Trapezoidal, Rectangular, U (Round Bottom, Palmer Bowlus), Parshall 

Flume calculation is mobiledevicefriendly as of February 9, 2016 Register to enable "Calculate" button. Units in flume calculation: cm=centimeter, ft=foot, gal=U.S. gallon, hr=hour, m=meter, MGD=million gallons (US) per day, min=minute, s=second Links on this page: Equations Variables Error Messages References Introduction Head is measured in the flume upstream of the throat  in the socalled "approach channel". For Parshall flumes, head is measured upstream from the throat a distance of 2/3 of the length of the approach channel (x=length of approach channel in the above diagram). For the other three flumes, head is measured upstream from the throat a distance of 3 to 4 times the maximum expected head. This location is somewhat arbitrary because the head does not vary too much with position, so the exact location of the head measurement is not as important as for a Parshall flume. Since the rectangular, trapezoidal, and U flumes can have a raised throat (a hump), it is important to note that head is measured from the top of the hump rather than from the bottom of the approach channel. This web page has calculations for four types of flumes  Parshall, rectangular, trapezoidal, and U shape. Each has advantages and disadvantages related to construction, installation, head measurement, sedimentation, and analysis. Parshall flumes are the most common. They were studied extensively in the mid 1900s. Their analysis is well documented in many texts. Their analytical maturity is exemplified by having both ASTM and ISO standards written for them (ASTM, 1991; ISO, 1992). Recently, Parshall flumes have gone out of favor due to their construction complexity and likelihood to trap sediment compared to newer flume designs. Rectangular and trapezoidal flumes function by having a constriction at the throat and/or a raised invert (bottom) at the throat. Either feature can cause critical flow at the throat in a properly operating flume. These flumes are simpler to construct, can be more easily fit into an existing channel, and can trap less sediment than a Parshall flume. However, the methodology relating discharge to measured head is more complex. Uflumes (round bottom flumes), similar to PalmerBowlus flumes but with a semicircular throat, are ideal for use in culverts or pipes. Critical flow is achieved by narrowing the throat or by raising the bottom of the flume at the throat. Analysis of U flumes is similar to that of the trapezoidal flume. All flumes must be built with their dimensions in strict accordance with specifications in published documents such as the ISO and ASTM standards. Otherwise, discharge analysis must be conducted for the specific flume beginning with theory and proceeding to experimentation to modify the theory by physical observations. Regarding analysis of flumes, flumes (like weirs) are designed to force a transition from subcritical to supercritical flow. In the case of flumes, the transition is caused by designing flumes to have a narrowing at the throat, raising of the channel bottom, or both. Such a transition causes flow to pass through critical depth at the flume throat. At the critical depth, energy is minimized and there is a direct relationship between water depth and velocity (and flowrate). However, it is physically very difficult to measure critical depth in a flume because its exact location is difficult to determine and may vary with flowrate. Through mass conservation, the upstream depth is related to the critical depth. Therefore, flowrate can be determined by measuring the upstream depth, which is a highly reliable measurement. The LMNO Engineering flume calculations are based on ASTM and ISO standards for flumes. These standards were developed from theoretical relationships and modified by experimental observations conducted over several decades. Our calculations are valid only for unsubmerged flows. An unsubmerged flow can be identified by the drop in water depth at the flume throat. In submerged flow, the downstream water backs up into the throat swallowing the drop making the drop difficult or impossible to identify. Analysis of submerged flow requires two head measurements  one in the approach channel and one in the throat.
LMNO Engineering decided to follow the ISO methodology for the four flume types. ISO presents the methodology as a series of equations and graphs which have been agreed upon by an international panel after decades of research involving theory and experimentation. The ISO standards explain the validity and accuracy of their methodology. For Parshall flumes, the ASTM and ISO methods present similar, but not identical, methods. We have selected to follow the ISO method because it presents equations that are valid for a wider range of flume sizes. Variable definitions can be found in the Variables section. Parshall Flume (ISO 9826, 1992) Q = C h^{n} where Q is in m^{3}/s and h is in m Rectangular Flume Order of computations (ISO 4359, 1983): C_{v} can only be computed if hbC_{d}/A<0.93. Trapezoidal Flume Order of computations (ISO 4359, 1983): Let H=h and obtain C_{s} from the graph below. Note that the graph is only valid for 0.02 < mH/b < 5. Then, C_{v} from numerical solution of: C_{v} can only be computed if hbC_{s}/A < 0.93. Since C_{s} and C_{v} are functions of both H and h, recompute H = h C_{v}^{2/3}, C_{s}, C_{v}, and Q. ISO 4359 suggests recomputing Q three times, but we recompute Q until there are at least four significant digits of accuracy. Then, V and F are computed from the final Q. UFlume Order of computations (ISO 4359, 1983): Let H = h and obtain C_{u} from the graph below. Note that the graph is only valid for 0.1 < H/d < 3. Then, C_{v} from numerical solution of: C_{v} can only be computed if hdC_{u}/A < 0.93. Since C_{u} and C_{v} are functions of both H and h, recompute H=h C_{v}^{2/3}, C_{u}, C_{v}, and Q. ISO 4359 suggests recomputing Q three times, but we recompute Q until there are at least four significant digits of accuracy. Then, V and F are computed from the final Q.
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Back to calculation Herschy, Reginald W. 1995. Streamflow Measurement. E & FN Spon (an imprint of Chapman and Hall). 2ed. International Organization of Standards (ISO 4359). 1983. Liquid flow measurement in open channels  Rectangular, trapezoidal, and Ushaped flumes. Reference number: ISO 43591983(E). International Organization of Standards (ISO 4359). 1999. Technical Corrigendum 1 for: Liquid flow measurement in open channels  Rectangular, trapezoidal, and Ushaped flumes. Reference number: ISO 4359:1983/Cor.1:1999(E). International Organization of Standards (ISO 9826). 1992. Measurement of liquid flow in open channels  Parshall and SANIIRI flumes. Reference number: ISO 9826:1992(E). ISO documents can be downloaded as .PDF files for a fee at http://webstore.ansi.org. USBR. 1997. U.S. Department of the Interior, Bureau of Reclamation. Water Measurement Manual. 1997. 3ed. Available from http://www.usbr.gov/tsc/techreferences/mands/wmm/index.htm .
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