What is the magnitude of the pressure differential across the boundary of a spherical liquid droplet _______________?
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Answer: D. p = 2T/r
Explanation
Surface tension at a curved liquid interface creates an inward radial pressure differential. For a spherical liquid droplet, the Young-Laplace equation accounts for surface tension across two orthogonal planes. Solving the spherical droplet equilibrium yields the exact pressure difference formula equal to two T over r. The Young-Laplace equation relates internal pressure, surface tension, and droplet radius of curvature. Smaller droplets experience much higher internal pressures due to inverse proportionality with radius. Spherical droplets maintain uniform internal pressure owing to complete geometric symmetry.
Meteorologists study droplet pressure differentials when analyzing cloud formation and rain particle growth. Spray nozzle design in agriculture and coating industries relies on droplet pressure calculations. Emulsion stability in chemical engineering depends on balancing interfacial tension and internal pressures. Option A uses incorrect multiplication of tension and radius, resulting in improper dimensional units. Option B represents the pressure differential for a cylindrical jet rather than a spherical droplet. Option C halves the pressure value incorrectly, missing the factor of two derived from spherical geometry.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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