Category: Fluid Mechanics

The cross section of a pipe is most frequently circular, but other shapes may be encountered. For example, the rectangular cross section of many domestic hotair heating ducts should be apparent to most people living in the United States. The situation for a horizontal duct is illustrated in Fig. 3.14; the cross-sectional shape is quite arbitrary—it doesn’t have…

Newton’s law of viscosity relating the shear stress to the velocity gradient has a ready interpretation based on momentum transport resulting from molecular diffusion. As an introduction, consider first the situation in Fig. 3.7, which shows a plan of two trolleys on frictionless tracks. Fig. 3.7 Lateral transport of momentum between two trolleys on frictionless tracks.…

3.1. Introduction In chemical engineering process operations, fluids are typically conveyed through pipelines, in which viscous action—with or without accompanying turbulence—leads to “friction” and a dissipation of useful work into heat. Such friction is normally overcome either by means of the pressure generated by a pump or by the fluid falling under gravity from a…

Momentum. The general conservation law also applies to momentum M, which for a mass M moving with a velocity u, as in Fig. 2.13(a), is defined by: Fig. 2.13 (a) Momentum as a product of mass and velocity; (b) velocity components in the three coordinate directions. Strangely, there is no universally accepted symbol for momentum. In this text and elsewhere, the…

2.1. General Conservation Laws The study of fluid mechanics is based, to a large extent, on the conservation laws of three extensive quantities: 1. Mass—usually total, but sometimes of one or more individual chemical species. 2. Total energy—the sum of internal, kinetic, potential, and pressure energy. 3. Momentum, both linear and angular. For a system viewed as a…

Finally, consider the shape of the free surface for the situation shown in Fig. 1.20(a), in which a cylindrical container, partly filled with liquid, is rotated with an angular velocity ω—that is, at N = ω/2π revolutions per unit time. The analysis has applications in fuel tanks of spinning rockets, centrifugal filters, and liquid mirrors. Fig. 1.20 Pressure…

Variation of pressure with elevation. Here, we investigate how the pressure in a stationary fluid varies with elevation z. The result is useful because it can answer questions such as “What is the pressure at the summit of Mt. Annapurna?” or “What forces are exerted on the walls of an oil storage tank?” Consider a hypothetical differential…

Mass, weight, and force. The mass M of an object is a measure of the amount of matter it contains and will be constant, since it depends on the number of constituent molecules and their masses. On the other hand, the weight w of the object is the gravitational force on it, and is equal to Mg, where g is the local gravitational…

There are three physical properties of fluids that are particularly important: density, viscosity, and surface tension. Each of these will be defined and viewed briefly in terms of molecular concepts, and their dimensions will be examined in terms of mass, length, and time (M, L, and T). The physical properties depend primarily on the particular…

1.1. Fluid Mechanics in Chemical Engineering Aknowledge of fluid mechanics is essential for the chemical engineer because the majority of chemical-processing operations are conducted either partly or totally in the fluid phase. Examples of such operations abound in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries. There are two principal…