Getting access to the state of turbulent flow from limited sensor measurements in engineering systems is a major challenge. Development of technologies to accurately estimate the state of the flow is now possible with the use of machine learning. We present a supervised machine learning technique to reconstruct turbulent vortical structures in a pump sump from sparse surface pressure measurements. For the current flow reconstruction technique, a combination of multilayer perceptron and three-dimensional convolutional neural network is utilized. This technique provides accurate flow estimation from only a few sensor measurements, identifying the presence of adverse vortices. The dependence of the model performance on the amount of training data, the number of input sensors, and the noise levels are investigated. The present machine learning-based flow estimator supports safe operations of pumps and can be extended to a broad range of applications for industrial fluid-based systems.