Flow Meters

Flow meters are devices that are used to measure the rate of flow of fluids. In wastewater treatment, the choice of flow meters is especially critical because of the solids that are transported by the wastewater flow. In all cases, the possibility of solids being lodged onto the metering device should be investigated. If the flow has enough energy to be self-cleaning or if solids have been removed from the waste-water, weirs may be employed. Venturi meters and critical-flow flumes are well suited for measurement of flows that contain floating solids in them. All these flow-measuring devices are suitable for measuring flows of water.

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.

3.1.1 Rectangular Weirs

A weir is an obstruction that is used to back up a flowing stream of liquid. It may be of a thick structure or of a thin structure such as a plate. A rectangular weir is a thin plate where the plate is being cut such that a rectangular opening is formed in which the flow in the channel that is being measured passes through. The rectangular opening is composed of two vertical sides, one bottom called the crest, and no top side. There are two types of rectangular weirs: the suppressed and the fully contracted weir. Figure 3.1 shows a fully contracted weir. As indicated, a fully contracted rectangular weir is a rectangular weir where the flow in the channel being measured contracts as it passes through the rectangular opening. On the other hand, a suppressed rectangular weir is a rectangular weir where the contraction is absent, that

Recording drum

Indicator scale k i 1 }

Recording drum

Indicator scale

Fully Contracted Weir

Weir

Contraction

; Fully , contracted flow

- Crest

Connecting pipe

Float well

Rectangular weir

FIGURE 3.1 Rectangular weir measuring assembly.

Weir

Contraction

Connecting pipe

; Fully , contracted flow

- Crest

Float well

Rectangular weir

FIGURE 3.1 Rectangular weir measuring assembly.

Weir Bevel

Beveled edge of crest of weir

FIGURE 3.2 Schematic for derivation of weir formulas.

Beveled edge of crest of weir

FIGURE 3.2 Schematic for derivation of weir formulas.

is, the contraction is suppressed. This happens when the weir is extended fully across the width of the channel, making the vertical sides of the channel as the two vertical sides of the rectangular weir. To ensure an accurate measurement of flow, the crest and the vertical sides (in the case of the fully contracted weir) should be beveled into a sharp edge (see Figures 3.2 and 3.3).

To derive the equation that is used to calculate the flow in rectangular weirs, refer to Figure 3.2. As shown, the weir height is P. The vertical distance from the tip of the crest to the surface well upstream of the weir at point 1 is designated as H. H is called the head over the weir.

Channel walls

Channel walls

Rectangular Weir Figure

Suppressed rectangular

FIGURE 3.3 Various types of weirs.

Suppressed rectangular

FIGURE 3.3 Various types of weirs.

From fluid mechanics, any open channel flow value possesses one and only one critical depth. Since there is a one-to-one correspondence between this depth and flow, any structure that can produce a critical flow condition can be used to measure the rate of flow passing through the structure. This is the principle in using the rectangular weir as a flow measuring device. Referring to Figure 3.2, for this structure to be useful as a measuring device, a depth must be made critical somewhere. From experiment, this depth occurs just in the vicinity of the weir. This is designated as yc at point 2. A one-to-one relationship exists between flow and depth, so this section is called a control section. In addition, to ensure the formation of the critical depth, the underside of the nappe as shown should be well ventilated; otherwise, the weir becomes submerged and the result will be inaccurate.

Between any points 1 and 2 of any flowing fluid in an open channel, the energy equation reads

where V, P, y, z, and ht refer to the average velocity at section containing the point, pressure at point, height of point above bottom of channel, height of bottom of channel from a chosen datum, and head loss between points 1 and 2, respectively. The subscripts 1 and 2 refer to points 1 and 2. g is the gravitational constant and y is the specific weight of water. Referring to Figure 3.2, the two values of z are zero. V called the approach velocity is negligible compared to V2, the average velocity at section at point 2. The two Ps are all at atmospheric and will cancel out. The friction loss ht may be neglected for the moment. yj is equal to H + P and y2 is very closely equal to yc + P. Applying all this information to Equation (3.1), and changing V2 to Vc, produces

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