Solution verification is a mathematical exercise used to quantify the numerical accuracy of a numerical computation. Hence, it is critical to determine the quality and credibility of the numerical results, this being a necessary step to achieve prediction - computations and results with a quantified and adequate degree of uncertainty that can be confidently used in projects without reference data. The performance of solution verification studies is particularly important for transient flows, as the numerical uncertainty at a given time, t, affects the simulation accuracy at later times, t+\Delta t, in a cumulative, non-linear, and unpredictable way. However, performing precise solution verification exercises can be challenging due to the inherent cost, uncertainty quantification estimation, and numerical and physical interpretation of the results. These are the main reasons for the limited number of solution verification studies in many scientific and engineering areas. Therefore, the VVUQ community is responsible for changing this scenario by teaching, simplifying, and promoting the utilization of solution verification assessments in science and engineering. This study performs comprehensive solution verification studies to assess the numerical accuracy of distinct transient flow simulations. It aims to demonstrate the role of solution verification to understand and trust the numerical results of a simulation. Also, it intends to promote and illustrate that such exercises can be simpler and more relevant than often expected by the CFD community. Three transient flow problems are simulated and analyzed to accomplish these objectives: i) a triple-point problem, ii) the Taylor-Green vortex transitional flow, and iv) the Richtmyer–Meshkov mixing flow developed in LANL's vertical shock tube. The numerical uncertainty of the simulations is estimated using grid refinement studies and the method developed by Eca and Hoekstra [1]. The results confirm the importance of performing solution verification to guarantee the quality of a numerical simulation. As expected, the data show that finer grid resolutions reduce the numerical uncertainty and the variability of the solutions upon grid refinement. They also indicate that the selected verification technique [1] provides reliable estimates of numerical uncertainty for transient flows. Most notably, the results indicate that solution verification can also be critical in identifying and understanding the simu