 Wall-shear and pressure-drop balance in a tube

ID: wall-shear-and-pressure-drop-balance-in-a-tube

An axial force balance on fluid between two remote cross-sections of a cylindrical tube gives

a \int_{x_{1}}^{x_{2}} \int_{0}^{2 π} σ_{r x} (a, θ, x) d θ d x = π a^{2} [p (x_{2}) - p (x_{1})]

when every immersed body between the sections is force-free.

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