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Toroidal Bubbles

July7

A quite amazing phenomena, toroidal bubbles can be found in many fluids. Technically, During the collapse of a bubble near a surface, a high-speed liquid jet often forms and subsequently impacts upon the opposite bubble surface. The jet impact transforms the originally singly-connected bubble to a toroidal bubble, and generates circulation in the flow around it. (extract from: “Vortex ring modelling of toroidal bubbles”vortex modelling). This movie illustrates, among other examples, an amazing toroidal bubble, created by a humpback whale.

What is a bubble?
blowing bubbles
Check post support for the answer!

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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