+ 0.0066(0.17) + 0.0024(0.09)] = 0.45 + 0.27 = 0.72 Ans

5.2.3 Outlet Control of Grit Channels

Grit channels (or chambers) are examplesofunitsthatusetheconceptofdiscrete settling in removing particles. Grit particlesarehardfragmentsofrock,sand,stone, bone chips, seeds, coffee and tea grounds, and similar particles. In order for these particles to be successfully removed, theflow-through velocitythroughtheunits must be carefully controlled. Experience has shown that this velocity should be maintained at around 0.3 m/s. This controlisnormallycarriedoutusingapropor-tional weir or a Parshall flume. A grit channelisshownin Figure 5.9 andapropor-tional flow weir is shown in Figure 5.10. A proportional flow weir is just a plate with a hole shaped as shown in the figure cut through it. This plate would be installed at the effluent end of the grit channel in Figure 5.9. The Parshall flume was discussed in Chapter 3.

FIGURE 5.9 A grit channel. (Courtesy of Envirex, Inc.)
FIGURE 5.10 Velocity control of grit channels: (a) proportional-flow weir; (b) cross section of a parabolic-sectioned grit channel.

As shown in the figure, the flow area of a proportional-flow weir is an orifice. From fluid mechanics, the flow Q through an orifice is given by

where Ko is the orifice constant, t is the width of flow over the weir, and h is the head over the weir crest. There are several ways that the orifice can be cut through the plate; one way is to do it such that the flow Q will be linearly proportional to h. To fulfill this scheme, the equation is revised by letting h3 2 = h1/2h. The revised equation is

Thus, to be linearly proportional to h, Ko th112 must be a constant. Or,

Kot1 h1/2 = Kot2h12 = constant ^ th112 = const (5.23)

Equation (5.23) is the equation of the orifice opening of the proportional-flow weir in Figure 5.10. If the equation is strictly followed, however, the orifice opening will create two pointed corners that will most likely result in clogging. For this reason, for values of h less than 2.5 cm, the side curves are terminated vertically to the weir crest. The area of flow lost by terminating at this point is of no practical significance; however, if terminated at an h of greater than 2.5 cm, the area lost should be compensated for by lowering the actual crest below the design crest. This is indicated in the figure.

The general cross-sectional area of the tank may be represented by kwH, where k is a constant, w is the width at a particular level corresponding to H, the depth in the tank. Now, the flow through the tank is Q = vh(kwH), where vh is the flow-through velocity to be made constant. This flow is also equal to the flow that passes through the control device at the end of the tank. The height of the orifice crest from the bottom of the channel is small, so h may be considered equal to the depth in the tank, H. From the equation of continuity, vh( kwH) = Ko th1,2h = K'01 hmH = const( H) (5.24)

Therefore, for grit chambers controlled by a proportional-flow weir, the width of the tank must be constant, which means that the cross-section should be rectangular.

For grit chambers controlled by other critical-flow devices, such as a Parshall flume (the proportional flow weir is also a critical-flow device), the flow through the device is also given by Q = Ko i h312. Thus, the following equation may also be obtained:

Solving for H,

which is the equation of a parabola. Thus, for grit chambers controlled by Parshall flumes, the cross-section of flow should be shaped like a parabola. For ease in construction, the parabola is not strictly followed but approximated. This is indicated in the upper right-hand drawing of Figure 5.10. The area of the parabola is

Coordinates of the proportional-flow weir orifice. The opening of the weir orifice needs to be proportioned properly. To accommodate all ranges of flow during operation, the proportioning should be done for peak flows. For a given inflow peak flow to the treatment plant, not all channels may be operated at the same time. Thus, for operating conditions at peak flow, the peak flow that flows through a given grit channel will vary depending upon the number of channels put in operation. The proportioning of the orifice opening should be done on the maximum of the peak flows that flow through the channel.

Let lmpk be the l of the orifice opening at the maximum peak flow through the channel. The corresponding h would be hmpk. From Equation (5.23), ih = const = lmpkhmpk and, l2 h mpk mpk h = --------i---------

Let lmpk = ;- w and hmpk = Zompk, where Zompk is the maximum depth in the channel corresponding to the maximum peak flow through the channel, Qmpk. Then, h=

ompk 2

This equation represents the coordinate of the proportional-flow weir orifice.

Coordinates of the parabolic cross section. Let Ampk be the area in the parabolic section corresponding to Qmpk. From Equation (5.28),

Ampk o wmpkZompk (5.31)

where 1 wmpk is the top width of the parabolic section corresponding Zompk. From Equation (5.27) and the previous equation, the following equation for c can be obtained:

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