By G. Hauke
ISBN-10: 1402085362
ISBN-13: 9781402085369
ISBN-10: 1402085370
ISBN-13: 9781402085376
This booklet offers the principles of fluid mechanics and shipping phenomena in a concise means. it really is appropriate as an advent to the topic because it comprises many examples, proposed difficulties and a bankruptcy for self-evaluation.
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Extra info for An Introduction to Fluid Mechanics and Transport Phenomena
Sample text
3. If the flow is stationary, then streamlines, trajectories and streaklines coincide. 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.
As boundary condition we will need the position of a particle at a given time. Then, the variable time t can be eliminated to reach the equation of the trajectory in explicit or implicit form. 9 (Trajectory). For the flow field of the above example, determine the trajectory of the fluid particle that passes through the point (x0 , y0 ), at t = 0. Solution. 4 Streamlines, Trajectories and Streaklines 25 which implies C1 = x0 /e C2 = y0 /e Finally, the trajectory is given in parametric form through the combination of 2 x = e(t+1) −1 x0 y y0 = e(t−1) 2 −1 This is a valid curve in two dimensions.
3. If the flow is stationary, then streamlines, trajectories and streaklines coincide. 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.
An Introduction to Fluid Mechanics and Transport Phenomena by G. Hauke
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