Flow Rate Through Slot

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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 v-notch weir, and the broad-crested weir. Weirs are called sharp-crested if their crests are constructed of thin metal plates, and broad-crested 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 sharp-crested or thin-plate weir.

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 V-Notch Weir. In the flow through a given slot, an increase in the flow rate builds up the water depth behind the slot plate so that the water depth just before the slot opening is greater than that at the edge of a weir. Therefore, the nappe through a slot is under the influence of the extra pressure of the water buildup behind the slot plate.

Water level-discharge relationships can be applied and meet accuracy requirements for sharp-crested weirs if the installation is designed and installed consistent with established ASTM and ISO standards.

Rectangular weirs and triangular or v-notch weirs are often used in water supply, wastewater and sewage systems. They consist of a sharp edged plate with a rectangular, triangular or v-notch profile for the water flow.

Broad-crested weirs can be observed in dam spillways where the broad edge is beneath the water surface across the entire stream. Flow measurement installations with broad-crested weirs will meet accuracy requirements only if they are calibrated.

The area of the water as it flows through the chute is 0.240 m 2. The flow rate can be found in m 3 /s using the formula: Q = Av. Q = (0.240 m 2)(5.00 m/s) Q = 1.20 m 3 /s. The flow rate can be converted to liters per second using: 1 m 3 /s = 1000 L/s. The flow rate of the water in the chute is 1200 L/s. As a general rule, Flow Rating (GPM/ft) in a gravel-packed well = O.D. Open Area (in2/ft). (.50 blockage factor). (.31 conversion factor) at an entrance velocity of 0.1 fps. Open area percentage varies from 2% to over 20%, depending upon casing size and slot width. The equation to determine the flow rate for a Rectangular Submerged Orifice is: Where: = Flow Rate through the orifice (cfs). = The cross sectional area of the open rectangular orifice in square feet (height x width). = Height (elevation) difference between the upstream and downstream still water surfaces.

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 V-notch 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 cd b (2 g)1/2 h3/2 (1)

where

q = flow rate (m3/s)

h = elevation head on the weir (m)

b = width of the weir (m)

g = 9.81 (m/s2) - gravity

cd = discharge constant for the weir - must be determined

cd must be determined by analysis and calibration tests. For standard weirs - cd - is well defined or constant for measuring within specified head ranges.

The lowest elevation (h = 0) of the overflow opening of the sharp-crested weirs or the control channel of broad-crested weirs is the head measurement zero reference elevation.

Rectangular Weir Flow Rate Measurement Calculator

cd - discharge constant

b - width of weir (m)

h - height of weir (m)

Flow Rate Through Slot

Flow Rate Through Slot Machines

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) h3/2 (1b)

Flow Rate Through Soil Media

Flow rate through soil

where

q = flow rate (ft3/s)

h = head on the weir (ft)

Flow Rate Through Trench Drain

b = width of the weir (ft)

Alternative with height in inches and flow in gpm:

Triangular or V-Notch Weir

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)

where

θ = v-notch angle

Broad-Crested Weir

For the broad-crested weir the flow rate can be expressed as:

q = cd h2 b ( 2 g (h1 - h2) )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 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 Rate Through Slot Jackpots

Related Topics

  • Flow Measurement - 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

Flow Rate Through Slot Machine

Related Documents

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  • Comparing Flowmeters - A limited comparison of flowmeter principles - regarding service, rangeability, pressure loss, typical accuracy, upstream pipe diameters, viscosity and relative costs
  • Flow Rate Calculated based on the Velocity-Area Principle - Flow rate or discharge in an open conduit, channel or river can be calculated with the velocity-area principle
  • Flowmeters and Turndown Ratio - Rangeability - Turndown ratio for flow measurement devices like orifices, venturi meters etc.
  • Froude Number - Introduction to the Froude Number
  • Types of Fluid Flow Meters - An introduction to different types of fluid flowmeters - Orifices, Venturies, Nozzles, Rotameters, Pitot Tubes, Calorimetrics, Turbine, Vortex, Electromagnetic, Doppler, Ultrasonic, Thermal, Coriolis
  • Waste Water - Flow Capacity - In sewage piping and pumping systems the fluid flow rate must be kept within certain limits to avoid operating problems
  • Weirs - Flow Measurement Standards - Standards of weir flow measurements

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