Calculate Fanno flow ratios from pressure loss factor for critical adiabatic and isothermal flow.
Fanno ratios are calculated for critical exit flow. For example the Fanno pressure ratio (P/P*) equals the ratio of inlet pressure (P) over the critical exit pressure (P*). Critical flow occurs when the exit Mach number = 1 for adiabatic flow, or the exit Mach number = √γ for isothermal flow where γ is the specific heat ratio. The inlet Mach number at critical flow is dependent on the duct pressure loss factor (fL/D). Fanno ratios are normally calculated for adiabatic flow. This calculator includes the option to calculate Fanno ratios for isothermal flow. For isothermal flow the temperature ratio = 1.
The pressure loss factor is calculated from the Darcy friction factor and the minor loss factors
`fld = (f L) / D + K `
where :
fld = pressure loss factor
f = Darcy friction factor
L = pipe length
D = pipe internal diameter
K = sum of minor loss factors
Minor losses can also be accounted for using an equivalent length. For critical flow (high velocity and high Reynolds numbers) the flow is assumed to be fully turbulent. The Von Karmen rough pipe equation is used to calculate the Darcy friction factor (fd). The Von Karmen Equation is independent of Reynolds number and fluid viscosity.
Use the Result Plot option to plot the Fanno flow ratio lines for pressure ratio, temperature ratio, density ratio, speed of sound ratio, and velocity ratio, versus either Mach number or pressure loss factor, and versus either flow type (adiabatic or isothermal) or specific heat ratio.
Reference : Fluid Mechanics, Frank M White, McGraw Hill
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