By G. Hauke
This publication provides the principles of fluid mechanics and delivery phenomena in a concise manner. it's appropriate as an advent to the topic because it comprises many examples, proposed difficulties and a bankruptcy for self-evaluation.
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Additional info for An Introduction to Fluid Mechanics and Transport Phenomena (Fluid Mechanics and Its Applications)
2 (Pressure jump across a bubble. Young-Laplace equation). Calculate the pressure jump across a spherical bubble in a ﬂuid at rest. Solution. Let us cut the bubble into two hemispheres and invoke force equilibrium. In each of the hemispheres, the pressure diﬀerence causes a force equal to (pin − pout )πR2 whereas the surface tension creates a force equal to Problems ¬ cut pout 45 R pin pin σ pout pout·πR² pin·πR² σ⋅2πR Fig. 8. Pressure jump across a bubble immersed in a ﬂuid. 3 summarizes the variables which are employed to calculate the three types of forces of most interest in engineering applications.
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. For example, the braking marks on a road indicate the position that a tire has been occupying while the wheel was being dragged. They depict, therefore, the trajectory of the tire. Another example is the path that a hiker follows to climb the peak Aneto.
C) The streakline that goes by x0 , y0 . 5 The ideal ﬂow around a corner placed at the axis origin is given by ux uy = = ax −ay with a a constant. Determine the streamlines and draw the streamline that goes by the point (1, 1) indicating the ﬂow direction for a > 0. Calculate the substantial derivative. 6 The velocity ﬁeld in an irrotational vortex, like the ones present in cyclones, is given by ux uy = = −Ky/(x2 + y 2 ) Kx/(x2 + y 2 ) Determine the streamlines and draw a few of them. 7 Check if the velocity ﬁeld of the above exercise can be expressed in polar coordinates as ur = 0 uθ = K/r and calculate the streamlines in polar coordinates.
An Introduction to Fluid Mechanics and Transport Phenomena (Fluid Mechanics and Its Applications) by G. Hauke