# Calculating Pressure Difference w/ Bernoulli Law for Bay Inlet

In summary, the conversation revolves around determining the size of an extra hole in a bay to reach a specific pressure value. The speaker mentions using the Bernoulli law and the difference between static and dynamic pressure inside and outside of the bay. They also mention not having any specific numbers and potentially having figured out the answer themselves.
I have a container with one inlet and one outlet. I have the area of the inlet, Ai, velocity vi of the air coming in, and mass flow mi (assume a plane with an air inlet to a bay). I don't know anything about the outlet (just that there is one). What I need to do is calculate the size of an extra hole to be made in the bay so that the pressure in the bay reaches a certain value P2, which is lower than the stagnation pressure of the air coming in the bay.

I approached the problem with the Bernoulli law, as I ignore the incompressibility of the air. So I have Pstag in the bay, which is static pressure + dynamic pressure of the air coming in, and outside the bay I have the ambient pressure. Is the pressure difference between the bay inside and outside Pstaginside-Pamb or does the dynamic pressure of the air outside the pressure play a role?

And after that?

I can explain more if it is not clear enough. Thank you in advance for all the tips.

Can you give the numbers too?

There are no numbers, it is just letters.
I will Close the topic, since I Think I might have figured out the answer.
Thank you anyway.

## What is Bernoulli's law?

Bernoulli's law is a principle in fluid dynamics that states that as the velocity of a fluid increases, the pressure of the fluid decreases. This law is based on the conservation of energy and is commonly used to calculate pressure differences in fluid systems.

## How is Bernoulli's law used to calculate pressure difference?

In the context of a bay inlet, Bernoulli's law can be used to calculate the pressure difference between the open bay and the narrow inlet. This is done by equating the potential energy (due to height) of the water in the bay to the kinetic energy (due to velocity) of the water in the inlet.

## What factors affect the pressure difference in a bay inlet?

The pressure difference in a bay inlet is affected by the velocity of the water in the inlet, the height of the water in the bay, and the cross-sectional area of the inlet. Additionally, the density and viscosity of the fluid can also play a role in the pressure difference.

## How is the pressure difference affected by changes in the velocity and height of the water?

As per Bernoulli's law, an increase in the velocity of the water in the inlet will result in a decrease in pressure. Similarly, an increase in the height of the water in the bay will result in an increase in pressure. These changes are directly proportional to the pressure difference.

## What are the limitations of using Bernoulli's law to calculate pressure difference in a bay inlet?

Bernoulli's law assumes that the flow of the fluid is steady, incompressible, and inviscid, which may not always be the case in a real-world bay inlet. Other factors such as turbulence, friction, and boundary effects can also affect the accuracy of the calculated pressure difference.

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