By Morton E. Gurtin (Eds.)

ISBN-10: 0123097509

ISBN-13: 9780123097507

This ebook offers an advent to the classical theories of continuum mechanics; particularly, to the theories of excellent, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. those theories are very important, not just simply because they're appropriate to a majority of the issues in continuum mechanics bobbing up in perform, yet simply because they shape an exceptional base upon which possible without difficulty build extra advanced theories of fabric habit. extra, even if awareness is proscribed to the classical theories, the remedy is sleek with a massive emphasis on foundations and constitution

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**Additional resources for An Introduction to Continuum Mechanics**

**Example text**

This chapter will show how to calculate the pressure ﬁeld in ﬂuids at rest and how to calculate the interaction forces between the ﬂuid and submerged surfaces. 1 The Fundamental Equation of Fluid Statics Let us take an arbitrary ﬂuid volume V , with surface S. 3) 0 0 −p where p is the pressure. 1. (a) The net force caused by the pressure depends on the pressure gradient, that is, on spatial variations of pressure. If the pressure is uniform, then it causes no net force over the ﬂuid particle. (b) The fundamental equation of ﬂuid statics can also be derived from a balance of forces over an inﬁnitesimal ﬂuid cube and applying Taylor series expansions to relate the pressure at opposite sides of the cube.

There are three tools employed in the laboratory and in computational ﬂuid dynamics (CFD) to visualize a velocity ﬁeld: streamlines, trajectories and streaklines. They are explained next. 3 (Streamline). The streamline is the line tangent at every point to the velocity vector. 4 Streamlines, Trajectories and Streaklines 21 v v v Fig. 6. The streamline is tangent to the velocity vector at every point. 4 (Trajectory). The trajectory or path is the track followed by a ﬂuid particle. Fig. 7. Trajectory.

Particle velocities at ﬁxed spatial points for a given time instant. represents the velocity of many diﬀerent particles as they travel through the same point x. 5) whose deﬁnition will be given later. 6) where x is the spatial coordinate and t time. 3 (Uniform ﬂow). 4 (Rotating ﬂow). 2, the Eulerian description would not give the velocity of a single particle, but the velocity at each spatial point when diﬀerent particles pass by. Thus, v(x, y, t) = ω −y x In this case, note that the particle acceleration is not simply the temporal derivative (which vanishes), but is given by the substantial derivative, explained below.

### An Introduction to Continuum Mechanics by Morton E. Gurtin (Eds.)

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