By G. Hauke
This booklet offers the rules of fluid mechanics and shipping phenomena in a concise means. it really is appropriate as an advent to the topic because it includes many examples, proposed difficulties and a bankruptcy for self-evaluation.
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Additional resources for An Introduction to Fluid Mechanics and Transport Phenomena
They depict, therefore, the trajectory of the tire. Another example is the path that a hiker follows to climb the peak Aneto. The same applies to ﬂuid particles. 22 2 Elementary Fluid Kinematics t0 t1 t2 t3 Fig. 9. Streakline (solid line) and trajectories (dashed lines) of the smoke particles (dots) from a chimney at successive time instants. Finally, streaklines are the easiest element to be seen in nature or an experimental rig. Examples include a plume in the sky, the spilled colored contaminant in a river or the injected smoke in an aerodynamic tunnel.
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. 8 (Streamline). Calculate the streamlines for the unsteady, twodimensional ﬂow ﬁeld given by, u v = 2x(t + 1) = 2y(t − 1) Particularize for the case in which the streamline passes through the point (x0 , y0 ) at all times. Solution. 2 Calculation of Trajectories A trajectory is the path followed by a ﬂuid particle.
11). Now we can proceed to deﬁning the volumetric and mass ﬂux. 7 (Volumetric ﬂow rate). The volumetric ﬂow rate Q is the volume of ﬂuid that crosses the surface per unit time, v · n dS Q= S Its dimensions are [Q] = L3 T−1 and its units in the SI, m3 /s. 5 The Concept of Flux 27 n Fig. 11. Exterior normal to the surface of a volume. 8 (Mass ﬂow rate). 24) S Its dimensions are [m] ˙ = MT−1 and its SI units, kg/s. n θ dA n v v S Fig. 12. Flux across a surface. 23), let us take the diﬀerential of area dA over the surface S of Fig.
An Introduction to Fluid Mechanics and Transport Phenomena by G. Hauke