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Water Resources Engineering
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
Natural channel sections are generally very irregular in shape, whereas artificial channels are usually designed with sections of regular geometry shapes. The trapezoid is a commonly used shape; the rectangle and triangle are special case of trapezoid. Since the rectangle has vertical sides, it is commonly used for channels built of stable materials, such as lined masonry, rocks, metal, or timber. The depth of flow y is the vertical distance from the water surface to the lowest point of the channel section. Stage is the elevation or vertical distance of the free surface above a datum. Top width T is the width of the natural section at the water surface. Water area A is the cross-sectional area of the flow measured normal to the direction of the flow. The wetted perimeter P is the length of the line of intersection of the channel wetted surface with the cross-sectional plane normal to the direction of the flow. Figure 14.11 shows the different geometric elements of channel section.
Flow Models for Rivers and Streams
Published in James L. Martin, Steven C. McCutcheon, Robert W. Schottman, Hydrodynamics and Transport for Water Quality Modeling, 2018
James L. Martin, Steven C. McCutcheon, Robert W. Schottman
Geometric properties include the area, wetted perimeter, hydraulic radius, and top width as functions of the water depth. The area refers to the “wetted area” or cross-sectional area of the water column perpendicular to the flow and is a function of the channel shape and water depth. The wetted perimeter is the perimeter of the channel wall contacted by the flow. As illustrated in Figure 3, the wetted perimeter for a rectangular channel is the width plus twice the water depth. The hydraulic radius is the area divided by the wetted perimeter. For very wide channels, the hydraulic radius is approximately equal to the depth.
Hydrogel-Based Composites in Perfusion Cell Culture/Test Device
Published in S. M. Sapuan, Y. Nukman, N. A. Abu Osman, R. A. Ilyas, Composites in Biomedical Applications, 2020
where μ is dynamic viscosity of fluid (Pa·s or kg/[m·s]), ρ is the density of fluid (kg/m3), and vin is the mean velocity of the fluid in the channel (mm/s). The hydraulic diameter of the trapezoidal duct DH is given by DH = 4*Cross-sectional area (mm2)/Wetted perimeter (mm). The wetted perimeter in this case is the total perimeter of cross section of channel, because the channel is fully filled with fluid, thus all channel walls are in contact with the fluid.
Critical Heat Flux Model for Vertical Annular Mist Flow Conditions in a Rod Bundle
Published in Nuclear Science and Engineering, 2020
It is given as the ratio of the channel flow area to the corresponding interfacial surface area where is the wetted perimeter. Substituting the definition of the equivalent diameter,, for a square array rod bundle into Eq. (1) yields the interfacial friction length as follows:
Hydraulic resistance in mixed bedrock-alluvial meandering channels
Published in Journal of Hydraulic Research, 2021
Roberto Fernández, Alejandro J. Vitale, Gary Parker, Marcelo H. García
The shear stress exerted by a uniform and steady flow on the bed of a channel is given by Eq. (1), where is the fluid density, is the acceleration of gravity, is the hydraulic radius, is the slope, and is the shear velocity (Eq. (2)). The hydraulic radius is the ratio of the hydraulic area to the wetted perimeter . In the case of a rectangular channel, it can be expressed as in Eq. (3), where is the mean flow depth and is the channel width: The average flow velocity can be determined with the Darcy–Weisbach (DW) equation (Eq. (4)). The DW friction coefficient may be related to a general friction coefficient as shown in Eq. (5). Both friction coefficients are related to the dimensionless Chezy coefficient as shown in Eq. (6): In this study, the average flow velocity is a known value calculated as shown in Eq. (7) where is the flow discharge. An expression for the dimensionless friction coefficient may be obtained by substituting Eq. (5) into Eq. (1) and solving for it as shown in Eq. (8): When the flow is hydraulically rough, the resistance law proposed by Keulegan (1938) may be used to express the bed shear stress, as shown in Eq. (9) where the friction coefficient is given by Eq. (10). Therein, = 0.41 is von Karman’s constant, and is the equivalent sand-grain roughness of Nikuradse (1933), which is commonly taken to be proportional to a representative sediment size as shown in Eq. (11). For example, Kamphuis (1974) used and Van Rijn (1982) used , where is the size for which 90% of the grains are smaller. Other values commonly adopted for may be found in Garcia (2008):