- #1
roldy
- 237
- 2
I've seen equations for Fanno flow and Rayleigh flow but I am confused on how to use them properly.
Fanno Flow
[tex]
\frac{P}{P^{*}}=\frac{1}{M}\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{\rho}{\rho^{*}}=\frac{1}{M}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{T}{T^{*}}=\frac{1}{\left(\frac{2}{\gamma+1}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{U}{U^{*}}=M\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{P_0}{P_0^{*}}=\frac{1}{M}\left[\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}
[/tex]
[tex]
T_0=T_0^{*}
[/tex]
Inlet conditions:
[tex]P_0=101325[/tex] Pa
[tex]T_0=288[/tex] K
[tex]M_0=0.1[/tex]
[tex]Area=0.1 m^2[/tex]
[tex]T_{wall}=3000[/tex]K
Friction Coefficient([tex]C_f[/tex])=0.2
Duct Length=10 m
Adiabatic, no work interaction, constant area
I guess my confusion comes from the * parameters. If I know my inlet conditions only, how can I calculate the exit conditions from these equations? What do the numerator parameters represent? Are they the values at the exit? The Mach number in these equations, are they any the given Mach number (in this case 0.1)?
Fanno Flow
[tex]
\frac{P}{P^{*}}=\frac{1}{M}\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{\rho}{\rho^{*}}=\frac{1}{M}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{T}{T^{*}}=\frac{1}{\left(\frac{2}{\gamma+1}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{U}{U^{*}}=M\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}
[/tex]
[tex]
\frac{P_0}{P_0^{*}}=\frac{1}{M}\left[\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}
[/tex]
[tex]
T_0=T_0^{*}
[/tex]
Inlet conditions:
[tex]P_0=101325[/tex] Pa
[tex]T_0=288[/tex] K
[tex]M_0=0.1[/tex]
[tex]Area=0.1 m^2[/tex]
[tex]T_{wall}=3000[/tex]K
Friction Coefficient([tex]C_f[/tex])=0.2
Duct Length=10 m
Adiabatic, no work interaction, constant area
I guess my confusion comes from the * parameters. If I know my inlet conditions only, how can I calculate the exit conditions from these equations? What do the numerator parameters represent? Are they the values at the exit? The Mach number in these equations, are they any the given Mach number (in this case 0.1)?