By G. Hauke

This publication offers the rules of fluid mechanics and delivery phenomena in a concise means. it really is appropriate 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 angular momentum equation with respect to an axis parallel to z that passes through the point O implies 40 3 Fluid Forces MO = I Ω˙ with MO the external moments around the z axis acting on the cube, I the moment of inertia and Ω˙ the angular acceleration around the z axis. Fig. 4 shows all the components of the stress tensor that contribute to the above moment balance. As in the previous section, the external moment is an inﬁnitesimal of third order while the moment of inertia is an inﬁnitesimal of fourth order.

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. Sometimes it is possible to eliminate t and write the same curve in explicit form, that is, as y(x). Getting t from the ﬁrst equation, t ln xx0 + 1 − 1 = and substituting in the second one, y y0 √ ln =e x x0 +1−2 2 −1 which is the equation of the trajectory in explicit form.

Vx (y) = (ρl − ρv )gδ 2 y 1 − µ δ 2 y δ 2 0 ≤ y ≤ δ(x) where ρl and ρv are the density of the ﬂuid in the liquid and vapor phase, respectively, and µ the liquid density. Find the volumetric ﬂow rate per unit width at any value of x. 9. Film condensation on a vertical plate. 10 Write the expression of the kinetic energy ﬂux across a surface S. 3 Fluid Forces The intensity of transport processes crucially depends on ﬂuid motion. This is one of the salient features of transport phenomena in ﬂuids.