The law of Newtonian viscosity is derived and the suite of continuum equations controlling the mechanics of fluids presented. Conditions for viscous flow to be considered incompressible are derived and the Navier–Stokes equations defined. Dimensional analysis is described along with the idea of similarity of two flow fields occurring on different spatial and temporal scales. The nature of the boundary and initial conditions for a flow domain are obtained that result in unique solutions of the linear form of the Navier–Stokes equations along with the specific boundary conditions on the flow fields that hold at fluid–solid and fluid–fluid interfaces. Analytical solutions of viscous flow are obtained for a range a specific, and simple, steady-state flow geometries. Time harmonic flow in straight conduits is determined as is the magnetohydrodynamic flow taking place in straight conduits filled with an electrically conducting fluid and a magnetic field applied perpendicularly to the conduit. In the guided exercises, the lubrication approximation is used to obtain approximate solutions for a range of flow scenarios.