Fanno Flow

Definition

Fanno flow describes the behavior of compressible flow in a constant area duct with friction. It is characterized by the fact that as the flow moves through the duct, there is a loss of total pressure due to friction, leading to changes in velocity and temperature. Understanding Fanno flow is crucial for analyzing aerodynamic and hydrodynamic systems where the effects of friction cannot be ignored, particularly in high-speed flows.

5 Must Know Facts For Your Next Test

1. Fanno flow assumes that the flow is steady, one-dimensional, and governed by the conservation of mass, momentum, and energy.
2. In Fanno flow, as friction acts on the flow, it causes a decrease in total pressure and can lead to a reduction in velocity until a point of choking is reached.
3. The Fanno line on a T-s diagram (temperature-entropy diagram) shows how temperature decreases while entropy increases due to frictional effects.
4. Fanno flow is typically analyzed using the Fanno flow equations, which relate mass flow rate, pressure, temperature, and Mach number through a duct.
5. Understanding Fanno flow is essential for applications such as rocket nozzles and high-speed airflows in aerodynamic designs.

Review Questions

• How does Fanno flow differ from isentropic flow, and what implications does this have for analyzing fluid dynamics?
  • Fanno flow differs from isentropic flow primarily due to the presence of friction in Fanno flow, which causes an increase in entropy and a decrease in total pressure. In contrast, isentropic flow assumes no friction and constant entropy. This difference is crucial for accurately modeling real-world systems where friction plays a significant role, allowing for more precise predictions of performance in applications like ducted flows or nozzles.
• Discuss the significance of the Mach number in relation to Fanno flow and how it impacts the characteristics of the fluid.
  • The Mach number is critical in understanding Fanno flow as it indicates whether the flow is subsonic or supersonic. In subsonic Fanno flows, increasing friction leads to a decrease in velocity and total pressure. However, if the flow becomes supersonic, the behavior changes; further friction increases total pressure losses while decreasing velocity until choking occurs. This relationship helps engineers design systems that effectively manage compressible flows.
• Evaluate how total pressure loss influences the design considerations for systems employing Fanno flow principles.
  • Total pressure loss in Fanno flow directly affects system efficiency and performance. When designing systems like rocket engines or air ducts, engineers must account for frictional losses to ensure optimal operating conditions. An accurate understanding of how total pressure drops impact velocity and temperature allows for better selection of materials and configurations to minimize adverse effects on performance while achieving desired operational goals.

Related terms

Isentropic Flow: A flow process where entropy remains constant, typically idealized and without friction or heat transfer.

Mach Number: A dimensionless quantity that represents the ratio of the speed of an object moving through a fluid to the speed of sound in that fluid.

Total Pressure: The sum of the static pressure and dynamic pressure in a fluid flow, representing the total mechanical energy per unit volume.