Open Channel Weirs  Volume Flow Measurements
Weirs can be used to measure flow rates in open channels and rivers  common for water supply and sewage plants.
Weirs are structures consisting of an obstruction such as a dam or bulkhead placed across the open channel with a specially shaped opening or notch. The flow rate over a weir is a function of the head on the weir.
Common weir constructions are the rectangular weir, the triangular or vnotch weir, and the broadcrested weir. Weirs are called sharpcrested if their crests are constructed of thin metal plates, and broadcrested if they are made of wide timber or concrete. If the notch plate is mounted on the supporting bulkhead such that the water does not contact or cling to the downstream weir plate or supporting bulkhead, but springs clear, the weir is a sharpcrested or thinplate weir.
Water leveldischarge relationships can be applied and meet accuracy requirements for sharpcrested weirs if the installation is designed and installed consistent with established ASTM and ISO standards.
Rectangular weirs and triangular or vnotch weirs are often used in water supply, wastewater and sewage systems. They consist of a sharp edged plate with a rectangular, triangular or vnotch profile for the water flow.
Broadcrested weirs can be observed in dam spillways where the broad edge is beneath the water surface across the entire stream. Flow measurement installations with broadcrested weirs will meet accuracy requirements only if they are calibrated.
Other available weirs are the trapezoidal (Cipolletti) weir, the Sutro (proportional) weir and the compound weirs (combination of the previously mentioned weir shapes). By combining Vnotch weirs with broad chested weirs  larger range of flow can be measured with accuracy.
Rectangular Weir
The flow rate measurement in a rectangular weir is based on the Bernoulli Equation principles and can be expressed as:
q = 2/3 c_{d} b (2 g)^{1/2} h^{3/2} (1)
where
q = flow rate (m^{3}/s)
h = elevation head on the weir (m)
b = width of the weir (m)
g = 9.81 (m/s^{2})  gravity
c_{d }= discharge constant for the weir  must be determined
c_{d} must be determined by analysis and calibration tests. For standard weirs  c_{d}  is well defined or constant for measuring within specified head ranges.
The lowest elevation (h = 0) of the overflow opening of the sharpcrested weirs or the control channel of broadcrested weirs is the head measurement zero reference elevation.
Rectangular Weir Flow Rate Measurement Calculator
The Francis Formula  Imperial Units
Flow through a rectangular weir can be expressed in imperial units with the Francis formula
q = 3.33 (b  0.2 h) h^{3/2} (1b)
where
q = flow rate (ft^{3}/s)
h = head on the weir (ft)
b = width of the weir (ft)
Alternative with height in inches and flow in gpm:
Triangular or VNotch Weir
The triangular or Vnotch, thinplate weir is an accurate flow measuring device particularly suited for small flows.
For a triangular or vnotch weir the flow rate can be expressed as:
q = 8/15 c_{d }(2 g)^{1/2} tan(θ/2) h^{5/2} (2)
where
θ = vnotch angle
BroadCrested Weir
For the broadcrested weir the flow rate can be expressed as:
q = c_{d} h_{2} b ( 2 g (h_{1}  h_{2}) )^{1/2 } (3)
Measuring the Levels
For measuring the flow rate it's obviously necessary to measure the flow levels, then use the equations above for calculating. It's common to measure the levels with:
 ultrasonic level transmitters, or
 pressure transmitters
Ultrasonic level transmitters are positioned above the flow without any direct contact with the flow. Ultrasonic level transmitters can be used for all measurements. Some of the transmitters can even calculate a linear flow signal  like a digital pulse signal or an analog 4  20 mA signal  before transmitting it to the control system.
Pressure transmitters can be used for the sharpcrested weirs and for the first measure point in broadcrested weir. The pressure transmitter outputs a linear level signal  typical 420 mA  and the flow must be calculated in the transmitter or the control system.
Related Topics

Flow Measurement
Flow metering principles  Orifice, Venturi, Flow Nozzles, Pitot Tubes, Target, Variable Area, Positive Displacement, Turbine, Vortex, Electromagnetic, Ultrasonic Doppler, Ultrasonic Timeoftravel, Mass Coriolis, Mass Thermal, Weir Vnotch, Flume Parshall and Sluice Gate flow meters and more.
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