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In this article, the buckling of a nanoplate at the bottom of a tank over which the fluid passes with a one-dimensional flow was investigated. Navier-Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Surface effects theory was used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, the effect of fluid viscosity and flow velocity was studied, and also the way surface effects change the critical buckling load of the nanoplates placed in the fluid was investigated. The results reported in this research are very helpful for developing and improving the performance of fluid-coupled nanostructures that have buckling potential.