Read e-book online An Introduction to Fluid Mechanics and Transport Phenomena PDF

By G. Hauke

ISBN-10: 1402085362

ISBN-13: 9781402085369

ISBN-10: 1402085370

ISBN-13: 9781402085376

This e-book provides the rules of fluid mechanics and shipping phenomena in a concise method. it's compatible as an advent to the topic because it comprises many examples, proposed difficulties and a bankruptcy for self-evaluation.

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Extra info for An Introduction to Fluid Mechanics and Transport Phenomena

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.

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An Introduction to Fluid Mechanics and Transport Phenomena by G. Hauke

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