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The flux average for a translating lubrication gap follows by integrating the pressure gradient between the endpoints:If $2Q$ were smaller than the minimum height, the integrand would be strictly positive everywhere, contradicting zero total pressure change. If it were larger than the maximum, the integrand would be strictly negative. ThereforeEquivalently,is a weighted average of the height with strictly positive weight ${\hat{h}}^{-3}$. This also identifies the constant flux uniquely.

For a symmetric gap $h(x)=\sqrt{1+x^2}$ on $[-1,1]$, unit lower-wall speed and equal zero gauge pressures at the ends, the flux average for a translating lubrication gap gives $Q=\pi /(4\sqrt{2})$. Integrating $p_x=6(h-2Q)/h^3$ gives the displayed odd pressure. It has a positive maximum at $x=-\sqrt{{\pi }^2/8-1}$ and a negative minimum at the opposite point. The converging and diverging portions of a symmetric gap therefore have opposite pressure lobes even though the geometry itself is even: the directed wall motion breaks reflection symmetry of the flow.