By comparing the two techniques to determine the critical point on the relationship curve between wetted perimeter and discharge for the estimates of the minimum ecological instream flow requirement (MEIFR), the uncertainty of the wetted perimeter method is analyzed. Under the assumptions of the triangular cross section channel and the uniform stable flow, an analytical solution of MEIFR is deduced. It is clearly shown that the results of MEIFR based on curvature technique (corresponding to the maximum curvature) and slope technique (slope being 1) are significantly different. It is found that the slope of the transition point with the maximum curvature is 0.39 and the MEIFR varies prominently with the variation of the slope threshold. This notes that if a certain value of the slope threshold is not available in the slope technique, the results of MEIFR via curvature technique by the wetted perimeter method are more certain. By applying the analytical solution of MEIFR in the rivers of Western Route South-to-North Water Transfer Project in China, it shows that the MEIFR value via curvature technique is 2.5%-23.7% of the multi-year average annual discharge, while that for slope technique is 11%-105.7%. This paper starts the research from the simple triangular cross section channels. More general conclusions rely on the more detailed research on various sections.