What is Fanno flow equation?
1. FANNO CURVE & FANNO EQUATION Dhaval Chauhan Mechanical Engineer. Fanno Curve Consider a flow of a fluid in a perfectly insulated (Q=0) constant area duct. Continuity equation: ṁ = ρ ∙ AC ∴ ṁ A = ρ ∙ C = Constant, G …( 1) Where G = Mass flow density.
What is fanno line expansion?
The Fanno line defines the possible states for a gas when the mass flow rate and total enthalpy are held constant, but the momentum varies. Each point on the Fanno line will have a different momentum value, and the change in momentum is attributable to the effects of friction.
What is fanno line and Rayleigh line?
Fanno line or Fanno curve (Governing equation) Adiabatic Flow of a Compressible Fluid Through a Conduit. Variation of flow properties and Mach number with duct length. Rayleigh Flow (Duct Flow with Heat Transfer and Negligible Friction)
What is critical length in Fanno flow?
Case 1: Fanno Flow: M is the inlet Mach number. The critical length of the pipe is the length required for the flow to choke at the exit (i.e. M = 1 at exit). With an inlet Mach no of 0.5 and a friction factor of 0.002, and pipe diameter of 6 inches the critical length is calculated to be 3207 inches.
What is the characteristics aspect of Fanno flow?
The characteristic aspect of Fanno flow is its consideration of friction. The main assumptions associated with Fanno flow are: the flow is steady, one- dimensional, and adiabatic through a constant-area duct, and the fluid is an ideal gas with constant specific heats.
What is fanno curve?
Flow in a constant area duct with friction and without heat transfers is described by a curve is known as Fanno line or Fanno curve. In supersonic flow region (B to F), the effect of friction will decrease the velocity and Mach number and to increase the enthalpy and pressure of the gas.
What is Fanno flow and Rayleigh flow?
Rayleigh flow refers to frictionless, non-adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered. For this model, the duct area remains constant and no mass is added within the duct. Therefore, unlike Fanno flow, the stagnation temperature is a variable.
What do the states on the Fanno line and Rayleigh lines represents what do the intersection points of these two curves represent?
The intersections represent the states at which all three conservation relations are satisfied.
What is the Mach number at room temperature?
Mach number is denoted by ‘M’. Mach number ranges from zero to infinity. It falls into several flow regimes. It is 340 m/s at room temperature.
What causes a normal shockwave?
Normal Shock Wave Equations. As an object moves through a gas, the gas molecules are deflected around the object. But when an object moves faster than the speed of sound, and there is an abrupt decrease in the flow area, the flow process is irreversible and the entropy increases. Shock waves are generated.
How do you calculate Mach flow?
The Mach number is a dimensionless quantity. Mathematically, the Mach number equation can be written as: M = v / c , such that v is the speed of the object and c is the speed of sound.
Which is the Fanno equation for choked flow?
The Fanno Line equation is for the flow which has sonic velocity (Mach no. = 1) at the duct (or pipe) exit plane, i.e. choked flow. As depicted in the diagram below for choked flow, the pipe exit pressure (P2) is same with the critical pressure (Pc) and the fluid velocity at pipe exit is same with sonic velocity]
How is a Fanno line plotted in a flow model?
Figure 1 A Fanno Line is plotted on the dimensionless H-ΔS axis. The Fanno flow model begins with a differential equation that relates the change in Mach number with respect to the length of the duct, dM/dx.
When does the Fanno flow reach its maximum entropy?
In the diagram, the Fanno line reaches maximum entropy at H = 0.833 and the flow is choked. According to the Second law of thermodynamics, entropy must always increase for Fanno flow. This means that a subsonic flow entering a duct with friction will have an increase in its Mach number until the flow is choked.
Why does the momentum of the Fanno line vary?
Theory. The Fanno line defines the possible states for a gas when the mass flow rate and total enthalpy are held constant, but the momentum varies. Each point on the Fanno line will have a different momentum value, and the change in momentum is attributable to the effects of friction.