What Is the Fanno Line Duct Friction Choking Length Calculator?
Fanno flow describes adiabatic, 1D flow in constant-area ducts with wall shear stress.
Wall friction continuously reduces stagnation pressure and drives the Mach number toward M = 1.
How Does the Fanno Line Duct Friction Choking Length Calculator Work?
The parameter 4fL*/D represents the maximum dimensionless length a pipe can have without choking.
If the physical pipe length L exceeds L*, the inlet Mach number must decrease, reducing the flow capacity of the line.
Fanno Line Duct Friction Choking Length Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
\frac{4 f L^*}{D} = \frac{1 - M^2}{\gamma M^2} + \frac{\gamma + 1}{2 \gamma} \ln\left[ \frac{(\gamma+1)M^2}{2\left(1 + \frac{\gamma-1}{2}M^2\right)} \right], \quad L^* = \frac{(4fL^*/D) D}{4 f}
Fanno line non-dimensional friction parameter for adiabatic choking length.
How to Use the Fanno Line Duct Friction Choking Length Calculator
- Input inlet Mach number, pipe diameter, and friction factor.
- Check maximum choking length L* and static pressure ratio P/P*.
Step-by-Step Example Calculation
High-Pressure Gas Relief Line
Input Values:
inletMachNumber:0.4
ductDiameterMeters:0.2
fanningFrictionFactor:0.005
specificHeatRatio:1.4
Worked Steps: Computes maximum allowable pipe length before frictional choking.
Understanding Your Result
L* represents the sonic choking length. At this distance, the exit reaches M = 1.
Factors That Affect the Result
- Higher inlet Mach numbers dramatically shorten L*, making high-speed gas lines prone to premature choking.
When Should You Use This Calculator?
- High-pressure gas vent lines, safety relief headers, natural gas transmission, and rocket engine feedlines.
Assumptions & Limitations
- Assumes steady, 1D, adiabatic flow of a calorically perfect gas.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical integration of the Fanno momentum equation.