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Question: consider the problem of a droplet of liquid with density...

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Consider the problem of a droplet of liquid with density ρ and dynamic viscosity μ formed at the bottom tip of a capillary tube of diameter d. The droplet volume (V) grows larger and larger until its weight exceeds the balancing force of surface tension  (unit: N/m), at which point it breaks away from the tip. The flow speed in the tube is u and the gravitational constant is g. Analyze this problem using (1) Buckingham PI theorem and (2) method of scales to determine the correlation between the nondimensional droplet volume and the other key non-dimensional parameters governing the dynamics of the detachment

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