The equilibrium conditions for two-dimensional (cylindrical) solid-liquid-fluid systems are developed, taking into account the possibility of constraints imposed on the motion of the contact lines. The solid surface is assumed to be rigid, insoluble, and nonreactive, but it may be rough or heterogeneous or both. The liquid may be volatile; therefore, the frequently used assumption of constant liquid volume is eliminated. A distinction is made between intrinsic and actual contact angles, and the main conclusion is that they may be different when constraints are imposed on the motion of the contact lines. However, the shape of the liquid-fluid interface is shown to be independent of such constraints.