  In this paper, we study the initial-boundary value problem of one-dimensional
isentropic compressible Euler equations with the source term
$\beta\rho|u|^{\alpha}u$. By means of wave decomposition and the uniform
a-priori estimates, we prove the global existence of smooth solutions under
small perturbations around the supersonic Fanno flow. Then, by Gronwall's
inequality, we get the smooth solution is time-periodic.
