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Amniotic Fluid Volume (AFV) is a crucial fetal biomarker when diagnosing specific fetal abnormalities. This study proposes a novel Convolutional Neural Network (CNN) model, AFNet, for segmenting amniotic fluid (AF) to facilitate clinical AFV evaluation. AFNet was trained and tested on a manually segmented and radiologist-validated AF dataset. AFNet outperforms ResUNet++ by using efficient feature mapping in the attention block and transposing convolutions in the decoder. Our experimental results show that AFNet achieved a mean Intersection over Union (mIoU) of 93.38% on our dataset, thereby outperforming other state-of-the-art models. While AFNet achieves performance scores similar to those of the UNet++ model, it does so while utilizing merely less than half the number of parameters. By creating a detailed AF dataset with an improved CNN architecture, we enable the quantification of AFV in clinical practice, which can aid in diagnosing AF disorders during gestation.