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Wind and Airflow
Published in James Jones, Demetri Telionis, Aeroform, 2023
So far, we described in some detail the flow over bodies in two dimensions, which we will call two-dimensional flow. The world of course is not two-dimensional. What we discussed so far is flow over cylindrical bodies that extend very far in the direction normal to the direction of the flow. Let us first define carefully the concept of such bodies. A cylindrical body is defined by straight generators parallel to each other that are touching a closed contour. A circular cylinder is a good example since its surface can be defined by the generators that touch a circle, and are parallel to the axis perpendicular to the plane of the circle (Figure 3.40 left). Another cylindrical body could be a section of a body with a rectangular cross-section, as shown in Figure 3.40 right. A cone is not a cylindrical body because its generators are not parallel to each other
Paleo- and Historical Flood Hydrology
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Victor R. Baker, Tao Liu, Lin Ji
The original formulation of PFH recognized the need to employ hydraulic engineering to quantify the geological interpretations made from the various indicators of paleoflood stages. Initially used to quantify the immense flooding that occurred during the last ice age (Baker, 1973), PFH was found to apply to the analysis of past flooding in the geological period of climates most similar to that of today, essentially equivalent to the past 10,000 years. Paleoflood stages were converted to discharges using simple hydraulic formulae, such as the Manning equation and slope-area methods, which relate the discharge of paleofloods to channel cross-sectional areas, flow depths, energy slopes, and measures of flow resistance. Starting in the 1980s computer flow models began to be employed in the PFH research to perform hydraulic step-backwater calculations in one dimension along the thread of main channel ways (e.g., Ely and Baker, 1985; Baker and Pickup, 1987). Multiple cross-sections are used along a channel reach that is long enough to achieve an energy-balanced calculation of multiple water-surface elevations for various potential paleoflood discharges. By matching the flood paleostage evidence to the calculated water-surface profiles paleodischarges are estimated. More recently further increases in computational capability have enabled the use of two-dimensional flow models. These are appropriate for the more complex channel geometries that pose problems for accurate representation in the one-dimensional models.
Continuity Equation
Published in Ahlam I. Shalaby, Fluid Mechanics for Civil and Environmental Engineers, 2018
A typical fluid flow involves a three-dimensional geometry; thus, the velocity may vary in all three dimensions (x, y, z) as: v(x, y, z). Additionally, if the velocity of the flow varies with time, t then the velocity would be: v(x, y, z, t). However, if the variation of velocity in certain directions is small relative to the variation in the other directions, it can be ignored with negligible error. Thus, in such a case, the flow can be modeled conveniently as a one- or two-dimensional flow, which is a lot easier to analyze. Therefore, the simplifying assumption of spatial dimensionality, from a three-dimensional flow to that of a one- or two-dimensional flow, is typically made in most engineering problems without sacrificing any required accuracy. It may be noted that if a one-dimensional flow is assumed, the flow may be alternatively defined along a streamline, s (defined in Section 3.4). Furthermore, the assumption regarding the spatial dimensionality of the flow is discussed in detail in a section below.
Magnetic dipole dynamics on Reiner–Philippoff boundary layer flow
Published in Numerical Heat Transfer, Part A: Applications, 2023
Yusuf O. Tijani, Adeshina T. Adeosun, Hammed A. Ogunseye, Hari Niranjan
The two dimensional flow of Reiner–Philippoff fluid over a stretching sheet in the existence of inhomogeneous applied magnetic field (magnetic dipole) and thermal radiation is the subject of this model. The fluid and its medium are not electrically conducting. The magnetic dipole with y-axis as its center and c be the distance from the center of the magnetic dipole to the x-axis. The temperature of the sheet is represented by Tw which is smaller compared to the ambient temperature of the sheet indicated by see Figure 2. The flow equations in regard to mass, momentum and energy conservation are similar to those in Na [1], Ahmed et al. [13] and Muhammad et al. [25].
Electrically Conducting Fluid Flow and Electric Potential in a Square Cavity Subjected to a Point Magnetic Source
Published in International Journal of Computational Fluid Dynamics, 2022
Pelin Senel, Munevver Tezer-Sezgin
The pressure equation is also obtained from differentiating Equations (16) and (17) with respect to x and y, respectively. Summation of the resultant equations and using the continuity equation, one has the pressure equation To visualise the planar flow in the cavity define the stream function for the two-dimensional flow as which satisfies the continuity equation. Then, the stream function equation is The non-dimensional forms of the magnetic field components and the magnetic field strength are with .
Influence of dilatancy on shear band characteristics of granular backfills
Published in European Journal of Environmental and Civil Engineering, 2021
Behzad Soltanbeigi, Adlen Altunbas, Ozer Cinicioglu
This study attempts to investigate strain localisation phenomenon in granular backfills. However, identification of localisation in element tests is troublesome as it is known that localised deformations do not always concentrate near the boundaries of granular bodies. Therefore, conventional measurement tools, which are capable of measuring dislocations at the boundaries, will not suffice to give a clear picture of interior deformations that control the overall response. Among diverse groups of measuring techniques, an optical method called PIV attracted wide recognition among researchers (Leśniewska, Niedostatkiewicz, & Tejchman, 2012; Muir Wood & Lesniewska, 2011; Niedostatkiewicz et al., 2011; Take, Bolton, & White, 2003; Zhuang, Nakata, & Lee, 2013). PIV is an indirect optical method originally used for the measurement of two-dimensional flow velocity in fluids (Adrian, 1991). It is a digital image-based surface displacement measurement technique that uses the first image as a reference and then searches for possible deformations at subsequent images (Take et al., 2003). Considering the applicability of this nonintrusive measurement technique to model tests under plane–strain conditions, PIV is adopted in this study for investigating the evolution of shear bands in sheared granular media.