The Turkish Straits System (TSS) regulates the transports of water, material and energy between the Black Sea and the Mediterranean Sea. Amidst existing environmental threats to the region surrounding İstanbul, the environmental footprint of the proposed Canal İstanbul project needs to be evaluated through methods of natural science. We take the elementary step to answer the particular problem of coupled strait dynamics by adding the Canal to an existing hydrodynamic model and estimate changes in their common response. Compared to the virtually unmodified exchange flow in the Bosphorus, the flow in the Canal has a weak lower layer current component, contrasted with intense currents at the exit controls at its junction with the Marmara Sea. The net flux through this simplest hypothetical TSS configuration is considerably increased for a given sea level difference across the system. The modified regime is expected to have climatological consequences.