Most infrared small target detection (ISTD) networks focus on building effective neural blocks or feature fusion modules but none describes the ISTD process from the image evolution perspective. The directional evolution of image pixels influenced by convolution, pooling and surrounding pixels is analogous to the movement of fluid elements constrained by surrounding variables ang particles. Inspired by this, we explore a novel research routine by abstracting the movement of pixels in the ISTD process as the flow of fluid in fluid dynamics (FD). Specifically, a new Fluid Dynamics-Inspired Network (FDI-Net) is devised for ISTD. Based on Taylor Central Difference (TCD) method, the TCD feature extraction block is designed, where convolution and Transformer structures are combined for local and global information. The pixel motion equation during the ISTD process is derived from the Navier–Stokes (N-S) equation, constructing a N-S Refinement Module that refines extracted features with edge details. Thus, the TCD feature extraction block determines the primary movement direction of pixels during detection, while the N-S Refinement Module corrects some skewed directions of the pixel stream to supplement the edge details. Experiments on IRSTD-1k and SIRST demonstrate that our method achieves SOTA performance in terms of evaluation metrics.