Open channel flow meters measure head and convert it to flow with a fixed equation for the primary device. Use this to check the flow your level transmitter or flow meter shows, or to build a check table. US units: head in feet, flow in cubic feet per second, gpm and MGD. The equation used and its valid range are shown with each result.
Parshall Flume Flow (Free Flow)
Formula
Free flow: Q, cfs = C x Ha^n (Ha in ft; C and n by throat width, ASTM D1941 and USBR Table 8-6) 3 in: Q = 0.992 x Ha^1.547 6 in: Q = 2.06 x Ha^1.58 9 in: Q = 3.07 x Ha^1.53 1 ft: Q = 4.00 x Ha^1.522 2 ft: Q = 8.00 x Ha^1.55 3 ft: Q = 12.00 x Ha^1.566 gpm = cfs x 448.83 MGD = cfs x 0.6463 Submergence = Hb / Ha. Free flow limit: 50% (1 to 3 in), 60% (6 and 9 in), 70% (1 to 8 ft), 80% (10 ft and up)
Inputs used
- Throat width
- Upstream head, Ha (at the 2/3 point of the converging section) (ft)
- Throat head, Hb (optional, for submergence check) (ft)
Worked example (fictional plant data)
- 12 in Parshall flume, Ha = 0.85 ft, Hb = 0.50 ft
- Q = 4.00 x 0.85^1.522 = 3.1235 cfs
- gpm = 3.1235 x 448.83 = 1,401.9 gpm
- MGD = 1,401.9 / 694.44 = 2.0187 MGD
- Submergence = 0.50 / 0.85 = 58.8%, below the 70% limit, so free flow applies
Sharp-Crested Weir Flow
Formula
90° V-notch (Cone): Q = 2.49 h^2.48 Other V-notch angles: Q = 2.5 x tan(angle / 2) x h^2.5 Rectangular, contracted: Q = 3.33 (L - 0.1 n h) h^1.5 (n = number of end contractions) Rectangular, suppressed: Q = 3.33 L h^1.5 Cipolletti: Q = 3.367 L h^1.5 (Q in cfs, h and L in ft. Valid for h of 0.2 ft or more, h no more than L/3, crest height at least 2 h.)
Inputs used
- Weir type
- Head on the crest (measured 4 heads or more upstream) (ft)
- Crest length (rectangular and Cipolletti only) (ft)
Worked example (fictional plant data)
- 90° V-notch weir, head 0.75 ft
- Q = 2.49 x 0.75^2.48 = 1.2200 cfs
- gpm = 1.2200 x 448.83 = 547.6 gpm
- MGD = 547.6 / 694.44 = 0.7885 MGD
Cautions
- Measure head at the right place: Parshall flumes at two thirds of the converging section length upstream of the throat; weirs at least four heads upstream of the crest.
- Zero the level sensor to the flume floor or weir crest, not the channel bottom.
- These are free flow equations. A submerged flume or a drowned weir reads high.
- Settled or out of level flumes, poor approach flow, grease and debris on weir plates all add error. ASTM D1941 gives about plus or minus 5% for a good Parshall installation.
References
- U.S. Bureau of Reclamation, Water Measurement Manual, chapter 7 (weirs) and chapter 8 (Parshall flumes).
- ASTM D1941, Standard Test Method for Open Channel Flow Measurement of Water with the Parshall Flume.
Results are estimates for operator and technician use. Equations follow the references above; always check against the instrument manual, your calibration procedure and plant data.
This calculator also appears on ActivatedSludge.com, our consulting site. Results are for training and operator use; always follow your plant’s procedures.