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Porous Ceramics
Published in Debasish Sarkar, Ceramic Processing, 2019
Samuel Paul David, Debasish Sarkar
Where μ is absolute viscosity and d is the hydraulic diameter. The value of d is simply the cell diameter for circular channels and cell width for square channels. For non-circular channels, the hydraulic diameter is the ratio of four times the cross-sectional area of flow through the channel to the perimeter of the channel wetted with fluid contact. In general, the liquid flow obeys Darcy’s law when their Reynolds number is between 1 and 10 (Re =1 – 10). The flow generally follows the linear regime between 2 to 5 of Reynolds number [38]. The integration of the pressure gradient changes these respective equations as following: Pi2−Po22PL=μkνsPi2−Po22PL=βρνs2
Rivers
Published in Richard J. Chorley, Stanley A. Schumm, David E. Sugden, Geomorphology, 2019
Richard J. Chorley, Stanley A. Schumm, David E. Sugden
Particles fall through water at velocities dependent on their size, the largest particles falling more rapidly than the smaller particles, and upon the viscosity of the water. However, temperature changes are sufficient to affect the viscosity of flow. Changes in the viscosity of water will, in turn, change the velocity at which a particle of a given size will fall, and hence its effective (hydraulic) diameter. Figure 12.7A shows sand bedforms as a function of stream power and sediment diameter. For example, an increase in viscosity with falling water temperature could have the effect of decreasing the effective diameter of a particle from a to b in figure 12.7A thereby decreasing channel roughness at a given stream power (i.e. the product of mean bed shear stress and mean flow velocity), as well as increasing velocity and decreasing water depths. This has been documented for the Missouri River, where a significant fall in the water level, as a result of decreased roughness, caused grounding of barges and other river craft on sandbars as temperature decreased and flow velocity increased. Reservoir regulators were accused of not permitting sufficient water to flow through the channel in order to maintain river transport, and yet it was shown that discharge from the upstream reservoirs remained constant during the temperature change. It should be noted that antidunes do not appear in Figure 12.7A because their formation depends on a gravity-controlled, free-surface effect. In reality each grain size exhibits its own bedform regimes and Figure 12.7B shows these for a diameter of 0.19 mm in respect of variations in flow depth and mean velocity.
Boundary-Layer Flow
Published in William S. Janna, Introduction to Fluid Mechanics, Sixth Edition, 2020
Because laminar and turbulent flows are so different, it is extremely important that a criterion be established for transition, In pipe flow, the Reynolds number based on hydraulic diameter is used to determine the type of flow. In flow over a flat plate, again the Reynolds number is used, but here it will be based on distance downstream along the plate: Re=Uxv
Chevron Angle Effect on Plate and Shell Heat Exchangers Measured with Particle Tracking Velocimetry
Published in Heat Transfer Engineering, 2022
Leonel Beckedorff, Giovani S. M. Martins, Kleber V. de Paiva, Amir. A. M. Oliveira, Jorge L. G. Oliveira
Dimensionless numbers obtained with the local mean velocity, v(x,y), as the characteristic flow velocity allow the comparison among the three channels. The Reynolds number, Re, is the ratio of flow momentum rate to viscous force [38]; it is calculated with the hydraulic diameter, the local mean velocity, and water properties at room temperature: where ρ is the fluid density and µ is its dynamic viscosity. The hydraulic diameter is the ratio between four times the minimum free-flow area and the wetted perimeter; it can be determined according to Martin [30]:
Numerical and experimental study of the influence of extended surfaces in rectangular channel subjected to constant heat flux
Published in Experimental Heat Transfer, 2023
Haneen M. Al-Ali, Naseer H. Hamza
where the hydraulic diameter is the cross-sectional area of channel per the wetted perimeter. The diffuser and entrance region are set up to ensure fully developed flow through the test section as shown in Figure 1. The Reynolds number value varied as 427.44, 641.16, 855.26, 1069.07, and 1282.9 according to the variation of flow rate values.