Air duct calculator - AllDuctCalc™ - HVAC Air Duct Calculator v2 Updated 10/26/15: Provide inputs in the blue boxes, other inputs optional.

 
Sheet Metal Duct Friction Loss Calculator. 1. Enter Duct Airflow (CFM), Duct Velocity (FPM), Duct Length and the number of bends. 2. Read Round Duct Diameter (inches) and Friction Loss Per 100' of duct (inches of water). 1. Enter Friction Loss Per 100' of duct (inches of water), Duct Airflow (CFM), Duct Length and the number of bends.. Capital 1 auto navigator

October 9, 2023 by GEGCalculators. The size of a return air duct should generally be based on the HVAC system’s capacity. A common rule of thumb is to aim for approximately 400-450 CFM (cubic feet per minute) of airflow per ton of HVAC capacity. For example, a 2-ton system might require a return duct with a size of around 16 inches in diameter.The Engineering ToolBox (2004). Air Duct Calculator. [online] Available at: https://www.engineeringtoolbox.com/air-duct-calculator-d_813.html [Accessed Day …A duct size calculator, commonly known as a ductulator, depends on factors like the size of the space you’re heating or cooling, air flow …Dec 3, 2023 · The Duct Pressure Loss Calculator is an essential tool used to estimate the pressure drop or loss that occurs within a duct system due to various factors such as friction, length, diameter, velocity of airflow, and gravity. Its primary function is to calculate the pressure loss (ΔP) occurring in the duct, offering insights into the system’s ... The Ductulator - Duct Sizing Calculator is a hand held rotating calculator used for sizing supply and return duct systems using the equal friction design method. Includes scales for friction loss per unit length, air volume, air velocity, round duct diameter, and rectangular duct diameters. One side uses English units, the other side uses ...Undersized return air ducts result in the ducts and grills being more noisy than usual and the air conditioner components becoming stressed, thus reducing the lifetime of the unit. Use our handy return air duct size calculator or charts below to help you determine the correct return air vent size for your home.DUCTULATOR. Sizing air ducts is essential task for HVAC Engineers, it requires quick tool to aid HVAC designer to determine air duct dimensions while drafting AC layouts. DUCTULATOR Software, uses two methods to size air ducts based on velocity or static regain method, taking into account the air properties at given temperature and elevation ...JP Lamborn Co. ( JPL ) began producing flexible air ducts in 1961. Today the company operates four state-of-the-art manufacturing facilities and is the largest family-owned flexible air duct manufacturer in North America. JPL’s core values of manufacturing high-quality products, providing excellent service, innovation, and strong business ...DUCTULATOR. Sizing air ducts is essential task for HVAC Engineers, it requires quick tool to aid HVAC designer to determine air duct dimensions while drafting AC layouts. DUCTULATOR Software, uses two methods to size air ducts based on velocity or static regain method, taking into account the air properties at given temperature and elevation ... Free HVAC Duct Sizing - in SI/Metric or US/Imperial units. Welcome to CalcuDUCT - the quick and easy way to size ducts for any HVAC application. All Duct Calculator. An inclusive air duct calculator for diameter, velocity, CFM, and pressure drop of various types of duct. It will also determine round duct equivalents for rectangle, flat oval, and elliptical (flattened round) duct. Duct roughness and air properties are adjustable and includes a metric option. Open Calculator.Example of big metal round and rectangular ducts (3,000+ CFM airflow). To figure out exactly how big ducts you need for central air conditioning systems, we have prepared complete CFM duct charts for all different kinds of ducts:. Duct sizing chart for flex ducts (round ducts with 5-20 inch diameter).; Duct sizing chart for metal ducts (round ducts …Download HVAC Duct Quantities, Weight and Area Calculation Sheets. Air Duct quantity can be estimated in sq. meters or kilograms. These excel sheets will enable you to calculate or estimate the duct weight or the duct surface area.Perfect for one time or a limited number of HVAC projects. Includes residential load calculator, plus duct sizing, equipment selection and cost analysis software for one low price This software includes all the features and capabilities of the permanent version, however it will expire on your computer 60 days after purchase. Only $49.Adjustable Absolute Duct Roughness. If selected, Flexible roughness is 0.003 ft when. straight and fully stretched tight at 0% compression. (adjusted at other compressions), otherwise the. original method of constant 0.01 ft roughness is used. Use ASH RAE 2013 Flex Compression.Kurb Air Duct Calculator. ductulator.app. Calculation Method. Static Pressure Loss [inW/100ft] Air Flow [CFM] 3000 FPM. Round Duct Air Velocity. Infinity FPM. …Duct thickness. Refers to the thickness of the goods on the actual duct. Duct density. Refers to the density of the material from which the duct is made. Duct weight. Refers to the weight of the current duct per meter. Media density. Refers to the density of the medium flowing through the actual duct. Set to air in the initial position. Media ...The ASHRAE Duct Fitting Database (DFDB) app allows you to perform pressure loss calculations for all 200+ ASHRAE duct fittings in both I-P and SI units. Use this mobile app in the field for quick duct pressure loss calculations. The inputs can be adjusted by touch, and installation is automatic. Available via iTunes®, the app is now universal ...Ductulator - Duct Diameter Calculator. Enter the required volume & velocity to see the necessary duct diameter. Required Air Volume. m³/sec m³/hr. Required Air Velocity. m/sec. Duct Diameter. mm. Health and Safety Executive recommended minimum duct …A simple volume unit converter to convert air flow volumes from ... Calculate the equivalent size of spiral ducting when you have only been given the rectangular duct dimension (it works the other way also) Open the ES Calculator. System Pressure Calculator. The System Pressure Calculator helps you work out the resistance in pascals that ...A duct calculator is a tool used to determine the correct size of ducts in an HVAC system. How do I use a duct calculator? You’ll need to know the air volume flow rate, the velocity …mdot = Q / (cp x Δt) Calculate air mass flow rate from cooling load.Duct thickness. Refers to the thickness of the goods on the actual duct. Duct density. Refers to the density of the material from which the duct is made. Duct weight. Refers to the weight of the current duct per meter. Media density. Refers to the density of the medium flowing through the actual duct. Set to air in the initial position. Media ...AIR DUCT CALCULATOR : by Michael J. Rocchetti PE Mechanical Engineer . Metric Units. Flow rate M^3/S: Velocity M/S: Pressure Pascals: Temperature C: Length Meter: Duct Material: Uncoated Carbon Steel: PVC Plastic Pipe (smooth) Aluminum (smooth) galvanized steel (medium smooth) galvanized steel (average smooth) fiberglass duct …This calculator allows for calculating the mixed air temperature of a third air source. An example of a third air stream is a Bypass air duct that goes from the supply air plenum back to the return air plenum. Trane has an excellent Engineers Newsletter describing Dehumidify with Constant-Volume Systems.Aug 21, 2023 · Cleaning helps not only remove them, but may also remove blockages that can help make your system run more efficiently. Keep reading to learn more about the cost of duct cleaning services. 2024 Duct Cleaning Costs. Calculate local project costs by entering your zip code. Typical Price Range. $ 450 - $ 1,000. Air Duct Calculator. KALK.PRO's duct calculator will help you estimate the required duct size of the ventilation system for quality air exchange …The pressure drop across a valve can be calculated using the valve’s Cv (flow coefficient) value and the flow rate. The equation is: Pressure Drop (psi) = (Cv × Q^2) / (SG × ΔP) where Q is the flow rate (in gallons per minute), SG is the specific gravity of the fluid, and ΔP is the pressure drop across the valve.The head loss calculator below is based on formula (1) : Air Volume Flow - q - (cfm) Equivalent duct diameter - d e - (inches) Duct Length - (feet) Equivalent Diameter - …Knowledge is power, so although we can't always correct the problems we see with duct work, I'm hoping that with some knowledge we can make some little chang...Minor or Dynamic losses in duct systems are pressure losses caused by. Minor or dynamic pressure loss in air duct system components can be expressed as. Δpminor_loss = ξ ρ v2 / 2 (1) where. ξ = minor loss coefficient. Δpminor_loss = minor pressure loss (Pa (N/m2), psf (lb/ft2)) ρ = density of air (1.2 kg/m3, 2.336 10-3 slugs /ft3)Best prices guaranteed. We match other Aussie retailers*. Use our sizing calculator below to determine the minimum size required for your room or house. Remember for ducted systems only include the air conditioned spaces, exclude areas like …Air Duct Calculator/Ductulator with Sleeve. 4.2 out of 5 stars. 18. $15.60 $ 15. 60. FREE delivery Apr 29 - May 2 . Add to cart-Remove. Trane Ductulator and Charging Calculator Kit - Trane Flex Ductulator with Sleeve, Metal Ductulator, R-22 Charging Calculator, R410A Charging Calculator.The Duct Sizing Calculator is a hand held sliding calculator used for sizing supply and return duct systems using the equal friction, or velocity reduction design method. Front of calculator includes scales for friction, velocity, round duct size, weight per linear foot of round duct, surface area in square feet per lineal foot of round duct ...Duct Calculator Elite TM is an industry leading tool designed to simplify the job of duct sizing for HVAC professionals. This app allows users to calculate duct size, velocity, pressure drop, and flow rate for ductwork . Duct Calculator Elite TM features a highly intuitive interface which allows users to easily enter values with precision (without the …Free HVAC Duct Sizing - in SI/Metric or US/Imperial units. Welcome to CalcuDUCT - the quick and easy way to size ducts for any HVAC application.HVAC Ductwork Sizing Calculator. On this page: How to size your HVAC ductwork? Understanding measurement units for ducts. Using Modernize's HVAC and …The cross-sectional area of the duct is: Then the mass flow rate of air through the duct and the rate of heat loss become. therefore, or 5688 kJ/h. The cost of this heat loss to the home owner is. Conversion: 1 Therm = 105,480 kJ. Conclusion: The heat loss from the heating ducts in the basement is costing the home owner 4 cents per hour.Duct Sizer ( Ductulator) for HVAC air ducts. It is designed for calculating and sizing duct dimensions according to air volume CFM, roughness, velocity, etc. It is available in SI and British IP units. Duct sizing needs a ductulator or software but this excel calculator performs the same calculations.Aug 21, 2023 · Cleaning helps not only remove them, but may also remove blockages that can help make your system run more efficiently. Keep reading to learn more about the cost of duct cleaning services. 2024 Duct Cleaning Costs. Calculate local project costs by entering your zip code. Typical Price Range. $ 450 - $ 1,000. ADI DUCTULATOR. Based on research conducted by Texas Tech University as well as Tennessee Tech University, to study the efect of compression in flexible duct on air flow efficiency, ADI created the Ductulator. This Duct Size Calculator's data is based on flexible duct laying in a straight line on a level surface,and nearly fully stretched (4% ...Get free shipping on qualified Ducting & Venting products or Buy Online Pick Up in Store today in the ... resistant, 4-ply aluminum foil laminate that encapsulates a high density, corrosion resistant wire helix. This forms an air tight and easy to use air duct. View Product. Explore More on homedepot.com. Doors & Windows. 1 Panel 36 x 79 ...Cleaning helps not only remove them, but may also remove blockages that can help make your system run more efficiently. Keep reading to learn more about the cost of duct cleaning services. 2024 Duct Cleaning Costs. Calculate local project costs by entering your zip code. Typical Price Range. $ 450 - $ 1,000.By knowing how to calculate static pressure in air duct systems, you can determine that the right push of air counteracts the resistance in airflow. In a static pressure calculation, we are looking for the push of air to exceed the resistance. Otherwise, the system won't be able to circulate air throughout the ducts.Updated March 25, 2024. Show Your Love: The ductulator calculator is a specialized tool used in the HVAC industry to determine the most efficient duct sizes for air distribution …Nov 11, 2023 · The Duct Area Calculator is a powerful tool designed to help individuals and professionals in the HVAC industry determine the cross-sectional area of rectangular and circular ducts. This essential calculation aids in optimizing airflow, ensuring efficient ventilation systems, and maintaining optimal indoor air quality. The formula for air duct sizing involves the calculation of air velocity (V) and duct cross-sectional area (A) to determine the air volume flow rate (Q), expressed in cubic feet per …Highlights. Your air ducts deliver cool and hot air throughout your home. There are sheet metal, fiberglass-lined, fiberboard, and flexible ducts. Some signs you need a cleaning include dirty vents and a pest infestation. Air duct cleaning costs $380 on average and ranges between $270 to $490. Rectangular duct is rounded up to the nearest 1/4 inch. Calculations are for 60°F dry air at sea level, from 5 to 3000 cfm (approximately standard air which is 0.075lb da /ft³). If "ASHRAE 2013" is selected, Flexible roughness is 0.003 ft when straight and fully stretched tight at 0% compression (adjusted at other compressions), otherwise the ... Cleaning helps not only remove them, but may also remove blockages that can help make your system run more efficiently. Keep reading to learn more about the cost of duct cleaning services. 2024 Duct Cleaning Costs. Calculate local project costs by entering your zip code. Typical Price Range. $ 450 - $ 1,000.Example 2.5 ton Duct System Diagram. Sizing for a 2.5 Ton unit, we start with a 16" supply at 875 CFM -1125 CFM. We then take a 7" and 5" run (-200 CFM) off of this section bringing the remaining total to 675 CFM - 925 CFM. A drop from 16" to 14" in now required to keep pressure and velocity up.Get free shipping on qualified Ducting & Venting products or Buy Online Pick Up in Store today in the ... resistant, 4-ply aluminum foil laminate that encapsulates a high density, corrosion resistant wire helix. This forms an air tight and easy to use air duct. View Product. Explore More on homedepot.com. Doors & Windows. 1 Panel 36 x 79 ...Purpose and Learning Objectives. The purpose of this presentation is to introduce new and optimized techniques for designing high performing VAV systems at minimal cost. At the end of this presentation, you will be able to: Size VAV duct mains cost effectively. Select VAV boxes for minimum life cycle cost. Duct-U-Lator. This app works as a Ductulator and Pressure Loss (friction) calculator which has the following functions. Converts Duct Shape or Size to Another. Determines Sizes for a Given Friction Rate. Determines Sizes for a Given Velocity. Determines Sizes for a Given Velocity and a Friction Loss Rate (simultaneous output) Air Duct Calculator. Double-sided. Side 1 = standard ducloator with calculations for both round and rectangular duct. Side 2 = Continental vs competitive cross reference for some common GRDs and a Grille sizing chart. Qty 25/package.An Air duct pressure drop calculation is essential for designing and operating HVAC (Heating, Ventilation, and Air Conditioning) systems. Understanding how to calculate pressure drops in air ducts allows mechanical engineers to design more efficient and effective systems, ensuring optimal airflow and comfort in residential and commercial …Volume is the cross-sectional area multiplied by the length of the duct.; Density is the density of the material the duct is made of.; Diameter is the diameter of the round or spiral duct.; Width and Height are the dimensions of rectangular, oval, or flat oval ducts.; Length is the length of the duct.; For insulated ducts, you calculate the weight …Mar 4, 2023 · Duct Sizing Calculator. The duct sizing calculation involves determining the proper ductwork size needed for an HVAC system. The formula used in this calculation is Q=VA, where Q is the airflow rate, V is the air velocity, and A is the area of the duct. Enter 6" into the Duct Height (Optional) field. The results table show a 10"x6" duct. This calculator can also be used to simply convert round to rectangular or vice versa. It is unnecessary to consider the duct material, length, or air volume since it is just a physical, geometric calculation. Assume we have an 18" round duct.Apr 6, 2024 · The Duct Size Calculator is a quick reference tool for approximating duct size and equivalent sizes of sheet-metal duct and flexible duct. A new duct-sizing calculator from ASHRAE and the Air Distribution Institute (ADI) allows HVAC air-distribution-system designers to size ducts more accurately, especially flex ducts under varying amounts of ... Updated March 25, 2024. Show Your Love: The ductulator calculator is a specialized tool used in the HVAC industry to determine the most efficient duct sizes for air distribution …Duct-U-Lator. This app works as a Ductulator and Pressure Loss (friction) calculator which has the following functions. Converts Duct Shape or Size to Another. Determines Sizes for a Given Friction Rate. Determines Sizes for a Given Velocity. Determines Sizes for a Given Velocity and a Friction Loss Rate (simultaneous output)The circuit of the cold air ducts is calculated for 100% of the necessary flow. On the other hand, for the hot air ducts, one admits 50% to 75% of the cold air flow according to thermal loads. The variation between the temperature of the buildings in summer and the air in the cold air duct is 50 to 55.5 °F (10 to 13°C).V = 0.408 Q/D 2. Components. = Air velocity inside the duct (feet/s) = Air flow rate inside the duct (GPM) = Air flow rate inside the duct (inches) Metric Equation. Determine the following formula, which can be used to calculate the air duct velocity: V …The Ductulator - Duct Sizing Calculator is a hand held rotating calculator used for sizing supply and return duct systems using the equal friction design method. Includes scales for friction loss per unit length, air volume, air velocity, round duct diameter, and rectangular duct diameters. One side uses English units, the other side uses ...These calculations are divided in four areas: 1. Diameter converter, which allows converting circular to equivalent rectangular ducts. 2. Calculator of different ventilation parameters, with which will be able to obtain the diameter, the air speed, the airflow and the dynamic pressure of your installation. 3.An HVAC duct calculator or ductulator is a tool that can be used to calculate the ideal size of your HVAC ducts. It factors in the area size and temperature, air flow velocity, friction loss, and static pressure of the HVAC system.Apr 25, 2022 · At 350-400 CFM per 12,000 BTUs of heating capacity, there’s enough airflow to circulate heated air through supply ducts and pull cool air back to the furnace or air handler through the cold air returns. A 3-ton unit, or 36,000 BTUs, would need a blower capable of moving 3 x 350-400 CFM, so a total of 1,050 to 1,200 CFM. The Duct Area Calculator is a powerful tool designed to help individuals and professionals in the HVAC industry determine the cross-sectional area of rectangular and circular ducts. This essential calculation aids in optimizing airflow, ensuring efficient ventilation systems, and maintaining optimal indoor air quality.Volume is the cross-sectional area multiplied by the length of the duct.; Density is the density of the material the duct is made of.; Diameter is the diameter of the round or spiral duct.; Width and Height are the dimensions of rectangular, oval, or flat oval ducts.; Length is the length of the duct.; For insulated ducts, you calculate the weight …Updated March 25, 2024. Show Your Love: The ductulator calculator is a specialized tool used in the HVAC industry to determine the most efficient duct sizes for air distribution … Ducting Calculators and Air Volume Converter. Nordfab can offer technical assistance with determining whether our ducting is best for your application and with designing duct installations. Please contact us with your requirements. Input CFM Input Velocity (FPM) Ideal Round Duct Diameter Duct Friction in Straight Duct. Calculate. Highlights. Your air ducts deliver cool and hot air throughout your home. There are sheet metal, fiberglass-lined, fiberboard, and flexible ducts. Some signs you need a cleaning include dirty vents and a pest infestation. Air duct cleaning costs $380 on average and ranges between $270 to $490.Enter 6" into the Duct Height (Optional) field. The results table show a 10"x6" duct. This calculator can also be used to simply convert round to rectangular or vice versa. It is unnecessary to consider the duct material, length, or air volume since it is just a physical, geometric calculation. Assume we have an 18" round duct.Minor or Dynamic losses in duct systems are pressure losses caused by. Minor or dynamic pressure loss in air duct system components can be expressed as. Δpminor_loss = ξ ρ v2 / 2 (1) where. ξ = minor loss coefficient. Δpminor_loss = minor pressure loss (Pa (N/m2), psf (lb/ft2)) ρ = density of air (1.2 kg/m3, 2.336 10-3 slugs /ft3)Diameter of Air Duct Sizing =√ ( (576 × 8) / (3.14 × 15)) = 9.8911 inch. Online ducting calculator to find the diameter of duct size. Sizing of air duct can be done using Velocity Method, Constant Pressure Loss Method and Static Pressure Recovery Method.The 922 velocity and air flow calculations are based on standard air at 29.92" hg at 70 °F. Tips. When we talk about positioning the pitot tube 10 straight duct diameters upstream and 3 straight duct diameters downstream of the tranverse plane, we need to first convert rectangular duct measurements into their equivalent circular diameters.Kurb Air Duct Calculator. ductulator.app. Calculation Method. Static Pressure Loss [inW/100ft] Air Flow [CFM] 3000 FPM. Round Duct Air Velocity. Infinity FPM. …This calculation Excel program makes it possible to carry out the calculation of the pressure losses on the duct works and air distribution systems. Download Duct Friction Loss Excel Calculator: Fan static head is calculated according to the duct friction loss. the more the value of friction loss is the more the static head of …Calculation Method. Static Pressure Loss [inW/100ft] Air Flow [CFM] 3000 FPM. Round Duct Air Velocity. Infinity FPM. Rectangular Duct Air Velocity. 0.00049 Absolute Roughness [Foot] 14.42.Download HVAC Duct Quantities, Weight and Area Calculation Sheets. Air Duct quantity can be estimated in sq. meters or kilograms. These excel sheets will enable you to calculate or estimate the duct weight or the duct surface area. Duct Calculator EliteTM is an industry leading tool designed to simplify the job of duct sizing for HVAC professionals. This app allows users to calculate duct size, velocity, pressure drop, and flow rate for ductwork . Duct Calculator EliteTM features a highly intuitive interface which allows users to easily enter values with precision ... Air Duct Calculators (Ductulator) 2/5. Watch on. This handy little device allows you to size your new air duct, and better understand what to expect from existing duct work. A Ductulator helps you properly size your ducts, estimate air loss, find the round or rectangular duct equivalent, and determine velocity. It can prevent some costly errors ...Quickly find the duct diameter best suited to your needs, based on the desired air flow rate and the air velocity in the network. The tool will give you the diameter best suited to your …

Enter 6" into the Duct Height (Optional) field. The results table show a 10"x6" duct. This calculator can also be used to simply convert round to rectangular or vice versa. It is unnecessary to consider the duct material, length, or air volume since it is just a physical, geometric calculation. Assume we have an 18" round duct.. Print me

air duct calculator

Jan 14, 2012 · The Duct Sizing Calculator is a hand held sliding calculator used for sizing supply and return duct systems using the equal friction, or velocity reduction design method. Front of calculator includes scales for friction, velocity, round duct size, weight per linear foot of round duct, surface area in square feet per lineal foot of round duct ... Updated March 25, 2024. Show Your Love: The ductulator calculator is a specialized tool used in the HVAC industry to determine the most efficient duct sizes for air distribution …At 350-400 CFM per 12,000 BTUs of heating capacity, there’s enough airflow to circulate heated air through supply ducts and pull cool air back to the furnace or air handler through the cold air returns. A 3-ton unit, or 36,000 BTUs, would need a blower capable of moving 3 x 350-400 CFM, so a total of 1,050 to 1,200 CFM.Duct Calculator - CDI Curbs. Air Duct Calculator. Flexible Duct Friction Loss Calculator. 1. Enter Friction Loss Per 100' of duct (inches of water), Duct Airflow (CFM), Duct Length …Now, we can use the previous equation to calculate the makeup air rate for kitchens and dryers under these conditions. (1) 400 – 190 = 210 CFM of makeup air (2) 200 – 190 = 10 CFM of makeup air. Makeup Air Duct Size. Below is a table of the average air inflow rates through different size ducts at different air pressures: Ductulator - Hand held rotating calculator used for sizing supply and return duct systems using the equal friction design method. Includes scales for friction loss per unit length, air volume, air velocity, round duct diameter, and rectangular duct diameters. One side uses English units, the other side uses Metric units. Duct type: Metal Ductboard Flex Size by: Friction rate Velocity Friction Rate: per 100 ft. in/wg Duct TEL : ft. * include fittings in the Duct TEL Enter either: CFM: or Duct Size: …The chart below can be used to estimate velocities in air ducts. The default values are for air flow 400 cfm (680 m3 /h) , duct size 8 in (200 mm) and velocity 1150 fpm (5.8 m/s) . Download and print Air Ducts - Velocity …Apr 25, 2022 · At 350-400 CFM per 12,000 BTUs of heating capacity, there’s enough airflow to circulate heated air through supply ducts and pull cool air back to the furnace or air handler through the cold air returns. A 3-ton unit, or 36,000 BTUs, would need a blower capable of moving 3 x 350-400 CFM, so a total of 1,050 to 1,200 CFM. Air Duct Calculators (Ductulator) 2/5. Watch on. This handy little device allows you to size your new air duct, and better understand what to expect from existing duct work. A Ductulator helps you properly size your ducts, estimate air loss, find the round or rectangular duct equivalent, and determine velocity. It can prevent some costly errors ...The average cost to replace ductwork is $1,400 to $5,600, depending on the home's size. Air duct replacement costs $25 to $55 per linear foot or $270 to $500 per duct for a crawl space, attic, or basement. New ductwork installation costs $2,400 to $6,600 for a house without HVAC ducts. Cost to replace ductwork by house size - chart..

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