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

By G. Hauke

This publication provides the principles of fluid mechanics and shipping phenomena in a concise manner. it truly is compatible as an creation to the topic because it comprises many examples, proposed difficulties and a bankruptcy for self-evaluation.

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Below, it is explained how streamlines, trajectories and streaklines are calculated. As an example, we will take the unsteady (non-stationary) twodimensional flow field given by u = 2x(t + 1) and v = 2y(t − 1). v v dl v Fig. 10. Streamline and differential of length. 1 Calculation of Streamlines Let dl be a differential of length along a streamline. 4. In polar coordinates, the infinitesimal lengths along the r and θ axes are dr and rdθ, respectively. 21) dr rdθ with u and v the velocity components in the r and θ directions, respectively.

2 Manometry A manometer is a device to measure the gage pressure. A typical manometer is depicted in Fig. 3. In order to derive the expression that gives the pressure in a manometer, the hydrostatic equation should be applied within the same fluid, from the point of measurement to the point of reference pressure. For the manometer of Fig. 1. 20). Solution. Within the same fluid, points at the same height have the same pressure. 16) within the columns of fluid a and b, p1 = p0 + ρa g(z0 − z1 ) p2 = patm + ρb g(z3 − z2 ) Combining the three above equations the desired result is attained.

The depth h as a coordinate axis. The Hydrostatic Pressure as a Function of Depth Frequently, instead of the vertical axis z, the depth with respect to the free surface h is employed (see Fig. 2). 19) Consequences. (a) The pressure at a point in a liquid depends on the depth of that point with respect to the free surface. (b) The pressure increases linearly with depth. (c) The pressure in a liquid does not depend on the shape of the container. 2 Applications 51 Patm ρa 0 3 1 2 z ρb Fig. 3. Manometer.

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