Fluid Mechanics 8.3 - Streamfunction Concept

This segment covers the streamfunction concept, how streamfunction relates to streamlines, and obtaining the volumetric flow rate between two streamlines. Table of Contents: 7:23 - Streamline and Streamfunction relation 8:53 - Volumetric flow rate between two streamlines Module 8: Conservation of Mass in Differential Form: As discussed in module 5, conservation of mass requires that the mass, M, of a system remain constant as the system moves through the flow field. However, if we consider a differential fluid element with sides dx, dy, and dz, the differential version of the fluid elements becomes the continuity equation, and it is valid for steady or unsteady flow as well as a compressible or incompressible flow. A streamfunction can be used to relate velocities, u and v, in two-dimensional flow. Student Learning Outcomes: After completing this module, you should be able to: 1) Apply the continuity equation to physical flows to find the velocity gradients 2) Determine whether a flow is physically possible by using the continuity equation 3) Find velocities given a stream function or find a stream function, streamlines, and volumetric flow rate, given the velocity profiles 4) Check whether the flow is irrotational or rotational 5) If irrotational, find the corresponding velocity potential This material is based upon work supported by the National Science Foundation under Grant No. 2019664. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.