= Momentum correction for lateral mass addition
{title2=$uu_x=-g(h+H)_x+(Q_x/A)(u_a-u)$}
In a sectionally uniform flow, a volume source $Q_x$ per downstream length brings axial velocity $u_a$. <Momentum conservation> gives the displayed source correction, with $A$ the wetted area. The head derivative is $[h+H+u^2/(2g)]_x=Q_x(u_a-u)/(gA)$. Removing fluid at the local velocity preserves the head in this approximation. Adding fluid at rest does not: its acceleration reduces that head. The volume source alone cannot specify the momentum exchange without a velocity assumption.
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