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MMLU-Pro / 12032 / Using the method of dimensional analysis, deduce a relationship between the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Using the method of dimensional analysis, deduce a relationship between the bubble diameter and the properties of water when bubbles are formed by a gas ejecting out from a small orifice underneath the water surface.

category

engineering

options

  1. D = f[(\sigma) / (g_c\rho d^2), {\mu^2 / (g\rho d^3)}]
  2. D = f[(\mu\sigma) / (g_c\rho d), {g / (\rho^2d^3)}]
  3. D = f[(g_c\sigma) / (g ho d^2), {\mu^2 / (g ho^2d^3)}]
  4. D = f[(g_c\sigma) / (\mu d^2), {g / (\rho^2d^3)}]
  5. D = f[(g_c\sigma) / (g ho d^2), {\mu^2 / (g ho^2d^3)}] / d
  6. (D^2 / d) = f[{(g_c\sigma) / (\rho d^3)}, {\mu / (g\rho^2d^2)}]
  7. D = f[(\rho\sigma) / (g_c d^2), {\mu / (g\sigma d)}]
  8. (D / d) = f[{(g_c\sigma) / (g hod^2)}, {\mu^2 / (g ho^2d^3)}]
  9. D = d^2 * f[(g_c\sigma) / (\rho d), {\mu^2 / (g_c\rho^2)}]

src

stemez-TransportPhenomena

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Source and history

upstream_id / Original problem ID
12032
task_id
6e454f4d-60ba-55ab-82d1-2b0907a1da96
task_key
default--test--12032
task_revision_id
1
config / split
default / test

Official source

initial import