Flows in ducts, channels, and pipelines are of great interest in fluid mechanics applications especially when flows can be studied in a parametrized geometrical configuration. This Worked Problem considers a 2D potential flow into a Venturi channel and is an example of a design of a parametrized fluidic device as an element of a more complex modular fluidic system (if we adopt a more complex fluid model). In this Worked Problem we illustrate the calculation of pressure and velocity by the Bernoulli Theorem and the curvy geometry parametrization. We also illustrate some features dealing with potential flows (i) an error bound on velocity and pressure (and not only on the potential solution) and (ii) visualization of the flow field (streamline) and pressure contours.
The physical principles illustrated in this Worked Problem deal with ideal fluid mechanics (non-viscous fluids) modelled by potential flows and based on Bernoulli Theorem. Velocity and pressure are influenced by the channel/constriction configuration (i.e., height and length of the throat and radius of curvature of the connection). Gravitational effects or other force fields could be applied.