The effect of outlet variations on upriver stage can be numerically calculated using the dynamic equation of gradually varied flow. However, in cases where little hydraulic information is known, application of such an equation can be problematic. We present an approximate closed-form solution to this equation, showing that the backwater curve is exponential in character. The solution also gives an explicit solution for this length scale, in this case an e-folding length, over which backwater effects extend, as well as providing an explicit representation of its physical dependencies. This calculation then provides a quick estimate for this length scale, useful when only estimates of regions under the influence of backwater effects is required. We apply our results to assess the flood risk for the country of Bangladesh due to variations in sea level.