By G. Hauke
This booklet offers 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 resources for An Introduction to Fluid Mechanics and Transport Phenomena
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 . 1. Stresses over an inclined plane. 2 Prove that the gage pressure cannot be lower than −patm . 3 As shown in the Figure, to experimentally determine the surface tension of a gas/liquid interface, the Du No¨ uy balance measures the force to detach a thin ring from a liquid double meniscus.
10 (Convective ﬂux). 29) S where φ is the property per unit mass. It represents the amount of that property that crosses the surface S per unit time. For example, for the property mass, mass per unit mass is the unity, φ = 1, and the mass ﬂow rate deﬁnition is recovered. The volumetric ﬂux is recovered for φ = 1/ρ. For the ﬂux of internal energy, the internal energy per unit mass is φ = e, where e represents the speciﬁc internal energy. 6. Note that for a positive ρφ, the convective ﬂux is positive for outgoing ﬂow (v · n > 0) and negative, for incoming ﬂow (v · n < 0).
6 (Flow acceleration in a converging nozzle). Let the stationary ﬂuid ﬂow in the nozzle of Fig. 4 with a decreasing cross sectional area between x = 0 and x = L be given by the one-dimensional velocity ﬁeld ⎫ ⎧ ⎫ ⎧ 1x ⎪ ⎨ V0 (1 + ⎨ vx ⎬ ⎪ )⎬ 2L v = vy = 0 ⎪ ⎩ ⎭ ⎪ ⎭ ⎩ vz 0 Calculate the acceleration of the ﬂuid particle. Solution. Since the ﬂuid ﬂow is in the x direction, ay = az = 0. Even though there is no temporal dependency of the ﬂow (∂vx /∂t = 0) the ﬂuid particle is still experiencing acceleration.