In engineering practices, especially those involved in the development of complex, new tools or equipment, there is typically insufficient data for pattern recognition or trend analysis. Budget and project timeline constraints often prevent the generation of additional data points from physical tests and high-fidelity computational modeling. Fortunately, small data can be sufficient to solve many engineering challenges when the underlying physics is well understood. Solid physics foundations, such as engineering mechanics and electromagnetics are applicable to many engineering problems. This paper uses one peculiar test failure of a flapper valve in closure tests as an example of analyzing small sample size engineering problems. Flapper valves are a shut-in device that help prevent the uncontrolled release of hydrocarbons in the event of a catastrophic incident in the oil and gas industry. These fail-safe valves, typically incorporate a flapper that is biased to close and is normally held open by an energized control mechanism. When the control mechanism is inactivated, the flapper gets caught in the fluid flow and dynamically closes. The flapper valve open/close testing involves the deformation of components in the flapper valve assembly, interaction between the components (e.g. friction, wear), fluid flow, and fluid structure interaction. Continuum mechanics and fluid dynamics are the fundamental to this case. Hypotheses are formulated based on physical test observations, quantitative data analysis, and physical intuition. These hypotheses are then evaluated and verified using physics-based simulations – including computational fluid dynamics, analytical fluid mechanics analysis, fluid structure interaction analysis and scientific knowledge on erosion and galling. Through this hybrid approach of data analysis and physics-based simulation, the hypotheses were verified, root causes of the failure were identified, the seemingly unexplainable observations in the physical test were explained, and the engineering problem was solved. This demonstrates that engineering problems can be solved with limited data when underlying physics is known.