Open-Channel Flow Measurement

Readings given by open straight tubes (Fig. 10-8d and 10-8e are too low due to flow separation. Readings of closed tubes oriented perpendicularly to the axis of the stream and provided with side openings (Fig. 10-8e) may be low by as much as two velocity heads. 

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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. 

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.). 

Flow meters fall into the broad category of meters for open-channel flow measurements and meters for closed-channel flow measurements. Venturi meters are closed-channel flow measuring devices, whereas weirs and critical-flow flumes are open-channel flow measuring devices. 

Nezu I Rodi W. 1986. Open-channel Flow Measurements with a Laser Doppler Anemometer. Journal... 

Robinson, A.R., Chamberlain, A.R. (1960). Trapezoidal flumes for open-channel flow measurement. Trans. American Society of Agricultural Engineers 3(2) 120-124. 

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. 

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 Measurement and Meters, Spon, London, 1949 Lakshmana Rao, Theory of Weirs, in Advances in Hydroscience, vol. 10, Academic, New York, 1975 and Merritt, Standard Handbook for Civil Engineers, 2d ed., McGraw-Hill, New York, 1976. 

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). 

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 ... 

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

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). 

Figure 11 Schematic diagram of the experimental facility for simultaneous measurement of turbulent velocity field and free-surface wave amplitude in an open channel flow using PIV (Li et al., 2005c).

Figure 13 plots an example of the processed PIV frame. The turbulent velocity field and its boundaries, solid wall, and liquid-free surface are simultaneously shown in Figure 13. The turbulence structures such as the coherent vortical structure near the bottom wall and its modification after release from the no-slip boundary condition near the free surface of the open-channel flow, and the evolvement of the free-surface wave can be seen in Figure 13. This simultaneous measurement technique for free-surface level and velocity field of the liquid phase using PIV has been successfully applied to the investigation of wave-turbulence interaction of a low-speed plane liquid wall-jet flow (Li et al., 2005d), and the characteristics of a swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall (Li et al., 2006c).

In dilute open-channel flows, solids concentration profile measurements showed es to be greater than e/ by an amount that varied with particle diameter (97). Pipeline flow measurements at low concentrations (25, 98) also showed differences of this type. 

The pitot tube allows us to measure a liquid height (a very easy thing to measure) and to j calculate a velocity from it by Bernoulli s equation. The device, exactly as shown in Fig. 5,6, is used for finding velocities at various points in open-channel flow and for determining the velocities of boats. 

The pitot tube shown in Fig. 5.6 is suitable for open-channel flow but not for flow of the atmosphere or flow in pipes. For the latter two it is combined with a second tube, called a static tube shown in Fig. 5,7. Here some kind of pressure-differerice-measuring device is used to indicate the difference between the pressures of the pitot and static tubes. The pressure at point 2 is given by Eq. 5.23. By arguments similar to those used with the pitot tube it can be shown that the pressure difference between point 2 and the inlet of the pressure-difference meter, due to the weight of fluid in the tube connecting them, is exactly [balanced by the pressure difference due to gravity from point 1 to the other side of the meter, and hence that the pressure-difference meter... 

Crabtree (2009) detailed most of the flow meters used in industrial plants. His classification for selecting measuring technology with respect to process application is reproduced in Table 6.3. All flow meters are suitable for clean liquids except for the Ultrasonic-Doppler instrument and only electromagnetic instruments are unsuitable for low conductivity fluids. Most instruments are suitable for high temperature operation or application under certain conditions except for the ultrasonic instruments. Many flow meters are suitable for gases. Few instruments can be used for open channel flow or pipes that are semifllled with the exception of weirs and flumes. 

A semi-emperical turbulent one-equation model is developed for rectangular open channel flows of water and viscoelastic fluids. The model is used to predict friction factor vs. Reynolds number relations, velocity profiles, eddy viscosity distributions and turbulent energy budgets. Comparisons are made between the model and the measured results using a Laser Doppler Anemometer. 

McQuivey, R.S. and V. Richardson, "Some Turbulence Measurements in Open Channel Flow", J. Hydraulics Div. Proc. ASCE., 209 (1969)... 

A weir (Fig. P5.25) is a notched plate that is used to measure the rate of flow (0 of fluid in a stream or open channel by measuring height Qi). Friction between the fluid and the plate can be ignored in this problem. 

This prediction serves as comparison for the further measurements mi non-Newtonian liquids and threads emerging form open channel flow instead of completely filled capillaries. 

Fig. 22.7 Dimensionless breakup length depending on gas-Weber numbers for threads from open channel flow. The inclination of the capillary was a = 49° and Newtonian test liquid was used. To compare the breakup length to completely filled capillaries, the prediction in (22.7) and (22.8) is plotted. Noticeable smaller breakup lengths are measured for the threads from open channel flow...

The measurement of the drop size is compared for different process conditions and capillary configurations. For low gas-Weber number, the drop size increases slightly in all cases. The curves for the completely filled capillaries proceed nearly horizontally up to Weg = 2.3. Afterward, the drop size of fi = 0.9 and F = 1.5 increases and the drop size for fi = 0.33 and V = 3 stays constant. Higher dimensionless viscosities promote the increasing drop size. In case of the threads emerging from open channel flow, a similar trend is identified as the plots in Fig. 22.10 indicate. When comparing drop sizes from completely filled capillaries and open channel flow at similar process condition, it became obvious that the gas-Weber number of sudden drop size growth is considerably lower in case of open channel flow. 

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... 

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