The lower end of a capillary tube of diameter $2.00 ext{ mm}$ is dipped $8.00 ext{ cm}$ below the

Question

The lower end of a capillary tube of diameter $2.00	ext{ mm}$ is dipped $8.00	ext{ cm}$ below the surface of water. What is the absolute pressure required in the tube to blow a hemispherical bubble at its end in water? (Surface tension of water = $7.3 	imes 10^{-2}	ext{ N/m}$, density of water = $1000	ext{ kg/m}^3$, $1	ext{ atm} = 1.01 	imes 10^5	ext{ Pa}$)

Professor PC Thomas Classes · Answer

The pressure must overcome hydrostatic pressure and the bubble's excess pressure. $P = P_{atm} + h ho g + \frac{2S}{r} = 1.01 	imes 10^5 + (0.08 	imes 1000 	imes 9.8) + \frac{2 	imes 7.3 	imes 10^{-2}}{1 	imes 10^{-3}} = 101000 + 784 + 146 = 101930	ext{ Pa} \approx 1.02 	imes 10^5	ext{ Pa}$.