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Pressure in radially symmetric annular potential flow

If the pressure at

r = b (t)

is

p_{\infty}

, the Unsteady Bernoulli equation gives

p (a, t) - p_{\infty} = ρ [\frac{d}{d t} (a \overset{a}{˙}) lo g \frac{b}{a} - \frac{( a a ˙ ) ^{2}}{2} (\frac{1}{a ^{2}} - \frac{1}{b ^{2}})] .

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- Small oscillation of a planar gas bubble in an annular liquid Pressure in radially symmetric annular potential flow 28

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