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**Especi**- Replies: 0

Hello everyone, I am quite struggling with a question from a problem sheet. I have looked information regarding to this but I still have a hard time visualizing this and sketching it. In the question I am asked to describe using a sketch how flow separation from the cylinder may be simulated by the addition of isolated vortices and explain how vortices can be used to complete the flow. In a separate point it asks again on a sketch to show how the separation points affect the drag component of force. Any help with this would be much appreciated as well as any sources that have further information on this topic.

Thank you very much for your assistance.

For some reason it did not show up , thank very much for your help.

I should have seen that this does not hold up for this case , I did come across the Able summation but I assumed that this would require something simpler. Could you possibly indicate a place to start from which I could prove the relation ?

Thank you for your help.

That is correct it should be k , my mistake.

I'll write briefly what I tried for this though I am not sure how correct it will be.

I started spliting the summation

to . I then wrote . I made the notation , substituted that in and tried prove the equality.When I tried to prove it by induction I assumed that the relation is true for

and tried to prove it for . I made use of some of the work I have done above but sadly nothing really came out of it.I'm quite sure I have made several mistakes and if you would be so kind as to point them out that would be great . Even more annoying is that in the places I have looked for explanations mention that this is relatively easy to do so there must be something really obvious that I keep missing.

Thank you again for your help.

**Especi**- Replies: 14

Hello everyone , this is the relation I am given. I am required to prove this either algebraically or with the help of diagram of areas in a subdivided rectangle( I have found this on the internet). I am a bit stuck at the algebraic part, the methods I am trying at the moment to prove this are by induction and by changing the order of the summation on the RHS but I seem to have made a mistake as I have not reached the desired result. Could anyone assist me in solving this ?:)

Thank you very much for your help.

Thank you very much for your help , I cold follow all of the proof now

Thank you very much for your reply , I can follow the proof easily but I sadly still have my question of "when did you know you needed to apply A1/2/3?", or do you apply them while trying to make the result match what we needed to prove ?

I'm sorry I ask so many questions and that some of them do not even make sense

These are the axioms we were given :

1

2

3

for any formulas p,q,r

And the deduction rule Modus Ponens

Again if I missed any brackets I apologize.

That does make sense and it is easier to follow though it does not resemble the solution give by the lecturer.

This is the solution given by him :

Axiom 3

Denote this formula by r

Axiom 1

2,3 Modus Ponens

Denote this by a

Axiom 2

4,5 Modus Ponens

I apologize if I missed any brackets , I tried to upload a picture of the solution but was unsuccessful.

This may sound as a silly question but how did he know when to apply Axioms ?

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