Flow Through A Rectangular Slot

This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate.

1. Viscous Flow Through Rectangular Slot
2. Flow Through A Rectangular Sloth
3. Air Flow Through Rectangular Slot
4. Flow Through A Rectangular Slotted

Formulas to Calculate Slot Drain ® Flow Rate. Unlike some other trench drain systems, it's fairly easy to figure out how much liquid a Slot Drain can handle. The width of the slot opening determines the flow rate. To calculate the flow rate of a Slot Drain, you can use these formulas: 1/2 inch slot opening = 11 gallons per minute per foot of slot. I have a rectangular duct measuring 80' x 40', containing a 1/4' thick orifice plate with a rectangular opening size of 70' x 28'. I have air flowing at 100,000 CFM through the duct at 40' W.C. Static pressure. I am trying to calculate the pressure drop across this orifice. The only equations I can find are for circular orifices in a circular pipe. Home United Facilities Criteria CD 1 Circular and rectangular slots. Slot due to convergence of flow to the wells. Are given in figures 4-6 through 4-9.

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In the case of a simple concentric restriction orifice the fluid is accelerated as it passes through the orifice, reaching the maximum velocity a short distance downstream of the orifice itself (the Vena Contracta). The increase in velocity comes at the expense of fluid pressure resulting in low pressures in the Vena Contracta. In extreme cases this may lead to cavitation when the local pressure is less than the vapour pressure of a liquid.

Downstream of the Vena Contracta in the recovery zone, the fluid decelerates converting excess kinetic energy into pressure as it slows. When the fluid has decelerated and returned to the normal bulk flow pattern the final downstream pressure has been reached.

The discharge coefficientcharacterises the relationship between flow rate and pressure loss based on the geometry of a nozzle or orifice. You can find typical values in our article on discharge coefficients for nozzles and orifices.

The relationships for flow rate, pressure loss and head loss through orifices and nozzles are presented in the subsequent section. These relationships all utilise the parameter, the ratio of orifice to pipe diameter which is defined as:

Where the point downstream of the orifice is sufficiently far away that the fluid has returned to normal full pipe velocity profile.

Horizontal Orifices and Nozzles

For orifices and nozzles installed in horizontal pipework where it can be assumed that there is no elevation change, head loss and flow rate may be calculated as follows:

Vertical Orifices and Nozzles

For orifices and nozzles installed in vertical piping, with elevation change, the following head loss and flow rate equations may be used:

Expansion Coefficient

The expansion coefficient takes account of the difference between the discharge coeffcicient for compressible and incompressible flows. It is defined as:

The expansion factoris typically determined empirically and can be calculated using one of the formulas below.

For incompressible fluids:

American Gas Association method as described in AGA 3.1:

International Standards Organistion method as described in ISO 5167-2:

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.

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.

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 c_d b (2 g)^1/2 h^3/2 (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

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.

Viscous Flow Through Rectangular Slot

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

c_d - discharge constant

b - width of weir (m)

h - height of weir (m)

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

Flow Through A Rectangular Sloth

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:

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 c_d (2 g)^1/2 tan(θ/2) h^5/2 (2)

where

θ = v-notch angle

Broad-Crested Weir

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

q = c_d 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

Air Flow Through Rectangular Slot

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 Through A Rectangular Slotted

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

Related Documents

• California Pipe Flow Metering Method - Measure discharge from the open end of partially filled horizontal pipes
• 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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