$6.(20\%)$ Attach a straw to a cardboard disk with a hole at center using tape or glue, and fold the corners of a piece paper upward so that the paper cups the cardboard disk with radius R as below. Attempt to lift the folded paper off a flat surface by blowing air or sucking air through the straw. This is same as the mechanism to lift the computer chips without touching it$.$

$($a$)(5\%)$ Determine if the blowing or suction is more effective in lifting the paper.

$($b$)(15\%)$ As shown in the picture below, the pressure below the paper is atmosphere pressure $p_r,$ and the pressure above the paper can be estimated by Bermoulli equation. Please determine the lifting force of the paper within the range of the cardboard with Radius $R,$ gap $h,$ and volume flow rate $Q$ from the straw $($Hint: when you solve your integration, please ignore the contributions as $r$