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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
As a boundary layer develops, it starts in a smooth, or laminar, state. Downstream, it transforms into a turbulent state, where the flow is irregular and contains eddies. Various physical conditions, such as wall or surface roughness or upstream turbulence, will affect the speed of this transition. In smooth-walled pipes, laminar flow occurs for Reynolds numbers (Re) of less than 2000, with fully developed turbulence for Re greater than 4000. The Reynolds number is a dimensionless number developed from dynamic similarity principles that represents the ratio of the magnitudes of the inertia forces to the friction forces in the fluid. Re= inertia force friction force
Local surface aeration at hydraulic structures
Published in Ian R. Wood, Air Entrainment in Free-Surface Flows, 2018
Helmut Kobus, Hans-Peter Koschitzky
Studies of local air entrainment and detrainment involve mostly experimental investigations on small scale models. Obviously, perfect dynamic similarity cannot be achieved; the modelling parameters as derived from dimensional analysis cannot be satisfied simultaneously in a small scale model using the same fluids, i.e. air and water. It is often argued that the bubble sizes generated by free-surface aeration always exhibit about the same absolute size and hence violate in a small scale model both geometric similarity (ratio bubble size to boundary scale) and dynamic similarity (ratio of bubble rising velocity to water velocity).
Analysis of fiber movement and deformation in a rotor unit by experiment
Published in The Journal of The Textile Institute, 2022
The diameter of rotors ranges 30–50 mm in the industrial field, but it is not large enough to shoot. So, the rotor cup is doubled to 88 mm in the experiment. According to the similarity theory of fluid mechanics, the internal shape should be consistent with the actual shape of the rotor, the same sliding surface angle, the same rotor groove type to ensure geometric similarity, the kinematic similarity is satisfied since both models rotate around a fixed axis. The dynamic similarity can be guaranteed by keeping the same Reynolds number which is defined as where v is the average linear velocity of the rotating flow field; l is the effective radius of the rotating flow field. In the case of the same dynamic viscosity and density, in order to ensure the same Reynolds number (about 106), the rotation speed in the rotor is set to half of the actual rotation speed.
Experimental and numerical studies on orifice spillway aerator of Bunji Dam
Published in Journal of the Chinese Institute of Engineers, 2020
Muhammad Kaleem Sarwar, Ijaz Ahmad, Zulfiqar Ali Chaudary, Habib-Ur-Rehman Mughal
Spillway flows were modeled using similarity equations based on Froudian relationships, as they represent the gravitational and inertial effects which are significant for free surface flow (Wang and Chanson 2016; Saneie, Kazemi, and Moghaddam 2016). The true dynamic similarity for geometrically similar models cannot be attained because it is not possible to fulfill Froude and Reynolds similarities simultaneously (Rafi et al. 2012). Furthermore, the scale effects for two-phase flow and air entrainment coefficient become insignificant if We (Weber number) >110 and Re (Reynold number) >1 × 105 (Pfister and Chanson 2014). These limits were considered in this study to minimize scale effects.
Particle dispersion and deposition in displacement ventilation systems combined with floor heating
Published in Science and Technology for the Built Environment, 2020
Yunus Emre Cetin, Mete Avci, Orhan Aydin
Reduced scale models can provide more economic and optional experimental studies compared to full scale investigations. To sustain the similar flow characteristics in both scale, geometric, kinematic and dynamic similarities must be satisfied (Etheridge and Sandberg 1996; Awbi 2003). Geometric similarity is easily ensured if the all dimensions of the real room is equally scaled down by the same scale factor. Identical velocity directions and equal velocity scale ratios of the same points of the both scales guarantee the kinematic similarity, and dynamic similarity is attained if the ratios of all the forces causing the fluid motion are equal.