Parshall flumes are one of several types of open channel flow measurement devices. The Parshall flume equations in this article are used for flow rate calculations with free flow conditions in the flume. See also, dimensions for Parshall flumes and conditions for free flow and submerged flow.
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Parshall flumes are widely used for open channel flow measurement, especially for flows containing suspended solids, as for example the flow in wastewater treatment plants. A Parshall flume has a converging section, throat, and diverging section, somewhat like a venturi flume. It also has prescribed variations in the channel bottom slope as shown in the diagram in the next section. Parshall flume equations are available for flow rate calculations based on a measured head, for a Parshall flume constructed with prescribed dimensions as discussed in the next section.
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Parshall Flume Configuration and Dimensions
The size of a Parshall flume is designated by its throat width. Dimensions are available for Parshall flume throat widths from 1 inch to 50 ft. The 1 inch flume will carry a flow of 0.03 cfs at 0.2 ft of head, while a 50 ft Parshall flume will carry 3,000 cfs at a head of 5.7 ft. The diagram at the left shows the overall configuration of a Parshall flume. The picture at the right shows a small Parshall flume in operation for open channel flow measurement. Standard dimensions for Parshall flumes with throat widths from 1 ft to 8 ft are shown in the table below the figure at the left.
For the range of throat widths in the table, the other dimensions in the diagram are constant at the following values:
E = 3'-0", F = 2'-0", G = 3'-0", K = 3 inches, N = 9 inches, X = 2 inches, Y = 3 inches.
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Free Flow and Submerged flow in a Parshall Flume
The flow through a Parshall flume is said to be “free flow" when the flow rate through the throat of the flume is not affected by the downstream flow. When this is the case, a hydraulic jump should be visible in the Parshall flume throat. If the downstream level is high enough so that flow is backed up into the throat, the hydraulic jump isn’t visible, and the flow is said to be submerged flow. A quantitative criterion to differentiate between free flow and submerged flow uses head measurements at two locations, Ha and Hb as shown in the diagram at the left. That criterion for several ranges of throat width is summarized here:
For 1" < W < 3" : free flow for Hb/Ha< 0.5; submerged flow for Hb/Ha > 0.5
For 6" < W < 9" : free flow for Hb/Ha< 0.6; submerged flow for Hb/Ha > 0.6
For 1’ < W < 8’ : free flow for Hb/Ha< 0.7; submerged flow for Hb/Ha > 0.7
For 8’ < W < 50’ : free flow for Hb/Ha< 0.8; submerged flow for Hb/Ha > 0.8
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The Parshall Flume Free Flow Equation
The Parshall flume free flow equation is Q = CHan, where Q is the flow rate through the flume in cfs, Ha is the head over the flume in ft (measured at the point shown for Ha in the diagram above), and C and n are constants for a Parshall Flume of given throat width. Values for C and n are given in the table at the right for selected throat widths ranging from 1 in to 50 ft.
Graphs and tables are available for determination of the flow rate through a Parshall flume under submerged flow conditions.
Open channel flow rate measurement is usually done by measuring a change in water depth. It can be done with a weir or flume. Common types are the sharp crested weir (including V-notch weir, rectangular weir, and cipolletti weir), the broad crested weir, the Parshall flume and venturi flume.