This free course examines the basic kinematics of two-dimensional fluid flows. Section 1 introduces the diﬀerential equations for pathlines and streamlines. Section 2 introduces a scalar ﬁeld, called the stream function, which for an incompressible ﬂuid provides an alternative method of modelling the ﬂow and ﬁnding the streamlines. Sections 2 and 3 derive the stream functions for several simple two-dimensional ﬂow types (the uniform ﬂow, source, doublet and vortex), and suitable combinations of these are used to model more complicated ﬂows. Section 4 introduces the idea of diﬀerentiation following the motion, and Euler’s equation is developed in Section 5.
Course learning outcomes
After studying this course, you should be able to:
derive the pathlines and the streamlines in Cartesian and polar form from a velocity field
derive the stream function from a velocity field
model different flows from a combination of uniform flows, sources, sinks and doublets
use the continuity equation to determine whether an inviscid flow is incompressible
understand how Euler’s equation is derived, what it represents, and use it to find the pressure distribution from a velocity.