Piston opening

[squeaks]

Can someone explain this to me.
Minimum Required Opening Distance for a Coaxial Piston Valve

Abarrel=pi*r^2
Avalve=2pi*2r*X(open)
Abarrel=Avalve
pi*r^2=4piRX(open)
X(open)=R/4

I understand the area calculation for the barrel, that's just a circle. I don't understand the area for the valve though. What kind of shape is that calculating for? Someone please help.
Thanks

[SpudBlaster15]

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[squeaks]

No, no no. I'm want to know what shape that is that he is getting the formula from. I know I'm calculating how far the valve is opening.

[SpudBlaster15]

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