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Bernoulli paper pin cotton reel help please!!!

Hi, can anyone help on this question please?

"We consider an apparatus that consists of a cotton reel, a post card and a drawing pin. The pin is only used to keep the centre of the card at the centre of the hole in the reel. You hold the post card underneath the cotton reel and blow through the hole in the reel from the top. If you blow hard through the hole the card stays up by itself, despite its weight pulling it down and the downward jet of air impinging on it.

a is the radius of the hole in the reel and b is the radius of the entire reel.

U is the speed of the air leaving the system along the postcard.


Show that the speed of the air leaving the central hole is given by W=U*b/a.


Attempt:
Assuming U is the same as the speed of air blown (???)

A1*U = A2*W

W = U*A1/(A2)

W = U*(Pi*b^2)/(Pi*a^2) = U*b^2/a^2

where A1 is the area of the cross section of the reel and A2 is the area of the cross section of the central hole of the reel.

I'm pretty sure my answer is way off so has anyone got any suggestions? Thanks!

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