Elementary Supplements of Fluid Dynamics

Abstract

Hydrodynamic forces, resultants of pressure distributions, have been discussed in connection with the conservation of momentum of control volume. One ingredient of the theory is still missing: the “circulation.” It is basic for the understanding of the most important of these forces, the lift. Its connection to the vortex vector, Eq. (1.50), ie to the rotation, is derived below. The effects of viscosity on Newtonian fluids (for the constitutive relations, see Sec. 4.2.1) are illustrated and the Navier-Stokes equations derived. The essential parameters of similarity solutions and, hence, of model testing in wind tunnels as well as in water channels are discussed. The boundary layer that develops in the flow along a plate is calculated. The irrotational motion of ideal fluids, which enters the solution, eg of the outer flow, is studied by means of potential theory, and a brief account of the singularity method is given. One application is the von Karman vortex trail in the wake behind a blunt body moving through a viscous fluid, with the notion of drag as a byproduct. Moving walls in contact with a fluid pose a nonstationary boundary value problem of interest in earthquake engineering and, eg they function as wave makers in a swimming pool. The effects of compressibility and Mach number are discussed in connection with stationary efflux from a pressure vessel into open air, a problem often encountered in engineering. It is, eg a strong source of noise in connection with the operation of steam power plants. For shock waves formed in supersonic flows, the reader is referred to the special literature on gas dynamics.