The tidal range in alluvial estuaries is influenced by river discharge. In the upper part of the estuary, where the river's cross-sectional area is similar to that of the estuary, the river discharge affects tidal damping. This is because the fresh water discharge can be more significant than the tidal flow, impacting the tidal range. The river discharge primarily influences tidal damping through friction, especially at a critical point where the estuary transitions to a more riverine character. This study expands on an existing equation to include the effect of river discharge and shows that it can have a considerable impact on tidal damping in the upper reach of the estuary.