Relation between force and viscous loss for flow in conduits of variable cross section equation 7.5-6 gives the relation F_f→s = pSE_v between the drag force and viscous loss for straight conduits of arbitrary, but constant, cross section. Here we consider a straight channel whose cross section varies gradually with the downstream distance. We restrict ourselves to axisymmetrical channels, so that the force F_f→s is axially directed. If the cross section and pressure at the entrance are S₁ and p₁, and those at the exit are S₂ and P₂, then prove that the relation analogous to Eq. 7.5-7 is where interpret the results.

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F» = pS„Ë, + p„(S, – S») S2) 1(1 2 S, Sm S2, P;S¡ + P2S2 Pm Si + S2