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This table shows that the value of K(8/ 15)tan| is nowhere near 4.16. From Figure 3.4, however, the value of K for 6 greater than 90° is 0.58. Therefore,

4.16 = 0.58 tan 2*, and tan| = 13.45, 6 = 171.49, say 171°

Given available head of 0.2 m, provide a freeboard of 0.3 m; therefore, dimensions: notch angle = 171°, length = 2 m, and crest at notch angle = 0.2 m + 0.3 m = 0.5 m below top elevation of approach channel. Ans

3.1.3 Trapezoidal Weirs

As shown in Figure 3.3, trapezoidal weirs are weirs in which the cross-sectional area where the flow passes through is in the form of a trapezoid. As the flow passes through the trapezoid, it is being contracted; hence, the formula to be used ought to be the contracted weir formula; however, compensation for the contraction may be made by proper inclination of the angle 6. If this is done, then the formula for suppressed rectangular weirs, Equation (3.8), applies to trapezoidal weirs, using the bottom length as the length L. The value of the angle 6 for this equivalence to be so is 28°. In this situation, the reduction of flow caused by the contraction is counterbalanced by the increase in flow in the notches provided by the angles 6. This type of weir is now called the Cipolleti weir (Roberson et al., 1988). As in the case of the rectangular and triangular weirs, trapezoidal weirs are area and intrusive flow meters.

3.1.4 Venturi Meters

The rectangular, triangular, and trapezoidal flow meters are used to measure flow in open channels. Venturi meters, on the other hand, are used to measure flows in pipes. Its cross section is uniformly reduced (converging zone) until reaching a point called the throat, maintained constant throughout the throat, and expanded uniformly (diverging zone) after the throat. We learned from fluid mechanics that the rate of flow can be measured if a pressure difference can be induced in the path of flow. The venturi meter is one of the pressure-difference meters. As shown in b of Figure 3.5, a venturi meter is inserted in the path of flow and provided with a streamlined constriction at point 2, the throat. This constriction causes the velocity to increase at the throat which, by the energy equation, results in a decrease in pressure there. The difference in pressure between points 1 and 2 is then taken advantage of to measure the rate of flow in the pipe. Additionally, as gleaned from these descriptions, venturi meters are intrusive and area meters.

The pressure sensing holes form a concentric circle around the center of the pipe at the respective points; thus, the arrangement is called apiezometric ring. Each of these holes communicates the pressure it senses from inside the flowing liquid to the piezometer tubes. Points 1 and 2 refer to the center of the piezometric rings, respectively. The figure indicates a deflection of Ah. Another method of connecting piezometer tubes are the tappings shown in d of Figure 3.5. This method of tapping is used when the indicator fluid used to measure the deflection, Ah, is lighter than water such as the case when air is used as the indicator. The tapping in b is used if the indicator fluid used such as mercury is heavier than water.

The energy equation written between points 1 and 2 in a pipe is

where P is the pressure at a point at the center of cross-section and y is the elevation at point referred to some datum. V is the average velocity at the cross-section and ht is the head loss between points 1 and 2. y is the specific weight of water. The subscripts

Pressure

Pressure

FIGURE 3.5 Venturi meter system: (a) flushing system; (b) Venturi meter; (c) coefficient of discharge. (From ASME (1959). Fluid Meters—Their Theory and Application, Fairfield, NJ; Johansen, F. C. (1930). Proc. R. Soc. London, Series A, 125. With permission.) (d) Piezometer taps for lighter indicator fluid.

FIGURE 3.5 Venturi meter system: (a) flushing system; (b) Venturi meter; (c) coefficient of discharge. (From ASME (1959). Fluid Meters—Their Theory and Application, Fairfield, NJ; Johansen, F. C. (1930). Proc. R. Soc. London, Series A, 125. With permission.) (d) Piezometer taps for lighter indicator fluid.

1 and 2 refer to points 1 and 2, respectively. Neglecting the friction loss for the moment and since the orientation is horizontal in the figure, the energy equation applied between points 1 and 2 reduces to

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