A physics-informed deep learning framework called hidden fluid mechanics (HFM) is introduced to infer velocity and pressure fields from flow visualizations. HFM encodes the Navier-Stokes equations into neural networks, enabling the extraction of quantitative information from flow data without direct measurements. This approach is robust to low resolution and noise, making it suitable for applications in geophysical, biological, and engineering systems. HFM uses data on concentration fields of passive scalars, such as dye or smoke, to infer velocity and pressure fields. It is demonstrated for external flows, like flow past a cylinder, and internal flows, such as blood flow in aneurysms. The method is agnostic to geometry and boundary conditions, allowing flexible data acquisition and training. HFM can also estimate other flow parameters, such as Reynolds and Péclet numbers. The framework is validated using direct numerical simulations and shows good agreement with reference data. It is applicable to various fields, including biomedical imaging and fluid dynamics, and can be extended to other disciplines like electromagnetics. HFM offers a promising approach for quantifying fluid dynamics in complex systems, with potential clinical applications in vascular disease diagnosis.A physics-informed deep learning framework called hidden fluid mechanics (HFM) is introduced to infer velocity and pressure fields from flow visualizations. HFM encodes the Navier-Stokes equations into neural networks, enabling the extraction of quantitative information from flow data without direct measurements. This approach is robust to low resolution and noise, making it suitable for applications in geophysical, biological, and engineering systems. HFM uses data on concentration fields of passive scalars, such as dye or smoke, to infer velocity and pressure fields. It is demonstrated for external flows, like flow past a cylinder, and internal flows, such as blood flow in aneurysms. The method is agnostic to geometry and boundary conditions, allowing flexible data acquisition and training. HFM can also estimate other flow parameters, such as Reynolds and Péclet numbers. The framework is validated using direct numerical simulations and shows good agreement with reference data. It is applicable to various fields, including biomedical imaging and fluid dynamics, and can be extended to other disciplines like electromagnetics. HFM offers a promising approach for quantifying fluid dynamics in complex systems, with potential clinical applications in vascular disease diagnosis.