Pressure-driven power generation is one of a simple, green, and promising energy sources. Owing to the overlapping of the electric double layer inside, nanochannel is capable of providing a platform for this power generation approach. Unfortunately, relevant studies, either experimental or theoretical, are very limited in the literature. Here, we present for the first time a comprehensively theoretical study on the pressure-driven energy conversion in a conical nanochannel having carboxyl functional groups, focusing on the influence of its tip size and the solution pH. An anomalous dependence of both the power generated and the efficiency on the latter are observed. Although the charge density on the nanochannel surface increases monotonically with increasing pH, both the power generated and the efficiency exhibit a local maximum as pH varies. This is because the streaming potential has a local maximum as pH varies. Power density (power generated/tip end cross sectional area) also shows a local maximum as the tip radius varies, and the radius at which the local maximum occurs decreases with increasing bulk salt concentration. In addition to explain successfully the behavior reported in the literature, our study also provides desirable and necessary information for designing relevant devices. (C) 2019 Elsevier Inc. All rights reserved.