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Similarity scaling of a two-dimensional laminar plume

If

b (x) = B x^{- 1/5}

, balancing the momentum flux and transverse viscosity gives

Δ \sim (\frac{μ ^{2}}{ρB})^{1/3} x^{2/5}, U \sim (\frac{B ^{2}}{ρ μ})^{1/3} x^{1/5} .

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