Fluid Dynamics: Static Thrust on a Conv-Div Nozzle

• Kushwoho44
In summary, the conversation was about finding the static thrust generated by a convergent-divergent nozzle, with a known stagnation pressure at the inlet. The initial approach of using a control volume and the conservation of momentum equation did not yield the correct answer. The correct approach involved taking into account the forces in the jacket and the acceleration of the fluid, and also considering the borders at the non-horizontal walls of the nozzle and the "diffusor". The thrust is generated by the acceleration of the fluid and affects both the fluid and the rocket, following Newton's 3rd law.
Kushwoho44
Homework Statement

The attempt at a solution

Hi all, I am tasked with finding the static thrust generated by this convergent-divergent nozzle. The stagnation pressure is known the inlet.

Now, personally, I would've thought drawn a control volume around the entire nozzle. And then said:

Net_Thurst = Pressure_inlet *A_inlet -Pressure_outlet*A_outlet.

Now, this does not yield the correct answer. I am not asking for the answer, rather, what is wrong with my understanding of the problem?

Thanks for the help!

Kushwoho44 said:
Net_Thurst = Pressure_inlet *A_inlet -Pressure_outlet*A_outlet.

p0c > pc & Ain > Aout → that would mean the net thrust would push the rocket backwards. You have to take into account the forces in the jacket and the acceleration of the fluid.

Using the control volume like suggested in the hint makes it easier to solve the problem (think about the pressure distribution on the surface of the control volume).

Okay, that makes sense.

I have, to this far, thought of the pressure as driving the fluid flow.

Thus, I would've thought that the conservation of momentum equation applies:

p1A + p1A*V1^2 = p2A + p2A*V2^2

Though, it seems that we need to introduce a 'thrust' component. I don't really understand the physics of this. Where does the thrust component evolve from? And doesn't it violate the conservation of momentum equation.

Kushwoho44 said:
Okay, that makes sense.

I have, to this far, thought of the pressure as driving the fluid flow.

Thus, I would've thought that the conservation of momentum equation applies:

p1A + p1A*V1^2 = p2A + p2A*V2^2

Though, it seems that we need to introduce a 'thrust' component. I don't really understand the physics of this. Where does the thrust component evolve from? And doesn't it violate the conservation of momentum equation.

Sorry, a misunderstanding - maybe a language problem - I thought with thrust you ment the force pushing the rocket forwards.

If you make a FBD of the fluid in the nozzle you also have borders at the non-horizontal walls of the nozzle and the "diffusor", which you need for the sum of the forces in horizontal direction - so your equation is not complete.

The thrust will be generated by the acceleration of the fluid, i.e. a force affected it. The same force, but in the opposite direction accelerates the rocket (Newton's 3rd law). So I think that is what you ment with the equation in your first post, which I obviously misread.

1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) move and interact with each other and with solid objects. It involves understanding the forces that act on fluids, such as pressure and viscosity, and how they affect the behavior of the fluid.

2. What is a conv-div nozzle?

A conv-div nozzle, short for converging-diverging nozzle, is a type of nozzle that is used to accelerate the flow of a fluid, typically a gas, to supersonic speeds. It consists of a converging section that narrows the flow and a diverging section that widens it. This shape allows for efficient conversion of pressure energy into kinetic energy.

3. How does a conv-div nozzle produce thrust?

The converging section of a conv-div nozzle accelerates the flow of fluid, which increases its velocity and decreases its pressure. The diverging section then further accelerates the flow and expands it, resulting in a decrease in pressure and an increase in velocity. According to Newton's third law of motion, for every action there is an equal and opposite reaction. This means that as the fluid is accelerated out of the nozzle, an equal and opposite force (thrust) is produced in the opposite direction.

4. What is static thrust?

Static thrust is the amount of thrust produced by a propulsion system when the aircraft or object is not moving. It is a measure of the maximum amount of force that the system can produce at a standstill.

5. How is static thrust calculated for a conv-div nozzle?

Static thrust for a conv-div nozzle can be calculated using the following formula:
Static Thrust = (Nozzle Exit Pressure - Atmospheric Pressure) x Nozzle Exit Area
This formula takes into account the pressure difference between the nozzle exit and the surrounding atmosphere, as well as the size of the nozzle exit. The larger the pressure difference and the larger the nozzle exit area, the greater the static thrust will be.

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