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

By G. Hauke

This e-book provides the principles of fluid mechanics and delivery phenomena in a concise approach. 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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Example text

The latter represents the transport of a property in the fluid due to its macroscopic motion. 1. In the last term of the above equation, the index j is repeated and, using the Einstein summation convention on repeated indices, the sum symbol can be eliminated (see Appendix D). 15) If the substantial derivative is applied to the velocity vector, we obtain the acceleration of the fluid particle. 1 (Stationary or steady flow). , ∂· = 0. ∂t 18 2 Elementary Fluid Kinematics ρ y v1 H Sp S2 x h S1 L Fig.

Trajectory. The fluid particle follows the plotted line. 5 (Streakline). The streakline is the geometric place occupied by fluid particles that have passed by the same point at previous times. Fig. 8. The plume of a chimney is a streakline. Streamlines indicate the velocity direction. They can be visualized by implanting little flags inside the fluid and observing their orientation. The streamlines can be obtained by drawing lines tangent to the flags. They are a rather mathematical object. The trajectory is the path followed by a fluid particle.

1. Hydrostatics. Axes. 1 Hydrostatics Hydrostatics is the part of fluid statics dedicated to incompressible fluids. Let us calculate the pressure distribution in a liquid at rest. Take the coordinate axes of Fig. 1, where z is the upward vertical axis. 10) ⎩ ⎭ −ρg where the density ρ is constant. 11) = 0 ⎪ ∂y ⎪ ⎪ ⎪ ⎪ ⎩ ∂p = −ρg ∂z from where the pressure distribution p(x, y, z) can be calculated. 2. The pressure difference between two points inside a liquid depends only on the height difference between the points.

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