(Solved): please solve within 30 mins A gas bubble is placed in a liquid such that its center is kept fixed in ...

A gas bubble is placed in a liquid such that its center is kept fixed inside the liquid pool. Ignore gravity and buoyancy effects. While at a fixed position, the bubble continuously expands in size with time at a fixed rate. One may assume the expansion rate to be slow. The bubble expansion creates a flow in the surrounding liquid. Let \( v_{1} \) and \( v_{2} \) denote the magnitude of the non-zero velocity component in liquid at two radial positions \( r=12.5 \) and \( r=64.2 \), respectively. The radial position is with respect to the center of the bubble. Note that both the radial positions given are in the liquid side.