Solve Bernoulli's Equation for Pressure at Throat of Converging-Diverging Nozzle

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In summary, the conversation discusses a question about determining the pressure at the throat of a converging diverging nozzle. The problem includes information such as the pressure at the inlet, inlet and throat diameters, and water density. The conversation also mentions the use of Bernoulli's equation and Torricelli's Law to solve the problem, as well as the importance of studying the material thoroughly before attempting the question.
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MuzMond
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Homework Statement


Was flicking through a textbook and decided to give a question a try.

Flow through a converging diverging nozzle, determine pressure at throat picture attached.
Pressure at inlet = 50cm head, 4905PA
inlet dia = 2cm
throat dia = 1 cm
density of water = 1000kg/m^3
[/B]

Homework Equations


Bernoullis equation[/B]

The Attempt at a Solution


Cant find pressure at throat as both velocities are unknown,
Area of inlet = 3.142cm^2
area of throat = 0.785 cm^2.
We could make the outlet atmospheric, answer was around 7mH2o head.[/B]
 

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  • #2
MuzMond said:
1. Homework Statement
Was flicking through a textbook and decided to give a question a try.

This is generally not a good idea, unless you have studied all the material covered up to that point thoroughly.

Flow through a converging diverging nozzle, determine pressure at throat picture attached.
Pressure at inlet = 50cm head, 4905PA
inlet dia = 2cm
throat dia = 1 cm
density of water = 1000kg/m^3
2. Homework Equations
Bernoullis equation3. The Attempt at a Solution
Cant find pressure at throat as both velocities are unknown,
Area of inlet = 3.142cm^2
area of throat = 0.785 cm^2.
We could make the outlet atmospheric, answer was around 7mH2o head.

What you also need here, to find the inlet velocity, is known as Torricelli's Law:

https://en.wikipedia.org/wiki/Torricelli's_law

That's why you must study the figures included with the problem.
 

1. What is Bernoulli's equation and how does it relate to nozzle design?

Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between pressure, velocity, and elevation of a fluid. In the context of nozzle design, Bernoulli's equation is used to analyze the flow of fluid through a converging-diverging nozzle and determine the pressure at the throat of the nozzle.

2. What is a converging-diverging nozzle and how does it work?

A converging-diverging nozzle is a type of nozzle that has a converging section followed by a diverging section. This design allows for a supersonic flow of fluid through the nozzle. The converging section increases the velocity of the fluid, while the diverging section decreases the velocity and increases the pressure, resulting in a supersonic flow.

3. How is the pressure at the throat of a converging-diverging nozzle calculated using Bernoulli's equation?

The pressure at the throat of a converging-diverging nozzle can be calculated using the following equation:
Pt = P1 * (1 + (gamma - 1)/2 * M12)gamma/(gamma-1)
Where Pt is the pressure at the throat, P1 is the inlet pressure, gamma is the specific heat ratio, and M1 is the Mach number at the inlet.

4. What factors affect the pressure at the throat of a converging-diverging nozzle?

The pressure at the throat of a converging-diverging nozzle is affected by several factors, including the inlet pressure, the specific heat ratio of the fluid, and the Mach number at the inlet. The shape and size of the nozzle also play a role in determining the pressure at the throat.

5. How can the pressure at the throat of a converging-diverging nozzle be optimized?

The pressure at the throat of a converging-diverging nozzle can be optimized by adjusting the shape and size of the nozzle, as well as the inlet pressure and the specific heat ratio of the fluid. A higher inlet pressure and a larger specific heat ratio will result in a higher pressure at the throat. Additionally, the nozzle can be designed to have a longer or shorter diverging section to further optimize the pressure at the throat.

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