# 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.