# Conv-Div nozzle and Fanno flow (Gas Dynamics)

• aero_zeppelin
In summary, the conversation discusses the operation of a rocket nozzle with specific dimensions and inlet conditions. The goal is to determine the nozzle exit velocity and mass flow for a given back pressure, while taking into account various factors such as exhaust gas properties and flow conditions. The solution involves calculating the area ratio and Mach number at the exit, as well as considering the possibility of a shockwave upstream.
aero_zeppelin

## Homework Statement

A rocket nozzle is operating with a stretched out throat, (L = 50 cm and
D = 10 cm). If the inlet stagnation conditions are po1 = 1 MPa and To1 = 1500 K, determine the nozzle exit velocity and mass flow for a back pressure of 30 kPa. The diameter of the nozzle at the exit station is the same as at the inlet station: 30 cm. Treat the exhaust gases as perfect, with γ = 1.4 and R = 0.50 kJ/kg · K. Assume isentropic flow in variable-area sections and Fanno flow in constant-area sections with f = 0.22.

## The Attempt at a Solution

Before going into the actual solution, I'm getting confused with this kind of problems.

If you use the area ratio Aexit/A* = 9, then you get a Mach number at the exit of
Mexit= 3.8017 and a pressure ratio of Pexit/Po = 0.008558. If you use your actual pressures to get the pressure ratio you get Pexit/Po = 30/1000 = 0.03, which is higher than the one before.

So, does this mean that the flow is less than Mexit = 3.8017 at the exit and that there is a shockwave upstream of it?

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

## 1. What is a Conv-Div nozzle and how does it work?

A Conv-Div nozzle is a type of converging-diverging nozzle used in gas dynamics to accelerate the flow of a gas. It consists of two sections: a converging section where the cross-sectional area decreases, and a diverging section where the cross-sectional area increases. This shape allows for the conversion of pressure energy into kinetic energy, resulting in a supersonic flow at the nozzle exit.

## 2. What is the significance of Fanno flow in gas dynamics?

Fanno flow is a type of adiabatic flow in which the gas moves through a constant cross-sectional area duct with friction. It is important in gas dynamics because it allows for the analysis of heat transfer and pressure drop in a flow, which is crucial in the design of efficient propulsion systems, such as jet engines.

## 3. How is Fanno flow different from isentropic flow?

Fanno flow differs from isentropic flow in that it takes into account the effects of friction and heat transfer, while isentropic flow assumes adiabatic and reversible conditions. Fanno flow is also characterized by a constant Mach number, while isentropic flow is characterized by a constant entropy.

## 4. What factors affect the performance of a Conv-Div nozzle?

The performance of a Conv-Div nozzle is affected by various factors such as the inlet pressure, temperature, and Mach number, as well as the nozzle geometry and flow conditions. Friction and heat transfer also play a significant role in the performance of the nozzle.

## 5. How is Fanno flow used in the design of aerospace propulsion systems?

Fanno flow is an important concept in the design of aerospace propulsion systems, particularly in the analysis and optimization of jet engines. Understanding Fanno flow allows engineers to determine the optimal nozzle shape and flow conditions for efficient propulsion, as well as predict the performance of the engine at different operating conditions.

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