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.

F = pS, + p(S, S) S2) 1(1 2 S, Sm S2, P;S + P2S2 Pm Si + S2