(3) R is independent of r
Fig shows tube of radius r and bubble blown at its end A of radius R. Air moves inside tube at a speed v and comes to rest inside bubble. The force exerted by air as it comes to rest at B inside bubble.
F = pAv2 ...(1)
A = area of the bubble where air strikes it. The force on area at B due to excess pressure.
\(=(\frac{4S}{R})A\) ...(2)
The bubble is on brink of separating from tube if

From Eqn. (iii) we note, R does not depend on the radius r of the tube.