By G. Hauke
This e-book offers the principles of fluid mechanics and delivery phenomena in a concise approach. 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 info for An Introduction to Fluid Mechanics and Transport Phenomena
5 The Concept of Flux The ﬂux is a quantity used to measure the amount of a property transported across a surface per unit time. It is one of the most widely used concepts in ﬂuid mechanics. As examples of daily used ﬂuxes, we can cite the volumetric ﬂux and the mass ﬂux. Before proceeding, we need to deﬁne the normal vector to a surface. 6 (Normal vector). The exterior normal n at a point of a closed surface is the outward unit vector orthogonal to the surface at that point (see Fig. 11). Now we can proceed to deﬁning the volumetric and mass ﬂux.
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.
81 m/s2 ). (b) The electromagnetic force f v = ρe E + J × B (c) Inertial forces due to the acceleration of relative systems of reference ˙ × r + Ω × (Ω × r) + 2Ω × v) f m = −(a0 + Ω where a0 is the acceleration of the origin of the relative system; Ω is the ˙ its angular acceleration; r, the angular velocity of the reference system; Ω, position vector and v, the ﬂuid velocity with respect to the relative system of reference. 3 Surface Forces As the name indicates these forces act upon the surface of the ﬂuid particle or upon the surface of the considered ﬂuid domain.
An Introduction to Fluid Mechanics and Transport Phenomena by G. Hauke