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danielFiuza

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Hello Everyone,

I am trying to write the intersection of a physical problem in the most compact way.

I am not really familiar with Set Theory notation, but I think it has the answer.

It is about the intersection of two circular areas:

- Area 1: A

- Area 2: B

If I want to write this in Set Theory notation:

Until this point everything is okay. But I have an extra condition

- Extra condition: intersection area always smaller than B (or in other words, the intersection area needs to be contained in B).

(ie. The maximum intersection area can not be larger than B)

How can I write this? Is there any short mathematical symbol for that?

Kind regards,

Daniel

PS: Physically, I am trying to describe a situation as the following one:

' A jet of water of radius R1 impinging against a wall with a hole of radius R2, misaligned from the opening. The water is driven through the intersection area, given that the intersectio area is smaller always that the hole radius R2'

1) For a perfectly aligned jet with the opening:

- If the radius of the jet R1 is smaller than the opening radius R2, all the fluid from the jet goes inside. -> R1

- If the area of the jet R1 is larger than the hole area R2, only the area R2 drives fluids-> R2

2) Then extending this for different misalignments.

I am trying to write the intersection of a physical problem in the most compact way.

I am not really familiar with Set Theory notation, but I think it has the answer.

It is about the intersection of two circular areas:

- Area 1: A

- Area 2: B

If I want to write this in Set Theory notation:

**A_intersection = A ∩ B**Until this point everything is okay. But I have an extra condition

- Extra condition: intersection area always smaller than B (or in other words, the intersection area needs to be contained in B).

**A_intersection = min{A ∩ B, B}**(ie. The maximum intersection area can not be larger than B)

How can I write this? Is there any short mathematical symbol for that?

Kind regards,

Daniel

PS: Physically, I am trying to describe a situation as the following one:

' A jet of water of radius R1 impinging against a wall with a hole of radius R2, misaligned from the opening. The water is driven through the intersection area, given that the intersectio area is smaller always that the hole radius R2'

1) For a perfectly aligned jet with the opening:

- If the radius of the jet R1 is smaller than the opening radius R2, all the fluid from the jet goes inside. -> R1

- If the area of the jet R1 is larger than the hole area R2, only the area R2 drives fluids-> R2

2) Then extending this for different misalignments.

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