The momentum-conserving staggered-grid (MCS) scheme for two-layer shallow flow is revisited here. In the previous contribution, the MCS scheme has been successfully used to simulate various steady interfaces of two-layer shallow flow in channels of varying depth and width. In this contribution, the MCS scheme is extended to accommodate a time-dependent barotropic forcing; the barotropic tidal wave is assumed to be a harmonic function. In the MCS scheme, this barotropic forcing is assessed by applying suitable boundary conditions; and its presence would affect the exchange flow. The average exchange transport was then calculated for the barotropic forces with a range of amplitudes and periods, and the results obtained show good agreement with the analytical rigid-lid theory. Next, the MCS scheme is used to study the exchange flow in the Lombok Strait. Taking into account the geographical conditions of the Lombok Strait, a steady interface was simulated, which turned out to be the case of a maximal exchange flow with two controls at Karangasem Narrows (KN) and Nusa Penida Sill (NPS). Next, due to tidal waves in the period of April-May, the average exchange flow in Lombok Strait is estimated. Our findings agree well with the existing results.