The Fanno line on a T-s diagram has a maximum entropy point. At what Mach number does this occur?
Explanation
On a Temperature-Entropy (T-s) diagram, the Fanno line is a curve representing all possible states for a given Fanno flow. The vertex of this curve, which corresponds to the point of maximum entropy, occurs exactly at Mach 1. This illustrates the second law of thermodynamics, as friction drives the flow towards this state.
Other questions
What is the primary restriction of the Fanno flow model?
In the context of Fanno flow, what does the energy conservation equation T01 = T02 imply?
For subsonic Fanno flow (M < 1), how does the Mach number change as the flow moves downstream?
For supersonic Fanno flow (M > 1), how does the pressure change as the flow moves downstream?
What is the physical meaning of the 'choked flow' condition in Fanno flow?
In the summary of property changes for Fanno flow, which property decreases in subsonic flow but increases in supersonic flow?
According to the integration of the Fanno flow equations, what is the value of the dimensionless friction parameter (4fL_max/D) when the Mach number (M) is exactly 1?
What happens to the entropy of the flow in both subsonic and supersonic Fanno flow?
A flow of air (k=1.4) enters a pipe at Mach 3.0. According to the standard Fanno flow table, what is the value of the pressure ratio P/P* at this condition?
A Fanno flow system has a dimensionless friction of 4fL/D = 0.8. The flow starts at Mach 3.0, for which the maximum possible dimensionless friction (4fLmax/D) is 0.52216. What can be concluded about this flow?
What is the key characteristic of the supersonic branch of Fanno flow that distinguishes it from the subsonic branch regarding length?
For a converging nozzle feeding a Fanno flow pipe, what happens to the mass flow rate as the tube length is increased, assuming the flow remains choked at the exit?
In supersonic Fanno flow, the maximum dimensionless length (4fLmax/D) is a function of which two properties?
According to the Fanno Flow Standard basic Table (k=1.4), what is the Mach number (M) when the dimensionless friction (4fL/D) is 0.30500?
What is the relationship between the Fanning friction factor (f) used in the equations and the Darcy friction factor?
What is the trend of the stagnation pressure (P0) in Fanno flow?
Air flows in a pipe with a diameter of 0.05 m and length of 10 m. The exit conditions are M2=0.9 and the friction factor f=0.004. What is the value of the dimensionless friction parameter (4fL/D) for the entire pipe?
If a supersonic Fanno flow with an initial Mach number of M1=8 and k=1.4 is sent through a pipe with a dimensionless friction of 4fL/D = 0.9, what can be determined about the flow condition, given that the maximum 4fL/D for M=8 is 0.76820?
When a Fanno flow system is fed by a converging-diverging nozzle and is operating in the 'a-b' range as shown in Figure 9.8, what is the state of the flow?
What does the symbol P* represent in Fanno flow equations like P/P*?
Based on the Fanno flow table (k=1.4), for an inlet Mach number of 0.5, what is the ratio of the stagnation pressure to the critical stagnation pressure, P0/P0*?
What happens to the density (rho) of the gas in supersonic Fanno flow as it moves downstream?
Air (k=1.4) flows in a pipe and exits at M2=0.9. An engineer needs to find the conditions at the inlet, which is 10m upstream. The pipe diameter is 0.05m and the friction factor is 0.004. What is the value of (4fL_max/D) at the inlet (station 1)?
What is the key difference between the subsonic and supersonic branches of Fanno flow when a normal shock wave is considered?
In a system composed of a converging-diverging nozzle followed by a long tube, what determines the mass flow rate when the flow is supersonic in the tube?
What does a value of P0/P0* = 1.0089 in the Fanno flow table for k=1.4 signify?
Why can the Fanno flow model be used to approximate the emptying of a pressured container through a relatively short tube?
What is the trend of the temperature T for subsonic Fanno flow?
For a supersonic Fanno flow with an initial Mach number of 4.0 (k=1.4), what is the maximum dimensionless friction (4fL/D) the flow can sustain before a shock is required?
In the context of a shock wave occurring in a Fanno flow tube, if the Mach number just before the shock (Mx) is 3.0, what is the Mach number immediately after the shock (My)?
What is the limiting Mach number for supersonic Fanno flow as the dimensionless friction parameter 4fL/D approaches its maximum value for a given initial condition?
In Figure 9.8, which shows the Mach numbers at the entrance and exit of a tube for Fanno Flow, what does the region 'b-c' represent?
What is the theoretical maximum dimensionless length (4fL/D) for supersonic Fanno flow when k=1.4 and the initial Mach number approaches infinity?
How is the relationship between two points in a Fanno flow, (1) and (2), typically determined using the dimensionless friction parameter?
According to the Fanno flow table for k=1.4, what is the temperature ratio T/T* for a flow at Mach 2.0?
In the 'semi supersonic flow b--c' regime depicted in Figure 9.8, the text states the flow is 'double choked'. What does this mean?
What is the primary effect of increasing the pressure ratio (P2/P1) in a subsonic Fanno flow system with a constant length pipe?
In a Fanno flow problem, if the flow is determined to be choked with a shock wave, where is the shock located?
If a flow in a pipe has an initial Mach number M=0.2 and a dimensionless friction 4fL/D = 14.5333 (k=1.4), what can be said about the flow at the exit?
What is the value of the velocity ratio U/U* for a Fanno flow at Mach 0.85 with k=1.4?
In a converging-diverging nozzle feeding a Fanno flow tube, if the system is in the range 'c to infinity' (as depicted in Figure 9.8), what is the state of the mass flow rate?
What is the value of the density ratio rho/rho* for a Fanno flow at Mach 0.20 (k=1.4)?
If a shock occurs in a Fanno flow at M=1.6706, what is the Mach number of the subsonic flow immediately after the shock?
What is the primary reason that Fanno flow is considered a better model than Isothermal flow for rapid processes in short tubes?
For a choked Fanno flow (k=1.4) starting at M1=0.1, what is the required 4fL/D to reach M2=1?
On the Fanno line (T-s diagram), what happens to the flow properties as the flow moves 'up' the subsonic branch toward the choking point?
In a Fanno flow system with a constant length pipe fed by a converging nozzle, if the back pressure is lowered, what happens to the entrance Mach number M1?
For Fanno flow with k=1.4, what is the maximum Mach number (M) for which the flow is considered subsonic in the summary table of property changes?
If a Fanno flow starts at M=0.5 and the pipe is long enough to have a dimensionless friction 4fL/D of 0.5, what is the exit Mach number M2, given that (4fL_max/D) for M=0.5 is 1.0691 and for M=0.6 is 0.49082?