By G. Hauke
This ebook provides the rules of fluid mechanics and shipping phenomena in a concise method. it truly is compatible 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
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. 12. 26) Integrating dQ over the whole surface, the ﬂow rate Q is calculated. 5. Since n is the outward normal vector to the surface, then outgoing ﬂow rates are positive and inward ﬂow rates, negative. 9 (Mean velocity).
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.
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. 3. Summary of variables to calculate forces acting on a ﬂuid. 1 Determine the normal stress acting on the plane of the Figure, where the non-vanishing stress tensor components are: τxx = 35 kgf/cm2 , τyy = −7 kgf/cm2 and τxy = τyx = 2 kgf/cm2 .