Unlock the complexities of compressible flow with friction using our Fanno Line Flow Calculator. This essential tool helps engineers and students analyze adiabatic flow in constant-area ducts, determining critical parameters like Mach number, pressure, and temperature ratios, and the Fanno parameter for various flow conditions. Efficiently solve your fluid dynamics challenges.
Formula:
The Fanno Line Flow Calculator determines key dimensionless parameters based on the Mach number (M) and Specific Heat Ratio (γ). The primary equations used are:
- Fanno Parameter to Choke (4fL*/D):
4fL*/D = [(1 - M2) / (γM2)] + [((γ + 1) / (2γ)) * ln( (M2) / (1 + ((γ - 1) / 2)M2) )] - Static Pressure Ratio (P/P*):
P/P* = (1/M) * √[ ((γ+1) / (2 * (1 + ((γ-1)/2)M2))) ] - Static Temperature Ratio (T/T*):
T/T* = (γ+1) / (2 * (1 + ((γ-1)/2)M2)) - Velocity Ratio (V/V*):
V/V* = M * √[ (2 * (1 + ((γ-1)/2)M2)) / (γ+1) ]
Where:
- M = Upstream Mach Number (dimensionless)
- γ = Specific Heat Ratio (dimensionless, e.g., 1.4 for air)
- f = Friction Factor (dimensionless)
- L* = Length from current point to where M=1 (choked flow)
- D = Duct Hydraulic Diameter (length unit)
- P*, T*, V* = Static Pressure, Temperature, Velocity at Mach 1 (sonic conditions)