We evaluate the capability of convolutional neural networks (CNNs) to predict a velocity field as it relates to fluid flow around various arrangements of obstacles within a two-dimensional, rectangular channel. We base our network architecture on a gated residual U-Net template and train it on velocity fields generated from computational fluid dynamics (CFD) simulations. We then assess the extent to which our model can accurately and efficiently predict steady flows in terms of velocity fields associated with inlet speeds and obstacle configurations not included in our training set. Real-world applications often require fluid-flow predictions in larger and more complex domains that contain more obstacles than used in model training. To address this problem, we propose a method that decomposes a domain into subdomains for which our model can individually and accurately predict the fluid flow, after which we apply smoothness and continuity constraints to reconstruct velocity fields across the whole of the original domain. This piecewise, semicontinuous approach is computationally more efficient than the alternative, which involves generation of CFD datasets required to retrain the model on larger and more spatially complex domains. We introduce a local orientational vector field entropy (LOVE) metric, which quantifies a decorrelation scale for velocity fields in geometric domains with one or more obstacles, and use it to devise a strategy for decomposing complex domains into weakly interacting subsets suitable for application of our modeling approach. We end with an assessment of error propagation across modeled domains of increasing size.