fish swimming prediction model

Critical swimming speed (<i>U</i>_{<em>crit</em>}) is a key factor in assessing the swimming ability of fish in different flow conditions. However, the existing <i>U</i>_{<em>crit</em>} prediction models lack inconsistencies in unit and physical significance. We hypothesized that the thrust provided by fish to resist the force introduced by water flow at a critical swimming state was balanced and that the fish’s gravity was balanced with its buoyancy in water. Through mathematic derivation, we established a new <i>U</i>_{<em>crit</em>} prediction model and evaluated the influences of various factors on <i>U</i>_{<em>crit</em>} results. The new theoretical model considers <i>U</i>_{<em>crit</em>}<i> </i>as a function of the comprehensive coefficient <i>α</i>, gravitational acceleration <i>g</i>, and body length <i>L</i>, and uses a unified expression <i>U</i>_{<em>crit</em>} <i>=α(gL)</i>^{<em> 0.5</em>} to predict the <i>U</i>_{<em>crit</em>} of fish. We have validated the model using previous research data and found that the predictive results of the new theoretical model are more consistent with other empirical models. This new model provides a universal <i>U</i>_{<em>crit</em>} prediction method for various fish species, addressing the issue of inconsistency in the application of experimental results by different researchers, and offering a solid reference for fish stocks protection, fishway construction, and habitat restoration.