Open channel flows

Flow measurement in open unpressurised channels is a requirement generally associated with waste water systems and sewers. The use of a weir or notch to measure the flow of a liquid presenting a free surface is described in Volume 1, Section 6.3.8. The flow through a rectangular notch (Fig. 6.7a) is given by (Volume 1, equation 6.42)  

Alternatively, a flume can be employed where the rate of fall of a stream is slight or where the stream contains a large quantity of solid material (silt or debris). The most widely used is the venturi flume (Fig. 6.7c) for which the volumetric flow can be determined from03  

Type of Flowmeter Suitable for Minimum Measurable Flowrate (mmJ/s) Principle of Operation Typical Applications Comments 

Turbines, Pelton wheels Liquids and gases 140 (See Volume 1, Section 6.3.9) Fuel metering in aircraft High repeatability. Can be used at high temperatures and pressures 

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Current Meters. Various vane designs have been adapted for open-channel flow measurement. The rotating element is partially immersed and rotates rather like a water wheel. Operation is similar to that of vane anemometers. 

The most often used friction correlation for open channel flows is due to Manning (Trans. Inst. Civ. Engrs. Ireland, 20, 161 [1891]) and is equivalent to... 

This equation is cubic in hquid depth. Below a minimum value of Ejp there are no real positive roots above the minimum value there are two positive real roots. At this minimum value of Ejp the flow is critical that is, Fr = 1, V= V, and Ejp = (3/2)h. Near critical flow conditions, wave motion ana sudden depth changes called hydraulic jumps are hkely. Chow (Open Channel Hydraulics, McGraw-Hill, New York, 1959), discusses the numerous surface profile shapes which may exist in nommiform open channel flows. 

Information on other types of weirs can be obtained from Addison, op. cit. Gibson, Hydraulics and Its Applications, 5th ed.. Constable, London, 1952 Henderson, Open Channel Flow, Macmillan, New York, 1966 Linford, Flow Mea.surement and Meters, Spon, London, 1949 Lakshmana Rao, Theory of Weirs, in Advances in Hydroscience, vol. 10, Academic, New York, 1975 and Urquhart, Civil Engineering Handbook, 4th ed., McGraw-HiU, New York, 1959. 

In filters etc. the particles become largely static in a bed or cake and in such cases the fluid therefore passes through a fixed array of particles or a porous solid and experiences drag as it does so (Figure 2.9). The particles resist the flow, reduce the velocity and give rise to an enhanced pressure drop compared with that in open channel flow. 

The notch or weir, in which the fluid flows over the weir so that its kinetic energy is measured by determining the head of the fluid flowing above the weir. This instrument is used in open-channel flow and extensively in tray towers 3 where the height of the weir is adjusted to provide the necessary liquid depth for a given flow. 

Solids-liquid-gas mixing 275 Solids-liquid mixing 275 Solids—solids mixing 275 Sonic velocity 150, 156,158, 189 Sorel effect, thermal diffusion 589 Spalding, D. B, 393,562 Sparrow, E. M. 465, 564 Specific energy, open channel flow 98... 

In solving open channel flow equations, the THINC I code (Zernick et al., 1962) was the first calculational technique capable of satisfactorily assigning inlet flows to the assemblies within a semiopen core. In the THINC I approach, it was recognized that the total pressure distribution at the top of the core region is a function of inlet pressure, density, and velocity distributions. This functional dependence can be expressed as,... 

Rashidi, M. and Banerjee, S., Streak characteristics and behaviour near wall and interface in open channel flows, Transactions of AS ME, Journal of Fluids Engineering, Series 1112, pp. 164-70 (1990). 

A less well known effect occurs in open channel flow of a viscoelastic liquid, when the normal stress differences cause the free surface to bow upwards in the centre [Tanner (1985)]. 

Figure 5.1 Closeup, overhead view of a plume released isokinetically into a turbulent boundary layer in an open-channel flow. Flow direction is from left to right.

The sample data presented in this chapter were collected for fairly simple flow conditions. The flow was a unidirectional open-channel flow without large-scale flow meander, and the release condition was isokinetic in the direction of the bulk flow. Thus, chemical filaments were advected by the bulk flow in the stream-wise direction, while turbulent mixing acted to expand the plume size and dilute the chemical concentration. Changes in the flow and release conditions lead to significant variation in the plume characteristics and structure. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

Open-Channel Flow Measurement Open-channel flow measurements are usually based on measurement of liquid level in a flow channel constructed of a specified geometry. The two most common flow channels used are weirs and flumes. See Spitzer (2005, op. cit.). 

EXAMPLE 4.7 Measurements of the velocity profile in an open-channel flow (similitude in momentum transport)... 

You will be measuring velocity profiles in a fully developed open-channel flow (no change with longitudinal distance). To get an idea of which parameters you need to measure accurately, you need to perform an order-of-magnitude analysis on equation (4.26). 

What is turbulent flow We will use the simple illustration of a free-surface flow given in Figure 5.1 to describe the essential points of the turbulence phenomena. Turbulent open-channel flow can be described with a temporal mean velocity profile that reaches a steady value with turbulent eddies superimposed on it. These turbulent eddies are continually moving about in three dimensions, restricted only by the boundaries of the flow, such that they are eliminated from the temporal mean velocity profile, u in Figure 5.1. It is this temporal mean velocity profile that is normally sketched in turbulent flows. 

Figure 5.5. Large and small eddies in an open-channel flow. The large eddies perform most of the top to bottom transport.

This derivation can be found in a text on fluid mechanics or open channel flow. 

In contrast, Tamburrino and Gulliver (2002) related liquid film coefficient from Gulliver and Halverson (1989) and Lau (1975) to their measurements of Hanratty s P for open-channel flows in a flume. They could not get a A l relationship. Instead, their result was the following ... 

Nezu, L, and Nakagawa, H. (1993). Turbulence in Open Channel Flow. Balkema, Rotterdam, The Netherlands. 

Thomas, I. E. (1958). Dispersion in Open-Channel Flow, Ph.D. thesis, Northwestern University. 

Kuo Y, Tanner RI (1974) Use of open-channel flows to measure the second normal stress differences Rheol Acta 13 931... 

The flow of thin liquid films in channels and columns has also served as the basis of fundamental studies of wave motion (M7), the effects of wall roughness in open-channel flow (R4), the effects of surface-active materials (T9-T12), and the like. 

It is to be noted that, for laminar open channel flow, the Froude and Reynolds numbers are interrelated. Making use of (1), (3), and (19), it is easily shown that... 

Craya (C17), 1952 Treatment of stability problem in open channel flow. 

Escoffier (E5), 1961 Analysis of onset of instability in open channel flow and origin of waves of instability. Discussion of earlier instability criteria. 

Taylor and Kennedy (T8), 1961 Discussion of onset of wave formation and wave behavior in open-channel flow. 

Henderson, F. M. Open Channel Flow (Macmillan, London, 1966). 

Y. Nino, M.H. Garcia, Experiments on particle-turbulence interactions in the near-wall region of an open channel flow Implications for sediment transport, J. Fluid Mech. 326 (1996) 285-319. 

Specially-shaped open channel flow section device which may be installed in a canal, lateral, or ditch to measure the flow rate, such as that of an industrial effluent. Volume 2(1). 

Open Channel Flow For flow in open channels, the data are... 

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