# Parshall Flume Discharge Calculation – Open Channel Flow Measurement with Excel

## Where to find a Parshall Flume Discharge Calculation Spreadsheet

Parshall flumes are used for a variety of open channel flow measurement.  They are especially good for flows containing suspended solids, as for example the flow in wastewater treatment.  As seen in the picture at the right, the plan view of a Parshall flume is similar to that of a venturi flume, with a converging section, a throat, and a diverging section.  A Parshall flume, however, also has prescribed variations in the channel bottom slope as shown in the diagram in the next section.  Flow rate through a Parshall flume can be calculated based on a measured head, using equations that will be discussed in a later section.  A Parshall flume must be constructed with prescribed dimensions as shown in the next section.

Image Credit:   City of Batavia, Illinois

## Flume Configuration and Dimensions for Parshall Flume Discharge Calculations

The diagram at the left shows the general configuration of a Parshall flume with a plan and elevation view.  The width of the throat is typically used to specify the size of a Parshall flume.  The table at the right below, shows the standard dimensions for Parshall flumes with throat widths ranging from 1 ft to 8 ft.  Similar information is available for throat widths down to 1 inch and up to 50 ft.

Such a range of sizes covers a very wide range of flow rates.  A 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.   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′

## Free Flow and Submerged Flow in Parshall Flume Discharge Calculation

For “free flow” through a Parshall flume, the flow rate through the throat of the flume is unaffected by the downstream conditions.  For free flow, a hydraulic jump will be visible in the throat of the Parshall flume.  For flow situations where downstream conditions cause the flow to back up into the throat, the hydraulic jump isn’t visible, and the flow is said to be “submerged flow” rather than “free flow.”

The ratio between head measurements at the two locations, Ha and Hb, as shown in the diagram at the left above, can be used as a quantitative criterion to differentiate between free flow and submerged flow.  The values of Hb/Ha for free flow and for submerged flow, for several ranges of throat width from 1″ to 8′ are as follows:

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

The free flow equation for Parshall flume discharge calculation is QfreeC Han, where

• Qfree = the open channel flow rate through the Parshall flume under free flow conditions, cfs for U.S. units or  m3/s for S.I.
• Ha = the head measured at the correct point in the converging section of the Parshall flume as described in the previous section,  ft for U.S. units or m for S.I. units
• C and n are constants for a given Parshall flume throat width, W.

The tables below give the constants C and n in the equations for free flow Parshall flume discharge calculation for both U.S. units and for S.I. units.

The screenshot at the right shows a Parshall flume discharge calculation spreadsheet that will calculate flow rate through the Parshall flume under free flow conditions in S.I. units for a selected throat width and a specified value for the measured head.   This Excel spreadsheet and one for submerged flow calculation are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

## Excel Formulas for Submerged Flow Parshall Flume Discharge Calculation

The submerged flow equations for Parshall flume discharge calculation, as used by the Excel formulas in the spreadsheet below, are summarized for U.S. units and for S.I. units in the diagrams below:

The primary submerged flow equation Parshall flume discharge calculation is:                QsubmQfree – Qcorr, where

• Qsubm = the flow rate through the Parshall flume for a submerged flow condition, in cfs for U.S. units or  m3/s for S.I. units
• Qfree =  the flow rate calculated with the equation, Qfree = C Han, as described in the previous section, in cfs for U.S. units or  m3/s for S.I. units
• Qcorr is a flow correction factor calculated from the equations shown above for the correct throat width, W, in cfs for U.S. units or  m3/s for S.I. units

The screenshot of an Excel spreadsheet template shown at the left will carry out submerged flow Parshall flume discharge calculation in U.S. units for a selected throat width and a specified value for the measured heads, Ha and Hb.   This Excel spreadsheet and one for free flow calculation are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

References

1. U.S. EPA, Recommended Practice for the Use of Parshall Flume and Palmer Bowlus Flumes in Wastewater Treatment plants, EPA600/2-84-180, 1984

2. Wahl, Tony L., Equations for Computing Submerged Flow in Parshall Flumes, Bureau of Reclamation, Denver, Colorado, USA

3. U.S. Dept. of the Interior, Bureau of Reclamation, Water Measurement Manual, 2001 revised, 1997 third edition

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