Fanno Flow

Fanno flow describes the adiabatic flow through a constant area duct where the effect of friction is considered.

The ratio of pressure and choked pressure is inversely proportional to the Mach number, and increases as the heat capacity ratio nears 1. The ratio of density and choked density decreases as the heat capacity ratio nears 1, and also depends on the Mach number. The ratio of temperature and choked temperature decreases quadratically with the Mach number, and increases as the heat capacity ratio nears 1. The ratio of velocity and choked velocity increases as the heat capacity ratio nears 1, and also depends on the Mach number. The ratio of stagnation and choked stagnation pressure depends nonlinearly on the Mach number and heat capacity ratio.

Formula

${QuantityVariable["P"/Subscript["P", "*"], "Unitless"] == 1/(Sqrt[2]*QuantityVariable["Ma", "MachNumber"]*Sqrt[(1 + 0.5*QuantityVariable["Ma", "MachNumber"]^2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"]))/(1 + QuantityVariable["γ", "HeatCapacityRatio"])]), QuantityVariable["ρ"/SubStar["ρ"], "Unitless"] == (Sqrt[2]*Sqrt[(1 + 0.5*QuantityVariable["Ma", "MachNumber"]^2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"]))/(1 + QuantityVariable["γ", "HeatCapacityRatio"])])/QuantityVariable["Ma", "MachNumber"], QuantityVariable["T"/SubStar["T"], "Unitless"] == (1 + QuantityVariable["γ", "HeatCapacityRatio"])/(2*(1 + 0.5*QuantityVariable["Ma", "MachNumber"]^2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"]))), QuantityVariable["V"/SubStar["V"], "Unitless"] == QuantityVariable["Ma", "MachNumber"]/(Sqrt[2]*Sqrt[(1 + 0.5*QuantityVariable["Ma", "MachNumber"]^2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"]))/(1 + QuantityVariable["γ", "HeatCapacityRatio"])]), QuantityVariable[Subscript["P", "0"]/Subscript["P", "0*"], "Unitless"] == (2^((1 + QuantityVariable["γ", "HeatCapacityRatio"])/(2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"])))*((1 + 0.5*QuantityVariable["Ma", "MachNumber"]^2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"]))/(1 + QuantityVariable["γ", "HeatCapacityRatio"]))^((1 + QuantityVariable["γ", "HeatCapacityRatio"])/(2*(-1 + QuantityVariable["γ", "HeatCapacityRatio"]))))/QuantityVariable["Ma", "MachNumber"]}$

symbol	description	physical quantity
P/P_*	ratio of pressure and choked pressure	"Unitless"
Ma	Mach number	"MachNumber"
γ	heat capacity ratio	"HeatCapacityRatio"
ρ/ρ_*	ratio of density and choked density	"Unitless"
T/T_*	ratio of temperature and choked temperature	"Unitless"
V/V_*	ratio of velocity and choked velocity	"Unitless"
P₀/P_0*	ratio of stagnation and choked stagnation pressure	"Unitless"