= Elastic jump in a quadratic pressure-area tube
{title2=$q^2/\alpha+\alpha^3/3=\mathrm{constant}$}
An elastic jump is a short transition from a fast, narrow supercritical <collapsible tube flow> to a slower, wider subcritical flow. Neglecting body force and distributed friction across the jump conserves flux and the momentum flux shown above. Distinct upstream and downstream areas therefore obey $\alpha_2^3+\alpha_1\alpha_2^2+\alpha_1^2\alpha_2=3q^2/\alpha_1$. The flux function has its unique minimum at $\alpha=\sqrt q$, so an upstream state below this value has one conjugate state above it. The jump dissipates mechanical energy; it does not conserve a Bernoulli constant.
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