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.