Open channels uniform flow

Uniform flow was described earlier as it applies to hydraulic phenomena in general. In the case of open channels, uniform flow means that the water cross section and depth remain constant over a certain reach of the channel. This requires that the drop in potential energy owing to the fall in elevation along the channel be exactly consumed by the energy dissipation through boundary friction and turbulence. 

Measurements with the latter real-case solvent system give a more complex picture. Even for the one-plate design, achieving uniform flow conditions in each channel is an open issue. Preliminary experiments show that high-temperature, high-pressure operation gives better flow uniformity, which is also advantageous to speed up the polycondensation reaction (see Fig. 10). 

Consider a liquid flowing in an open channel of uniform cross section under the influence of gravity. The liquid has a free surface subjected only to atmospheric pressure. If the flow is steady, the depth of the liquid is uniform and the hydraulic slope of the free liquid surface is parallel to the slope of the channel bed. Consider a length AL in Figure 2.6 in which the... 

R4. Reinius, E., Steady uniform flow in open channels, Trans. Roy. Inst. Technol. Stockholm 179 (1961). 

In a closed pipe conveying fluid under pressure, there is no relation between the slope of the pipe and the slope of the hydraulic gradient. In uniform flow in an open channel, the water surface must be parallel to the bed of the stream, and consequently S is then also the slope of the bed, S0 thus we arrive at the important relation, for uniform flow only, that... 

In the case of pressure conduits, we have dealt with uniform and nonuniform flow without drawing much distinction between them. This can be done because in a closed pipe the area of the water section, and hence the mean velocity, is fixed at every point. But in an open channel these conditions are not fixed, and the stream adjusts itself to the size of cross section that the slope of the hydraulic gradient requires. 

A generalization of this concept of a monolithic multi-channel honeycomb structure is described in a patent by Hoover and Roberts [1978]. An integral support of porous ceramic material has a multiplicity of parallel passageways (or open channels). These passageways are substantially uniformly spaced. On the surface of these channels are coated with a permselective membrane layer. The feed stream flows inside the channels. The membrane, being the first layer in direct contact with the process stream, is selective to one or more species in the stream. In the normal cases of properly weued membrane pores, the permeate under a driving force will uansport through the membrane, any... 

Open Channel Flow For flow in open channels, the data are largely based on experiments with water in turbulent flow, in channels of suflFicient roughness that there is no Reynolds number effect. The hydraulic radius approach may be used to estimate a friction factor with which to compute friction losses. Under conditions of uniform flow where hquid depth and cross-sectional area do not vary significantly with position in the flow direction, there is a balance between gravitational forces and wall stress, or equivalently between frictional losses and potential energy change. The mechanical energy balance reduces to = g(zi — z. In terms of the friction factor and hydraulic diameter or hydraulic radius,... 

In a simple system where the open channel is inclined, the difference in the head between two points will equal the friction losses for a uniform cross section between the two points, which will also dictate the flow rate. 

Kironoto B.A. Graf W.H Reynolds. 1994. Turbulence characteristics in rough uniform open-channel flow. Proceedings of the ICE—Water Maritime and Energy 106(4) 333-344. 

Owen, W.M. (1952). Experimental study of water flow in annular pipes. Trans. ASCE 117 485-496 Owen, W.M. (1953). Correlation between pipe flow and uniform flow in a triangular open channel. Trans. HGC/34(2) 213-219 35(4) 659-660. 

Internal space and flow pattern. We have emphasized that the thermal FFF channel is open and uniform and that the flow pattern is parabolic. This mathematically defined flow pattern contrasts strongly with the microscopic flow pattern found in SEC columns. Because of the packing in such columns, the flow pattern is tortuous and poorly defined. 

Open-channel flow can be characterized as steady or unsteady. It also can be uniform or varied flow, which could be gradually or rapidly varied flow. A fe-mous example of rapidly varied flow is the hydraulic jump. 

The two photos in Fig. 22.11 illustrate the breakup of threads under the influence of cross-wind flow exemplary for threads emerging from open channel flow. The process conditions are the same except the increased dimensionless viscosity in Fig. 22.1 lb. In Fig. 22.1 la, there are Rayleigh waves on the thread, which grow due to surface tension. The cross-wind has no visible effect on the drop formation and the threads disintegrate into drops of quite uniform size. The higher viscous thread is longer as expected from the breakup length measurement. The thin liquid threads... 

Flow through an open channel of uniform cross section and slope (angle 0) can be calculated mathematically, when the depth of liquid is constant throughout the length of the channel. For a length of L, the accelerating force acting on the liquid... 

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