An air bubble of radius 0.10 mm is at a depth of 2 m in water. Take atmospheric pressure as 100 kPa, water density as 1000 kg/m³, surface tension as 0.05 N/m and g = 10 m/s². If the pressure inside the bubble is N kPa, find N.
Physics · Properties of solid and fluid · properties of fluid and surface tension
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Question

An air bubble of radius 0.10 mm is at a depth of 2 m in water. Take atmospheric pressure as 100 kPa, water density as 1000 kg/m³, surface tension as 0.05 N/m and g = 10 m/s². If the pressure inside the bubble is N kPa, find N.

Physics · Properties of solid and fluid · properties of fluid and surface tension

G1 Physics · Accepted Answer

Pressure in the surrounding water at depth 2 m is P(out) = P₀+ρgh. Therefore, P(out) = 100 kPa + [1000×10×2] Pa. The hydrostatic contribution is 20000 Pa = 20 kPa. Thus, P(out) = 120 kPa. Radius of the bubble: R = 0.10 mm = 1×10⁻⁴ m. Excess pressure due to surface tension: ΔP = 2S/R = 2×0.05/ [1×10⁻⁴] = 1000 Pa = 1 kPa. Therefore, P(in) = 120+1 = 121 kPa. Hence, N = 121.