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Merge pull request #360 from ORNL-AMO/ca-docs
Ca docs updates
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docs/dox-content/calculators/compressedAir/leak_survey/orifice_method_calculator.dox

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* techniques when the discharge coefficient @f$C_d@f$ is known. For surveys where geometry
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* details are unavailable, @f$C_d = 1.0@f$ serves as a conservative upper bound.
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*
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* @note This method differs from the orifice/pressure method used in the
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* @ref compressed_air_reduction_pressure_formula. Here the leak source is an unintended opening
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* of known (measured) diameter, so first-principles compressible-flow equations applied to the
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* hole geometry yield the best estimate. In the compressed air reduction calculator the flow
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* source is a manufactured end-use nozzle whose exact geometry may be unknown; empirically
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* fitted quadratic coefficients indexed by nozzle type are therefore used in place of a
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* geometry-based calculation.
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*
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* The calculation proceeds through the following steps:
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* 1. **Temperature conversion** – Convert air temperature from °F to °R.
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* 2. **Pressure conversion** – Add atmospheric pressure to gauge pressure to obtain absolute

docs/dox-content/calculators/compressedAir/operating_cost_calculator.dox

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*
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* - **Loaded** – the compressor delivers air at full capacity. The motor draws
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* full-load power proportional to the nameplate brake horsepower (BHP).
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* - **Unloaded** – the compressor is unloaded (inlet valve closed or fully open to
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* atmosphere) but the motor continues to run. Power consumption drops to a
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* fraction of full-load BHP (the *unloaded BHP percentage*).
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* - **Unloaded** – the compressor is unloaded but the motor continues to idle.
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* Power consumption drops to a fraction of full-load BHP (the *unloaded BHP percentage*).
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*
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* Load/unload control is one of the most common strategies for industrial
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* compressors. It is energy-efficient at high utilization but wastes electricity
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* at low utilization because the motor idles continuously rather than shutting
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* down. Quantifying both cost components helps engineers evaluate whether a
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* variable-speed drive (VSD) retrofit or a different control strategy is
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* economically justified.
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* Quantifying both cost components helps engineers evaluate whether a different
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* control strategy is economically justified.
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*
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* The four calculation outputs are:
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* 1. **Run Time Unloaded** – the complement of the loaded run-time percentage.
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* 1. **Run Time Unloaded** – percent of the time the compressor is unloaded.
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* 2. **Loaded Cost** – annual electricity cost while delivering air.
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* 3. **Unloaded Cost** – annual electricity cost while idling (no air delivery).
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* 4. **Total Annual Cost** – sum of the loaded and unloaded costs.

docs/dox-content/calculators/compressedAir/pipe_sizing_calculator.dox

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* fluid. The free-air flow rate @math{Q} is first converted to the actual
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* compressed-air volumetric flow at operating pressure using Boyle's Law:
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*
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* @formula{Q_{compressed} = Q \cdot \dfrac{P_{atm}}{P_{line} + P_{atm}}}
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* @formula{boyles-law; Q_{compressed} = Q \cdot \dfrac{P_{atm}}{P_{line} + P_{atm}}}
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*
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* The required cross-sectional area at the design velocity is:
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*
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* @formula{A_{ft^2} = \dfrac{Q_{compressed}}{v \cdot k_{60}}}
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* @formula{cross-sectional-area; A_{ft^2} = \dfrac{Q_{compressed}}{v \cdot k_{60}}}
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*
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* Converting from ft² to in² by multiplying by @math{k_{144}}:
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*

docs/dox-content/calculators/compressedAir/receiver_tank_calculator.dox

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* between two operating pressures for an existing or proposed tank.
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* 2. **General** – the simplest sizing method; computes the tank volume needed to supply a
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* known air demand within an allowable pressure drop.
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* 3. **Dedicated Storage** – sizes a tank that must independently supply a sustained flow
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* for a defined time interval by drawing down from a stored pressure.
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* 4. **Metered Storage** – extends Dedicated Storage by accounting for a metering (needle)
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* valve that continuously replenishes the tank during the demand event; also computes
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* the tank refill time after the event.
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* 3. **Dedicated Storage** – determines the amount of compressed air storage required to
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* support a short-duration event without causing system pressure to fall below an
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* acceptable minimum. Assumes storage alone supplies the additional air demand during
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* the event, with no significant compressor recovery during the storage discharge period.
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* 4. **Metered Storage** – used when a compressor can partially replenish the storage
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* volume during the demand event through a controlled recovery flow. The recovery flow
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* is typically regulated by a needle valve that meters air into or out of the storage
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* receiver at a slower fixed rate. Accounts for both the stored air and the metered
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* recovery flow available during the event, often reducing the required storage volume
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* compared to a storage-only design; also computes the tank refill time after the event.
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* 5. **Bridging Compressor Reaction Delay** – sizes a tank that must supply air during
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* the time the pressure signal propagates from a demand event back to the compressor
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* room and the compressor responds.
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/**
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* @defgroup receiver_tank_dedicated_storage_size_formula Dedicated Storage Method Tank Size Formula
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* @ingroup receiver_tank_calculator
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* @brief Sizes a tank that must supply a sustained flow for a defined duration from stored pressure.
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* @details The Dedicated Storage method is used when a process requires a fixed flow rate
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* for a known duration and the compressor cannot keep up. The tank is sized to
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* provide that flow over the demand period while the pressure falls from the
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* initial to the final value.
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* @brief Determines the compressed air storage volume needed to support a short-duration demand event without letting system pressure fall below an acceptable minimum.
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* @details Use this method when storage alone must supply the additional air demand during
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* the event, with no significant compressor recovery occurring during the storage
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* discharge period. The tank is sized so that pressure can fall from the initial
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* stored value to the minimum acceptable value while satisfying the full demand
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* flow rate for the duration of the event.
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*
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* @formula{receiver-tank-dedicated-storage-size;
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* V_{required} = \frac{k_{gal} \cdot t_{demand} \cdot Q_{flow} \cdot P_{atm}}{P_{in} - P_{out}}
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/**
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* @defgroup receiver_tank_metered_storage_size_formula Metered Storage Method Tank Size Formula
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* @ingroup receiver_tank_calculator
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* @brief Sizes a tank when flow is regulated through a metering (needle) valve.
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* @details The Metered Storage method extends the Dedicated Storage method for the case
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* where a needle valve or flow-control orifice continuously supplies air to the
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* downstream process at a controlled rate @math{Q_{metered}} during the demand
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* event. Only the net demand @math{(Q_{flow} - Q_{metered})} draws from the
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* stored volume, so the required tank is smaller than the Dedicated Storage size
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* for the same scenario.
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* @brief Sizes a dedicated storage tank when the compressor can partially replenish storage during the demand event through a controlled recovery flow.
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* @details Use this method when a compressor can partially replenish the storage volume
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* during the demand event through a controlled recovery flow. In many compressed
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* air systems this recovery flow is regulated by a needle valve that meters air
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* into or out of the storage receiver at a slower fixed rate @math{Q_{metered}}.
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* The calculator accounts for both the stored air and the metered recovery flow
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* available during the event: only the net demand @math{(Q_{flow} - Q_{metered})}
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* draws from the stored volume, often reducing the required tank size compared to
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* a storage-only design. This method is appropriate for intermittent, high-flow
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* applications where a controlled refill rate is desired.
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*
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* @formula{receiver-tank-metered-storage-size;
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* V_{required} = \frac{k_{gal} \cdot t_{demand} \cdot (Q_{flow} - Q_{metered}) \cdot P_{atm}}{P_{in} - P_{out}}
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/**
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* @defgroup compressed_air_nozzle_coefficients Nozzle Coefficient Lookup Table
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* @ingroup compressed_air_reduction_calculator
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* @brief Pre-calibrated quadratic coefficients for 13 standard compressed air nozzle types used
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* @brief Pre-calibrated quadratic coefficients for 12 standard compressed air nozzle types used
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* in the orifice/pressure measurement method.
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* @details These coefficients parameterize the quadratic flow-versus-pressure relationship for
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* each nozzle type. Given a supply pressure @math{P} @unitb{\psi}, the single-nozzle flow rate
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* listed in the table below. Each index (0–12) represents a distinct nozzle geometry; the
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* coefficients were fitted to measured flow data at known pressures.
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*
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* @note Indices 11 and 12 share identical coefficients and represent the same nozzle geometry.
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*
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* @heading{Coefficient Table}
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* @copydoc compressed_air_nozzle_coefficient_data
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* @defgroup compressed_air_nozzle_coefficient_data Nozzle Coefficient Data
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* @ingroup compressed_air_nozzle_coefficients
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* The following table lists the empirical quadratic coefficients @math{a}, @math{b}, and
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* @math{c} for each of the 13 supported nozzle types. Select the row whose index matches the
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* @math{c} for each of the 12 supported nozzle types. Select the row whose index matches the
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* @p nozzle_type field of @ref compressed_air_reduction::PressureMethodData.
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*
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* | Index | @math{a} @unitb{\scfm\per\psi\squared} | @math{b} @unitb{\scfm\per\psi} | @math{c} @unitb{\scfm} |
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* |:-----:|----------------------------------------:|--------------------------------:|------------------------:|
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* | 0 | @math{-2.200 \times 10^{-7}} | 0.018893 | 0.268476 |
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* | 1 | @math{-2.800 \times 10^{-5}} | 0.038377 | 1.061905 |
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* | 2 | @math{-7.600 \times 10^{-5}} | 1.537424 | 14.300000 |
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* | 3 | @math{-2.200 \times 10^{-5}} | 0.345931 | 5.780952 |
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* | 4 | @math{6.820 \times 10^{-4}} | 0.643182 | 13.833330 |
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* | 5 | @math{5.410 \times 10^{-6}} | 0.228851 | 2.968095 |
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* | 6 | @math{-2.100 \times 10^{-6}} | 0.075463 | 1.089857 |
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* | 7 | @math{-2.800 \times 10^{-5}} | 0.148710 | 1.841905 |
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* | 8 | @math{2.652 \times 10^{-3}} | 2.250152 | 46.566670 |
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* | 9 | @math{7.470 \times 10^{-4}} | 0.842056 | 15.957140 |
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* | 10 | @math{4.110 \times 10^{-4}} | 0.560649 | 10.161900 |
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* | 11 | @math{9.350 \times 10^{-4}} | 0.130792 | 4.429524 |
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* | 12 | @math{9.350 \times 10^{-4}} | 0.130792 | 4.429524 |
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* | Index | Nozzle Type | @math{a} @unitb{\scfm\per\psi\squared} | @math{b} @unitb{\scfm\per\psi} | @math{c} @unitb{\scfm} |
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* |:-----:|:-------------------|----------------------------------------:|--------------------------------:|------------------------:|
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* | 0 | 1.0 mm nozzle | @math{-2.200 \times 10^{-7}} | 0.018893 | 0.268476 |
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* | 1 | 1.5 mm nozzle | @math{-2.800 \times 10^{-5}} | 0.038377 | 1.061905 |
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* | 2 | 1/4" pipe, open | @math{-7.600 \times 10^{-5}} | 1.537424 | 14.300000 |
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* | 3 | 1/4" tubing | @math{-2.200 \times 10^{-5}} | 0.345931 | 5.780952 |
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* | 4 | 1/8" pipe, open | @math{6.820 \times 10^{-4}} | 0.643182 | 13.833330 |
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* | 5 | 1/8" tubing | @math{5.410 \times 10^{-6}} | 0.228851 | 2.968095 |
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* | 6 | 2.0 mm nozzle | @math{-2.100 \times 10^{-6}} | 0.075463 | 1.089857 |
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* | 7 | 2.5 mm nozzle | @math{-2.800 \times 10^{-5}} | 0.148710 | 1.841905 |
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* | 8 | 3/8" pipe, open | @math{2.652 \times 10^{-3}} | 2.250152 | 46.566670 |
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* | 9 | 3/8" tubing | @math{7.470 \times 10^{-4}} | 0.842056 | 15.957140 |
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* | 10 | 5/16" tubing | @math{4.110 \times 10^{-4}} | 0.560649 | 10.161900 |
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* | 11 | Air Knife | @math{9.350 \times 10^{-4}} | 0.130792 | 4.429524 |
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*
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* @note Indices 11 and 12 are identical and represent the same physical nozzle geometry.
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* @see compressed_air_reduction_pressure_formula for the formula that uses these coefficients.
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*/

docs/dox-content/calculators/treasureHunt/compressed_air_reduction_calculator.dox

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* @ingroup compressed_air_reduction_calculator
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* @brief Compressed airflow rate estimated from nozzle type and supply pressure.
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* @details The orifice/pressure method estimates flow rate using a quadratic equation fit to
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* empirical flow-versus-pressure data for 13 standard nozzle types (indices 0–12). Each nozzle
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* empirical flow-versus-pressure data for 12 standard nozzle types (indices 0–11). Each nozzle
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* type has a distinct set of coefficients @math{a}, @math{b}, and @math{c} from the lookup table
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* in @ref compressed_air_nozzle_coefficients. The single-nozzle flow rate is computed from the
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* supply pressure; total flow rate and annual consumption then scale with the number of nozzles.
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* @endsymtable
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*
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* @note The coefficients @math{a}, @math{b}, and @math{c} depend entirely on the selected nozzle
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* type. All 13 nozzle-type coefficient sets are listed in @ref compressed_air_nozzle_coefficients.
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* type. All 12 nozzle-type coefficient sets are listed in @ref compressed_air_nozzle_coefficients.
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*
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* @note This method differs fundamentally from the orifice method used in the
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* @ref orifice_method_calculator. Here the flow source is a manufactured end-use nozzle whose
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* exact orifice geometry may be unknown but whose flow characteristics have been empirically
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* characterised; a pre-fitted quadratic curve is therefore more accurate than a geometry-based
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* calculation. In the leak survey the source is an unintended opening of known diameter, so
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* first-principles compressible-flow equations applied directly to the hole geometry give the
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* best estimate.
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* @see compressed_air_nozzle_coefficients
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*/
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