In open channels

Eiquid Flow Measurement in Open Channels Using Thin Plate Weirs and Venturi Flumes, ISO 1438-1975(E), International Organization for Standardization, Geneva, Switzerland, 1975. 

Measurement by Liquid Level. The flow rate of Hquids flowing in open channels is often measured by the use of weirs (see Liquid-LEVEL measurement). The most common type is the rectangular weir shown in Figure 22e. The flow rate across such a weir varies approximately with the quantity. Other shapes of weirs are also employed. Standard civil engineering handbooks describe the precautions necessary for constmcting and interpreting data from weirs. 

The current meter is generally used for measuring velocities in open channels such as rivers and irrigation channels. There are two types, the cup meter and the propeller meter. The former is more widely used. It consists of six conical cups mounted on a vertical axis pivoted at the ends and free to rotate between the rigid arms of a... 

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. 

Two cases are considered. The first, the laminar flow of a thin film down an inclined surface, is important in the heat transfer from a condensing vapour where the main resistance to transfer lies in the condensate film, as discussed in Chapter 9 (Section 9.6.1). The second is the flow in open channels which are frequently used for transporting liquids down a slope on an industrial site. 

Three different types of turbulent flow may be obtained in open channels. They are tranquil flow, rapid flow, and critical flow. In tranquil flow the velocity is less than that at which some disturbance, such as a surge wave, will be transmitted, and the flow is influenced by conditions at both the upstream and the downstream end of the channel. In rapid flow, the velocity of the fluid is greater than the velocity of a surge wave and the... 

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. 

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). 

Manning and others gave values of C for various types of surface roughness [Bama (1969)]. A typical value for C when water flows in a concrete channel is 100 m1/2/s. In general, liquids such as water which commonly flow in open channels have a low viscosity and the flow is almost always turbulent. 

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)]. 

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. 

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. 

The stability of flow in open channels has been investigated theoretically from a more macroscopic or hydraulic point of view by several workers (Cl7, D9, DIO, Dll, 14, J4, K16, V2). Most of these stability criteria are expressed in the form of a numerical value for the critical Froude number. Unfortunately, most of these treatments refer to flow in channels of very small slope, and, under these circumstances, surface instability usually commences in the turbulent regime. Hence, the results, which are based mainly on the Ch<5zy or Manning coefficient for turbulent flow, are not directly applicable in the case of thin film flow on steep surfaces, where the instability of laminar flow is usually in question. The values of the critical Froude numbers vary from 0.58 to 2.2, depending on the resistance coefficient used. Dressier and Pohle (Dll) have used a general resistance coefficient, and Benjamin (B5) showed that the results of such analyses are not basically incompatible with those of the more exact investigations based on the differential rather than the integral ( hydraulic ) equations of motion. The hydraulic treatment of the stability of laminar flow by Ishihara et al. (12) has been mentioned already. 

In addition to the theories reviewed above, there are many treatments in the literature which deal with the hydraulics of wavy flow in open channels. Most of these refer to very small channel slopes (less than 5°) and relatively large water depths. Under these conditions, surface tension plays a relatively minor part and is customarily neglected, so that only gravity waves are considered. For thin film flows, however, capillary forces play an important part (K7, H2). In addition, most of these treatments consider a turbulent main flow, while in thin films the wavy flow is often... 

Keulegan (K13) applied the semiempirical boundary-layer concepts of Prandtl and von K arm an to the case of turbulent flow in open channels, taking into account the effects of channel cross-sectional shape, roughness of the wetted walls, and the free surface. Most of the results are applicable mainly to deep rough channels and bear little relation to the flow of thin films. 

There are numerous reports of investigations of the effects of roughness on flow in open channels. For instance, Reinius (R4) has reported on the effects of surfaces covered with various types of roughnesses (spheres, sand, etc.) on the flow of water in open channels, while Hama (HI) has reported... 

It is well known that in turbulent pipe flow the parabolic profile present in laminar flow becomes blunter, so that the ratio uma,x/u decreases. A similar effect has been found for the relatively deep flows in open channels at small slopes by Jeffreys (J4), who obtained values of us/u down to 1.06, and by Horton et al. (H19), who measured values as low as 1.1. It can be expected that in the flow of thin films the ratio will decrease in turbulent flow from the value of 1.5, but by a very much smaller amount than observed in the deep flows noted above. 

Keulegan (Kl3), 1938 Extension of Prandtl-von KdrmSn turbulent flow theories to turbulent flow in open channels. Effects of wall roughness, channel shape, and free surface on velocity distribution are considered. 

Vedernikov (V2), 1946 Theoretical treatment of wavy flow in open channels. Wavy flow and turbulent flow clearly distinguished. 

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. 

Ishihara et al. (12), 1961 Gives summary of recent Japanese work on wavy flow in open channels, and semitheoretical analysis of problem (wave velocities, frequencies, heights, lengths). Mostly small channel slopes considered. 

Mayer (M7), 1961 Experimental and theoretical study of wavy flow of water in open channel (slopes up to 5°). Data on growth of turbulent spots, local depths, surface velocity, length of entry zone, wave velocities, heights, frequencies, effect of surface-active materials. 

Reinius (R4), 1961 Studies of water flows in open channels at small slopes, Nr, = 50-13,000. Data on film thicknesses, film friction factors, effects of wall roughness. 

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

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

Ultrasonic meters are finding increasing application because of their ability to measure clear and dirty liquids in difficult situations. They are usually non-intrusive and present little or no obstruction to the flow. They are effective also in measuring flow in open channels (Section 6.2.5) and in partially filled pipes. They are, however, highly sensitive to flow conditions and should be calibrated with care. 

British Standard 3680 Methods of Measurement of Liquid Flow in Open Channels (1969-1983). 

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

Systems involving gravity and inertia forces include the wave action set up by a ship, the flow of water in open channels, the forces of a stream on a bridge pier, the flow over a spillway, the flow of a stream from an orifice, and other cases where gravity is a dominant factor. 

In the flow of water in open channels, fluid friction is a factor as well as gravity and inertia, and apparently we face the same difficulty here. However, for flow in an open channel there is usually fully developed turbulence, so that the hydraulic friction loss is exactly proportional to V2, as will be shown later. The fluid friction is therefore independent of Reynolds number, with rare exceptions, and thus is a function of the Froude number alone. 

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