Flow through a rectangular weir can be expressed in imperial units with the Francis formula
q = 3.33 (b - 0.2 h) h3/2 (1b)
q = flow rate (ft3/s)
h = head on the weir (ft)
b = width of the weir (ft)
Alternative with height in inches and flow in gpm:
The triangular or V-notch, thin-plate weir is an accurate flow measuring device particularly suited for small flows.
For a triangular or v-notch weir the flow rate can be expressed as:
q = 8/15 cd (2 g)1/2 tan(θ/2) h5/2 (2)
θ = v-notch angle
For the broad-crested weir the flow rate can be expressed as:
q = cd h2 b ( 2 g (h1 - h2) )1/2 (3)
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 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 sharp-crested weirs and for the first measure point in broad-crested weir. The pressure transmitter outputs a linear level signal - typical 4-20 mA - and the flow must be calculated in the transmitter or the control system.
Flow metering principles - Orifice, Venturi, Flow Nozzles, Pitot Tubes, Target, Variable Area, Positive Displacement, Turbine, Vortex, Electromagnetic, Ultrasonic Doppler, Ultrasonic Time-of-travel, Mass Coriolis, Mass Thermal, Weir V-notch, Flume Parshall and Sluice Gate flow meters and more.
Calculate the discharge length from the open end of a partially filled horizontal pipe.
A limited comparison of flowmeter principles - regarding service, rangeability, pressure loss, typical accuracy, upstream pipe diameters, viscosity and relative costs.
Turndown ratio (Rangeability) can be used to compare flow measurement devices like orifices, venturi meters etc.
An introduction to the different types of fluid flowmeters - Orifices, Venturies, Nozzles, Rotameters, Pitot Tubes, Calorimetrics, Turbine, Vortex, Electromagnetic, Doppler, Ultrasonic, Thermal, Coriolis.
Introduction to the Froude Number.
Flow rate or discharge in an open conduit, channel or river can be calculated with the velocity-area principle.
In sewage piping and pumping systems the fluid flow rate must be kept within certain limits to avoid operating problems.
Standards for weir flow measurements.
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