = 1.1724 1.1397 1.0691 0.8549
Calculate the Fanno line flow relations for a specific heat ratio of
1.4 and 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,velocity,P0,fanno] = flowfanno(1.4,[1.1 1.2],'temp')
mach = 0.6742 0 T = 1.1000 1.2000 P = 1.5556 Inf rho = 1.4142 Inf velocity = 0.7071 0 P0 = 1.1144 Inf fanno = 0.2630 Inf
gamma— Specific heat ratios
Specific heat ratios, specified as an array or scalar of N specific heat ratios.
gamma must be a real, finite scalar greater than 1 for these
Subsonic total pressure ratio
Supersonic total pressure ratio
Subsonic Fanno parameter
Supersonic Fanno parameter
fanno_flow— One Fanno flow
One Fanno flow, specified as an array of real numerical values. This argument can be one of these types.
|Fanno Flow Type||Description|
Mach numbers, specified as a scalar or array of N
real numbers greater than or equal to 0. If
Temperature ratios, specified as an array or scalar of N real numbers:
ratios, specified as an array or scalar of real numbers greater than
or equal to 0. If
Density ratios, specified as an array or scalar of real numbers. These numbers must be greater than or equal to:
Velocity ratios, specified as an array or scalar of N real numbers:
|Total pressure ratio|
Total pressure ratio, specified as a scalar greater than or equal to 1.
|Fanno parameter scalar|
Fanno Parameter, specified
as a scalar. In subsonic mode,
mtype— Input mode of Fanno flow
Input mode of Fanno flow, specified as one of these values.
|Default Mach number|
|Subsonic total pressure ratio|
|Supersonic total pressure ratio|
|Subsonic Fanno parameter|
|Supersonic Fanno parameter|
All outputs are the same size as the array inputs. If there are no array inputs, all outputs are scalars.
mach— Mach numbers
Mach numbers, returned as an array.
T— Temperature ratios
Temperature ratios, returned as an array.
P— Pressure ratios
Pressure ratios, returned as an array.
rho— Density ratios
Density ratios, returned as an array.
velocity— Velocity ratios
Velocity ratios, returned as an array.
P0— Stagnation pressure ratios
Stagnation (total) pressure ratios, returned as an array.
fanno— Fanno parameters
Fanno parameters, returned as an array.
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 . If the temperature is so high that molecules dissociate and ionize (static temperature 5000 K for air), you cannot assume a perfect gas.
Calculated as local static pressure over the reference static pressure for sonic flow.
Calculated as local static temperature over the reference static temperature for sonic flow.
Calculated as local density over the reference density for sonic flow.
Calculated as local velocity over the reference velocity for sonic flow.
Calculated as local total pressure over the reference total pressure for sonic flow.
This function uses Fanno variables given by the equation: F = f*L/D, where:
F is the Fanno parameter.
f is the friction coefficient.
L is the length of constant area duct required to achieve sonic flow.
D is the hydraulic diameter of the duct.
 James, John E. A. Gas Dynamics. 2nd ed. Boston: Allyn and Bacon 1984.
 Ames Research Staff. NACA Technical Report 1135. Moffett Field, CA: National Advisory Committee on Aeronautics, 1953. 667–671.