Why does every formula need an operating boundary?
A correct equation applied to the wrong basis gives a precise but wrong answer. A receiver formula that assumes isothermal behaviour will not describe a fast pressure collapse. A pipe velocity calculated from free air delivery rather than actual line flow will be wrong by a factor of eight at 7 bar(g). A power comparison that mixes shaft power with total package input will flatter one machine over another.
Each formula below is listed with the question it answers, the inputs it needs and the conditions under which it holds. Pressures in the equations are absolute unless stated. Temperatures in gas-law equations are in kelvin. Flows are free air delivery (FAD) at a stated inlet condition unless marked as actual flow.
| What every record states | Why it matters |
|---|---|
| Question and output | The physical quantity, where it applies and its unit |
| Inputs and units | Each input’s unit, reference basis and sensible range |
| Equation | The relationship written plainly, with dimensions consistent |
| Assumptions | Isothermal or adiabatic, steady or transient, dry or humid air |
| Limits | When the result should not be trusted and what to use instead |
Airflow and reference conditions
Converting flow between reference conditions
Q2 = Q1 × (P1 ÷ P2) × (T2 ÷ T1)
Use it to move a flow figure from one reference condition to another, for example from FAD at the compressor inlet to normal cubic metres (0 °C, 1.013 bar(a)), or to actual flow at line pressure. Where humidity changes significantly, use dry-air partial pressures. The FAD and reference condition conversion tool applies this relationship.
Compression ratio
r = Pdischarge,abs ÷ Pinlet,abs
At 7 bar(g) discharge and sea-level inlet, r is about 8. It drives power, discharge temperature and the choice between single-stage and two-stage compression.
Mass flow
ṁ = ρ × Q, with ρ = Pabs ÷ (R × T) and R about 287 J/(kg·K) for dry air
Mass flow is the same at every point in a leak-free system; volume flow is not. When comparing measurements taken at different points, compare mass flow or flow corrected to the same reference.
Demand, leakage and cycles
| Quantity | Formula | Use and limits |
|---|---|---|
| User demand | Q = n × q × duty × load factor | Coincident demand of one user group; duty and load factor are often estimates |
| Leakage by load/unload timing | Qleak ≈ QFAD × tload ÷ (tload + tunload) | Non-production test with users isolated; valid for a load/unload compressor |
| Leakage by pump-down | Qleak = V × (P1 − P2) ÷ (Patm × t) | V is total system volume; assumes near-constant temperature |
| Cylinder consumption | Q = A × stroke × cycles per minute × (Pabs ÷ Patm), times two for double-acting | Ignores dead volume in hoses and fittings, which can be significant |
The compressed air demand calculator and pneumatic cylinder consumption calculator apply these.
Storage and receivers
Receiver volume for a given draw
V = Q × t × Patm ÷ (P1 − P2)
V is the receiver volume needed to supply flow Q (FAD) for time t while pressure falls from P1 to P2. It assumes isothermal behaviour and no compressor contribution. If the compressor supplies part of the flow, Q becomes the excess of demand over supply. For fast events, real behaviour lies between isothermal and adiabatic, and the isothermal form slightly overstates usable storage.
Time to refill
t = V × (P1 − P2) ÷ (Patm × Qsurplus)
Qsurplus is compressor capacity minus demand during refill. Use the receiver transient storage calculator for the full method.
Piping and pressure drop
| Quantity | Formula | Notes |
|---|---|---|
| Velocity | v = Qactual ÷ A, A = π D² ÷ 4 | Use actual flow at line pressure, never FAD |
| Minimum diameter | D = √(4 Qactual ÷ π v) | Gives internal bore, not nominal size |
| Reynolds number | Re = ρ v D ÷ μ | Air viscosity about 1.8 × 10−5 Pa·s near room temperature |
| Pressure drop | Δp = f (Leq ÷ D) (ρ v² ÷ 2) | Darcy–Weisbach; f from Colebrook or Swamee–Jain |
The equivalent length Leq must include fittings, valves and filter housings. See the compressed air pipe sizing calculator.
Power, energy and efficiency
Three-phase electrical input
P = √3 × V × I × PF ÷ 1,000 (kW)
V is line-to-line voltage, I is line current and PF is power factor. Clamp-meter current alone, without measured power factor, overstates or understates input. A true power meter is better.
Specific power
Specific power = package electrical input (kW) ÷ FAD (m³/min)
Expressed in kW per m³/min at a stated pressure. Lower is better. Only compare machines at the same discharge pressure, reference condition and power boundary (total package input including fans and dryer if integrated).
Pressure and power
For an oil-injected screw compressor around 7 bar(g), each extra bar of discharge pressure needs about 7% more power. This rule of thumb follows from the compression work equation and is useful for screening pressure reductions; use the maker’s data for a firm figure.
Isothermal and adiabatic work
Isothermal: W = P1 V1 ln(r)
Adiabatic: W = (k ÷ (k − 1)) × P1 V1 × (r(k−1)/k − 1), with k about 1.4 for air
Real compressors lie between the two. The equations explain why intercooling and lower pressure ratios save power, but are not substitutes for tested performance data.
Annual energy
E (kWh/year) = loaded kW × loaded hours + unloaded kW × unloaded hours
Unloaded power on a load/unload screw can be a substantial fraction of loaded power, so unloaded hours matter. See the load unload cycle energy calculator.
Heat, cooling and moisture
| Quantity | Formula | Notes |
|---|---|---|
| Sensible heat | Q = ṁ × cp × ΔT | cp about 1.005 kJ/(kg·K) for air, 4.18 for water |
| Recoverable heat | Q = Pinput × frecoverable | f from the maker’s recovery data for the package |
| Ventilation air for a compressor room | Qair = heat rejected ÷ (ρ × cp × allowable rise) | Hot Indian summers leave little allowable rise; plan for 45 °C and above |
| Condensate | Water removed = moisture in at inlet − moisture remaining at pressure dew point | Use saturation tables at the relevant temperature and pressure |
Condensate is large in humid coastal plants in Andhra Pradesh and during the monsoon in Telangana. A refrigerated dryer giving a pressure dew point of about +3 °C removes most of it; desiccant dryers reach typical dew points of −20 °C or −40 °C for instrument and process air.
How to use the register well
- Write down the question first: what quantity, at what point, over what time.
- Find the formula that answers that question and read its assumptions.
- Convert every input to the stated unit and reference basis.
- Check that the operating case lies within the formula’s limits.
- Calculate, then sense-check the result against a known case or a measurement.
- Record the inputs, sources and assumptions alongside the answer.
The register explains and checks calculations. It does not replace a maker’s selection, a pressure-vessel design, an electrical safety procedure or a signed engineering decision.
How Reddy Compressors helps
Reddy Compressors, at Tarnaka in Secunderabad, has served industry since 2002 as an independent multi-brand compressed-air specialist. We sell new and used or refurbished compressors from ELGi, Atlas Copco, Ingersoll Rand, KAESER, Chicago Pneumatic and others, rent from our own fleet of 50–2,000 cfm at 2–30 bar, provide service, AMC and overhauls, carry out air audits and supply spare parts. We are not an authorised dealer of any brand. We have tie-ups with all major and reputed brands.
Our engineers use these same relationships when they size receivers, check pipework, compare offers or test a compressor’s delivery and power on site. If a calculation and a measurement disagree, we can help find out why. Our service teams cover the whole of Telangana and Andhra Pradesh, with supply across India.
What to send us
- The question you are trying to answer and the figure you have calculated
- Your inputs with their units and sources
- Compressor, dryer and receiver details (make, model, rating)
- Any measured pressure, flow, power or temperature data
- Site conditions such as ambient temperature and altitude
Frequently asked questions
What is the formula for compressed air receiver size?
The common isothermal formula is V = Q × t × Patm ÷ (P1 − P2), where Q is the free-air flow to be supplied from storage, t is the time and P1 − P2 is the allowable pressure fall. If the compressor supplies part of the demand, Q is only the shortfall. Fast events behave less favourably than the isothermal form suggests.
How do I calculate the power consumption of an air compressor?
For a three-phase motor, input power is √3 × voltage × current × power factor, divided by 1,000 for kW. Annual energy is loaded power times loaded hours plus unloaded power times unloaded hours. A true power meter gives better results than current readings alone, because power factor changes with load, particularly when the compressor is unloaded.
What is specific power and how is it calculated?
Specific power is the total package electrical input in kW divided by the free air delivery in m³/min at a stated pressure. It shows how much power each unit of delivered air costs. When comparing compressors, use the same pressure, reference condition and power boundary, ideally from tested data, because changing any of these changes the result significantly.
How do I convert FAD to actual flow at line pressure?
Multiply the free-air flow by the ratio of inlet absolute pressure to line absolute pressure, and by the ratio of line temperature to inlet temperature in kelvin. At 7 bar(g) and similar temperatures, actual flow is roughly one-eighth of FAD. Pipe velocities and some flow-meter readings use actual flow, so this conversion matters.
How much does each bar of pressure add to compressor power?
For oil-injected screw compressors working around 7 bar(g), a useful rule of thumb is about 7% more power for each extra bar of discharge pressure. It is a screening figure that helps show the value of reducing pressure losses or setpoints. For a specific machine, use the maker’s performance data at the pressures you are comparing.
Can you check our compressed air calculations?
Yes. Send us the question, your inputs and your result, and we will review the method, units and assumptions. Where it helps, we can measure pressure, power and compressor cycles on site to confirm the figures. We work with compressors of all major brands across Telangana and Andhra Pradesh, and supply equipment across India.
Related pages
Formulas used in our calculators
Each formula below is the method behind one of our browser calculators. Open the calculator pages to enter your own values.
Compressed air demand estimate
Average demand = Σ(number × air per tool × duty). Peak = Σ(number × air per tool) × simultaneity. The peak can never be lower than the average, so the design basis is the higher of the two. Design capacity = design basis × (1 + leakage) × (1 + growth).
Flow and reference-condition conversion
Q₂ = Q₁ × (P₁ / P₂) × (T₂ / T₁), with absolute pressure and absolute temperature. Dry-air basis; humidity is ignored. Unit factors: 1 m³/min = 16.667 L/s = 60 m³/h = 35.31 cfm.
Pressure unit and gauge/absolute conversion
Absolute pressure = gauge pressure + atmospheric (1.01325 bar at sea level). 1 bar = 14.504 psi = 100 kPa = 0.1 MPa. Hyderabad is about 540 m above sea level; atmospheric pressure there is roughly 0.95 bar, so enter the local value in the flow tool if it matters.
Receiver storage sizing
V = Q × t × P_atm / ΔP, where Q is the shortfall in free air (m³/min), t the time (min), ΔP the allowed pressure fall (bar) and P_atm = 1.013 bar. The same relation gives the hold-up time of an existing receiver: t = V × ΔP / (Q × P_atm). Isothermal; for a real system add a margin.
Pipe pressure drop and sizing
Darcy–Weisbach: ΔP = f × (L/D) × ρv²/2, with the friction factor f from the Swamee–Jain relation and air density taken at mean line pressure. Fittings are allowed for as extra equivalent length. Typical commercial steel roughness is about 0.046 mm.
Leakage flow and cost
Choked (critical) flow through an orifice: ṁ = Cd × A × P₀ × √(k / R T) × (2/(k+1))^((k+1)/(2(k−1))), converted to free air at 1.013 bar and 20 °C. Cost = flow × specific power × hours × tariff. Cd of a sharp-edged hole is about 0.6–0.8.
Specific power comparison
Specific power = input kW ÷ delivered flow (m³/min) at the same pressure and reference conditions. Annual cost = kW × hours × tariff. Use the full-load input power on the same test basis for both machines.
Rental versus ownership
Rental total = monthly hire × months + fuel/power. Ownership total = purchase price + running cost × months + service. Break-even month = (purchase) ÷ (monthly hire + monthly rental running − monthly ownership running). All prices are entered by you; none is a quotation.
Moisture load at the dryer inlet
Water in = air × relative humidity × saturation vapour density at intake (Magnus formula). Water the air can hold after compression = humidity ratio at saturation at the dryer inlet temperature and pressure × dry-air mass per m³ of intake air. Condensate = the difference. Flow is free air at intake conditions; indicative.
Adsorption dryer purge air
Purge flow = dryer flow × purge fraction. Energy = purge flow × specific power × hours × tariff. Heatless dryers are commonly in the range of 15–20% purge; heated and blower-purge types use less. Use the datasheet value for the dryer in question.
Compressor room ventilation
Heat to room ≈ input power × fraction rejected into the room (for air-cooled units, nearly all of it unless ducted). Airflow = heat ÷ (ρ × cp × ΔT), ρ = 1.2 kg/m³, cp = 1.005 kJ/kg·K. If the cooling air is ducted out of the machine, only the radiated part stays in the room.
Pneumatic cylinder air consumption
Air per stroke (free air) = swept area × stroke × (P + 1.013) / 1.013. The outstroke uses the full bore area π/4 × D²; the return stroke of a double-acting cylinder uses the bore area less the rod area π/4 × d². Enter rod 0 to ignore it (a small over-estimate).
Abrasive blasting air demand
Nozzle air treated as orifice flow at the nozzle pressure: free air = Cd × A × choked mass flow ÷ ρ₀. Venturi nozzles with an effective Cd near 0.9 are typical; use the supplier value. Add flow for the pot and for leaks. Nozzle numbers are the bore in sixteenths of an inch (No. 6 = 3/8 in = 9.5 mm). A nozzle wears larger in use, so size the compressor for the nozzle worn one size and replace it at that point.
Pressure budget and the cost of excess pressure
Required compressor pressure = point-of-use pressure + sum of losses. Savings = power × (reduction in bar) × saving per bar. A saving of roughly 6–8% of compressor power per bar of pressure is commonly quoted; it is indicative and varies with machine type and control, so edit it to suit.
Project payback and net present value
Simple payback = investment ÷ (annual saving − upkeep). NPV = −investment + Σ (saving − upkeep) / (1 + r)ⁿ over the life. Discounted payback is the year in which the discounted savings repay the investment; IRR is the discount rate at which NPV = 0. Enter your own figures.
Temporary air fuel logistics
Fuel per machine per day = loaded hours × loaded burn + unloaded hours × unloaded burn (stopped hours use none). Usable tank = tank × (fill level − lowest level). Autonomy = usable tank ÷ average burn while running. Weekly order = days × site litres a day + delay reserve, less fuel already on site. Take burn rates from the supplier datasheet for the actual load.
Compressor heat recovery
Recoverable heat = input power × recoverable fraction. Value = heat × hours × cost of the fuel replaced ÷ efficiency of the displaced boiler or heater. Recoverable fraction depends on the machine and the heat sink; use a measured or supplier figure.
Annular area and return velocity
Annular area = π/4 × (D_hole² − D_rod²). Actual flow at the back pressure = free air × (P_atm / (P_back + P_atm)). Velocity = actual flow ÷ area. A return velocity often quoted for efficient cuttings lift is around 15–25 m/s; confirm for your material.
Lifecycle cost comparison
Lifecycle cost (present value) = purchase + Σ (annual energy + annual maintenance) / (1 + r)ⁿ. Energy = input power at working load × hours × tariff. Equivalent annual cost = present value × r / (1 − (1 + r)^−years).
Load/unload cycle energy
Two input modes. Cycle timing: enter measured seconds per cycle. Fraction: enter the share of time loaded, unloaded and stopped (for example 40, 60, 0, from controller loaded/running hours); no cycle time is reported in this mode. Average kW = (P_load × t_load + P_unload × t_unload + P_stopped × t_stopped) ÷ (t_load + t_unload + t_stopped); the states must not overlap. Annual kWh = average kW × the hours this pattern runs. Unload energy = P_unload × unloaded fraction × hours. Average air delivered = loaded fraction × loaded FAD; effective specific power = average kW ÷ average air delivered. Unloaded power is never assumed to be zero: enter measured package kW (unloaded read after blowdown has settled). Scenario comparison: enter the predicted times after a change (bigger receiver, wider band, auto-stop) in the “after change” fields; the same powers, FAD and hours are used and the kWh difference is shown. An auto-stop timer is modelled by moving unload time into the stopped state (check the motor’s permitted starts per hour). For different day and night patterns, run the tool once per pattern and add the results. The rapid-cycling warning below 30 s per cycle is a screening value used by this tool. Money is shown only when you enter your own tariff.
Part-load fleet dispatch (single demand point)
Single-demand-point mode. Every on/off combination of the available machines is tried, with each online machine in turn as the trim machine. Base machines run fully loaded at their FAD and full-flow kW; the trim machine takes the remainder. A state is feasible only if the remainder is above 0, no more than the trim machine’s full flow, and (for a VSD trim) not below its minimum stable flow. Fixed-speed trim on load/unload: kW = x × loaded kW + (1 − x) × unloaded kW, with x = trim flow ÷ full flow (ignores extra blowdown losses with small storage). VSD trim: kW interpolated linearly between the minimum-flow and full-flow points. Specific power = total kW ÷ demand. N+1 check: with the largest online machine lost, all other available machines together must still cover the demand (assumes standby machines can start in time). Annual kWh = kW × hours at this demand. The lowest-power state that also passes N+1 is shown when the cheapest state does not. Use package kW and FAD at the same duty pressure for every machine. Not included: the demand sweep, annual load profile and scenario modes described on the page; run the tool once per demand band and weight each result by the hours in that band (annual kWh = Σ kW × hours).
Motor input from volts, amps and power factor
Three-phase screen (balanced supply, line-to-line voltage V_L): S (kVA) = √3 × V_L × I ÷ 1,000; P (kW) = S × PF; Q (kVAr) = √(S² − P²). Single-phase: drop the √3 and use phase voltage. The power factor must be measured in the same operating state: an induction motor’s PF falls sharply when the compressor unloads, so applying the loaded PF to unloaded amps overstates unloaded kW. Not valid on the supply side of a VSD (harmonics) or with unbalanced phases: use a true-RMS power analyser there. State the measurement boundary (motor only, or whole package) with every result.
Air demand duration curve summary
Regular-interval mode: every valid reading carries the same time weight (the logging interval), so leave out missing, negative and fault readings rather than entering them as 0 (enter 0 only when the plant was confirmed stopped). Readings are sorted from highest to lowest. Ep = the flow exceeded (reached or exceeded) for at least p% of the valid hours = the k-th highest reading with k = ⌈p × n ÷ 100⌉. Valid hours = n × interval. Coverage = valid hours ÷ scheduled hours × 100. Hours above capacity = number of readings above it × interval; air above capacity = Σ(reading − capacity) × interval. All flows must be on one basis, ideally FAD in m³/min. E1 needs at least 100 readings to differ from the maximum (with fewer, k = 1 for E1); a week at 1-minute or 5-minute logging gives plenty. The 90% coverage warning is a screening value used by this tool. Not included: timestamp import, irregular intervals and gap filling.
Adjusted energy baseline and avoided energy
Adjusted baseline = a + b × reporting production + c × reporting days (or hours) + d × reporting mean ambient temperature + non-routine adjustment. Avoided energy = adjusted baseline − measured reporting-period energy. The raw comparison (average baseline period − reporting period) is shown alongside, so both what the meter said and the adjusted result stay visible. Coefficients come from a regression on baseline data (see the fit tool below or your own analysis); set d = 0 if temperature is not used. Money is a separate step with your own tariff.
Baseline regression fit (one variable)
Ordinary least squares on n baseline periods: b = Σ(x − x̄)(E − Ē) ÷ Σ(x − x̄)², a = Ē − b × x̄. R² = 1 − SS_res ÷ SS_tot. RMSE = √(SS_res ÷ (n − 2)); CV(RMSE) = RMSE ÷ Ē × 100. Screening guide used by this tool: 20% for monthly regression baselines (the figure commonly cited from ASHRAE Guideline 14; check the edition you report against). The 2 × RMSE test for the saving and the 6-period minimum are also screening values used by this tool. Adjusted baseline = a + b × reporting production + non-routine adjustment; avoided energy = adjusted baseline − measured reporting energy. One driver only: for production plus days or temperature, fit with a spreadsheet and use the adjusted-baseline tool above. Use the same metering boundary in both periods.
Compressed-air station carbon ledger
Electricity: kWh = average kW × hours for compressors, dryers and other electric auxiliaries inside the boundary; emissions = kWh × grid factor (kg CO₂ per kWh, numerically the same as t CO₂ per MWh). Diesel: litres × diesel factor. Intensity = electricity emissions ÷ (average free air × 60 × hours) × 1,000. Pressure reduction: kWh saved = compressor kWh × bar reduced × saving per bar (rule of thumb about 7% per bar; edit it). The default grid factor of 0.7 is illustrative only, not an official value: use the CEA CO₂ baseline database edition for your reporting year and say whether it is location- or market-based. 2.68 kg CO₂ per litre of diesel is the IPCC 2006 default CO₂-only value at 0.84 kg/L; use your company’s source. Do not add this subtotal to a site total that already includes the same meters.
Energy effect versus emission-factor effect
Energy effect = (new kWh − old kWh) × old factor. Factor effect = new kWh × (new factor − old factor). The two add up exactly to new emissions − old emissions. Only the energy effect reflects a change in the compressed-air system; report the factor effect separately. Use the same boundary and the same basis (location- or market-based) in both periods. Factors here are illustrative: enter the published values you report against.
Specific power uncertainty budget
GUM method for y = P ÷ Q (a quotient, so relative uncertainties combine). For the power instrument and the flow meter, choose how the figure is stated: a ± specification limit (rectangular, u = a ÷ √3) or a calibration-certificate expanded uncertainty at k = 2 (normal, u = U ÷ 2). The installation estimate is a ± limit, rectangular. Repeatability (Type A): u = s ÷ √n, relative to P. Combined relative standard uncertainty u_c = √(Σ u_i²); expanded U = k × u_c (k = 2 gives about 95% for a near-normal result with enough readings). Comparison: the difference between the two specific powers is treated as real if it exceeds √(U₁² + U₂²) in absolute terms (independent measurements at the same k). Not covered: wrong boundary or units (errors, not uncertainty) and an unrepresentative test period.
Air criticality priority score
Enter one value per user group, in the same order in every list. Priority score = consequence (1–5) × likelihood of loss of the supply path (1–5). Any group with consequence 5 that depends on a single point of failure (enter 1) is flagged whatever its score. The score ranks where standby, storage, spares or rental cover are worth considering; it does not prove reliability. Default: the page example (instrument air, packaging, cleaning, workshop).
N+1 capacity and storage ride-through check
Shortfall with the largest unit out = demand − (total capacity − largest unit). Usable stored free air ≈ receiver volume × allowed pressure fall ÷ 1.013 bar (isothermal). Ride-through time = stored free air ÷ the flow not being supplied. Use capacities measured at the required pressure. This checks compressors only: dryers, controls, power and headers need their own N+1 test. Default: the page example (two 6 m³/min machines, 9 m³/min demand, 3 m³ receiver, 7 → 6 bar g).
Spare part stocking decision
Enter one value per part line, in the same order in every list. Part type: 1 = scheduled consumable, 2 = wear part, 3 = critical failure part, 4 = major assembly. A line is exposed when restoration time without stock is longer than the tolerable interruption and the consequence is 3 (significant) or more. Exposed wear and critical failure parts → stock on site or a guaranteed supply arrangement; exposed major assemblies → repair/exchange route and rental cover rather than stock; consumables → service plan, one set ahead (and one set kept on site if exposed). Exposure = consequence × (restoration − tolerable) days, used only to rank. Where a standby exists, enter as tolerable interruption how long you accept running without reserve. Default: the page example (thermostatic valve kit, temperature sensor, dryer drain valve, airend, separator element; day figures are illustrative).
Bad-actor ranking
Enter one value per asset or failure mode, in the same order in every list. Failure rate = events ÷ running hours × 1,000 (failures per 1,000 h); MTBF = running hours ÷ events. Score = (downtime hours + labour hours) × consequence weight (for example 1 fully redundant, 3 partial standby, 5 no backup). Items are ranked by score; the Pareto line lists the top items that together make up at least 80% of the total score. Items with failures that returned after a corrective action are marked. Default: the page example over twelve months (Compressor A, B, C, Dryer 1, Dryer 2).
Bid normalisation: Net flow and comparable cost
Flow is converted to m³/min (1 cfm = 0.0283168 m³/min; 1 L/s = 0.06 m³/min); this is valid only when the bids use the same reference conditions. Net flow = offered flow − internal consumption (dryer purge, drains). A bid whose data is not at the required pressure is not credited: it needs clarification, not arithmetic. Specific power = total package input kW ÷ net flow. Energy per year is compared like-for-like at the required net flow: specific power (on net flow) × required net flow × hours, so a larger machine is not charged for air the plant does not use. This assumes the specific power holds at that flow; for a VSD or a plant that runs mostly at part load, use each bidder’s supported part-load power for each hour band instead. Bids are ranked on energy only if they pass the net-flow check. Comparable installed cost = quoted price + required additions − confirmed discounts. Default: the page’s worked example B (20.0 m³/min net required at 8 bar g).
Performance acceptance check
Flow deviation = (measured FAD − required FAD) ÷ required × 100. Specific power = package input kW ÷ measured FAD; its deviation is against the declared value. Pressure margin = lowest measured pressure at the agreed point − required minimum. Disposition: mandatory evidence missing or test invalid → Hold; a pressure shortfall, or a flow or specific-power result outside tolerance by more than the measurement uncertainty → Reject; outside tolerance but within the uncertainty → Hold (shortfall not proven, retest); all within tolerance → Accept, or Accept with conditions if minor items are open. Enter the tolerance the contract states (0 if the full figure is required). For reference, the ISO 1217 Annex C bands for machines above 15 m³/min are commonly quoted as ±4% flow and ±5% specific energy; confirm from the standard. ISO 1217 Annex C tolerances already include measurement uncertainty; do not add it again when the contract uses them. The Hold-within-uncertainty rule is a default screening rule used by this tool; use the decision rule written in your contract. Default: the page example (20.0 m³/min required, 19.5 measured, 126.0 kW, declared 6.4 kW per m³/min).
Overhaul versus replacement: Energy and whole-pathway cost
Power at duty = demand × specific power. If the replacement can run at a lower pressure, its power is reduced by (bar reduction × saving per bar); about 7% per bar is a common rule of thumb for screw compressors. Annual energy = power × loaded hours. Present-value cost = pathway cost + (annual energy cost + maintenance) × PVF, where PVF = (1 − (1 + r)^−n) ÷ r (= n when r = 0), n up to 50 years. Break-even tariff = the tariff at which both present values are equal. Pathway costs should include inspection, package parts, labour, rental cover, testing and acceptance. Residual value is not included. Default: the page example (12 m³/min, 6,000 h, 7.0 vs 6.4 kW per m³/min).
Leak repair persistence
Coverage = re-checked ÷ eligible. Persistence = still passing ÷ re-checked; recurrence = leaking again ÷ re-checked (inspected items only). Unknown = eligible − re-checked. The persistence range assumes every unknown repair failed (low) or passed (high), each over all eligible repairs. Residual flow = estimated flow of recurred leaks + new leaks nearby; power = flow × specific power. Other outcomes = re-checked − passing − recurred (for example component removed). Default: the page example (120 eligible, 90 re-checked, 72 passing, 18 recurred, 11 of them quick couplings, 0.9 m³/min).
Section losses at the worst moment of a pressure dip
Section loss = upstream pressure − downstream pressure, all in bar(g) at the same timestamp: treatment = compressor-room header − after dryer/filters; distribution = after dryer/filters − area header; point of use = area header − machine inlet (hose, coupling, regulator, drop). If the area header is at or above the machine minimum while the inlet is below it, the shortfall is created locally. If the compressor-room header is above the minimum but the area header is below it, the shortfall is created in treatment or distribution. Only if the compressor-room header is itself below the minimum does the compressor state at the start of the dip separate capacity (all loaded), control response or storage (a machine unloaded, off or slow) and availability (a machine tripped or isolated). A negative section loss means the two sensors disagree: compare them on a common point.
Pressure event count, depth, duration and data coverage
An event starts at the first reading below the minimum and ends at the first reading back at or above it. Each reading is taken to represent one logging interval, so duration = number of readings below the minimum × interval. Depth = lowest reading in the event. Recovery time = time from the lowest reading to the first reading back at or above the minimum. Time below the minimum is duration-weighted over the logged time. Coverage = logged time ÷ campaign length; events in unlogged periods cannot be seen.
Cooler approach and margin against a baseline
Approach = fluid leaving the cooler − cooling medium entering it (for an air-cooled oil cooler: oil out − cooling air in). Rise in leaving temperature = change in cooling-medium inlet + change in approach. Margin = applicable limit − leaving temperature. A change in approach larger than the measurement uncertainty points to the cooler core, fan or airflow; an unchanged approach with a hotter outlet points to a hotter heat sink (ventilation, recirculation). Readings must be at matched duty.
Water-side heat duty of a water-cooled compressor
Q (kW) = density × flow × specific heat × (water out − water in) ÷ 3,600, with flow in m³/h, density 1,000 kg/m³ and specific heat 4.18 kJ/(kg·K) for clean water.
Particle concentration from active sampling time
Active time = recorded time − time with no flow. Accepted volume (m³) = sampling flow (L/min) × active time (min) ÷ 1,000. Concentration = particles counted ÷ accepted volume. One particle more or less changes the result by 1 ÷ volume.
Total oil from fractions with “less than” results
Lowest possible total = sum of the measured values (a “less than” fraction counts as 0). Highest possible total = sum of all values (a “less than” fraction counts at its reporting limit). If the highest possible total is at or below the limit, compliance is shown; if the lowest possible total is above it, the limit is exceeded; otherwise compliance cannot be shown. A fraction that was not measured leaves the highest total unknown. Stated measurement uncertainty is not included here.
Particle count, sample volume and ISO 8573-1 class
Volume (m³) = counter flow (L/min) × sampling time (min) ÷ 1,000. Concentration = count ÷ volume. ISO 8573-1:2010 maximum particles per m³ (0.1–0.5 / 0.5–1 / 1–5 µm): Class 1: 20,000 / 400 / 10; Class 2: 400,000 / 6,000 / 100; Class 3: not specified / 90,000 / 1,000; Class 4: not specified / not specified / 10,000; Class 5: not specified / not specified / 100,000. The class is the lowest number whose limits are all met. Counting uncertainty at the target limit ≈ ±1/√N, where N is the count the limit corresponds to in this volume. Classes 6 and 7 are mass-based (ISO 8573-8) and Class 0 is by agreement; neither is covered here. Check the edition your requirement cites.
Acceptance coverage at the use point
Sampling is complete when every planned visit was made. Acceptance needs, for every contaminant in the requirement, a valid and complete result that meets the requirement at the use point (or a documented equivalent point). An invalid sample is not a failure, and an uncollected or incomplete sample is never a pass. One valid adverse result means the requirement is not met.
Pumping-test discharge stability and volume check
Each reading is converted to m³/h (1 L/min = 0.06 m³/h; 1 L/s = 3.6 m³/h; 1 imperial gallon = 4.54609 L; 1 US gallon = 3.78541 L). Mean = average of the readings. Deviation = (reading − mean) ÷ mean. Drift = (last − first) ÷ first. Volume = mean rate × hours actually pumping (elapsed time − stops). A reading that differs from the median by a factor near 3.6, 4.5, 16.7 or 60 is flagged as a possible unit mix-up. Screening result: not yet usable for drawdown analysis if the discharge is outside tolerance, a reading is zero, a unit mix-up is flagged or the pump stopped within the step; fit for a volume check when the totaliser or tank agrees within the tolerance. Screening only: aquifer properties and yield are for the hydrogeologist.
Drawdown with a measuring-point correction
All levels are depths below the original measuring point (casing top). A level read from ground level is converted by adding the stick-up (height of the casing top above ground). Drawdown = pumping water level − static water level, both from the same point. A drawdown that falls by more than the step threshold between two readings is flagged: during constant-rate pumping the level should not rise, so check for a pump stop, a flow change or a misread tape. Original readings are kept; the correction is shown separately.
Well production balance
Production = closing − opening totaliser reading (if the meter rolled over: rollover value − opening + closing). Storage change = closing volume − opening volume. Residual = production + other inflows − deliveries − other known outflows − storage change, also shown as a share of total inflow. A positive residual means more water entered than can be accounted for; a negative one means more appears to have left or been stored than entered. Either is an investigation item, not proof of a leak or meter fault.
Supported well production: Water time, not power-on time
Supported production = Σ(confirmed delivery rate × hours delivering at that rate). Energised hours = delivering hours + hours energised with no delivery (dry running, air lock). The overstated figures are energised hours × nominal rate and window × nominal rate. Unaccounted hours = window − delivering − dry − stopped.
DTH hammer duty against two compressors
Required discharge pressure = hammer working pressure + pressure loss from compressor to hammer (hose, swivel, drill string, check valves) + water column to be lifted (0.0981 bar per metre of water). A compressor whose maximum working pressure is below the required pressure fails, whatever its flow. Available flow = data-sheet flow at the required pressure × (1 − site derating). Margin (%) = (available flow − hammer consumption) ÷ hammer consumption × 100. Use the same flow basis (FAD or scfm) for hammer and compressor. 1 bar = 14.504 psi; 1 m³/min = 35.31 cfm. Hole cleaning (annular velocity) is a separate check.
Air motor duty check
Shaft power P (W) = 2 × π × n × T ÷ 60. Motor speed = load speed × gear ratio. Motor torque required = load torque ÷ (gear ratio × gearbox efficiency); the same for the breakaway (starting) torque. Margins = motor torque from the curve ÷ torque required − 1. Air demand = motor consumption × number running together. Result: Pass when running torque, starting torque and air supply are all met on data read at or below the pressure available at the motor inlet; Hold when data are missing or read at a higher pressure; Fail when any requirement is not met. For a direct drive enter ratio 1 and efficiency 100%. Peak and stall torque are not checked here: compare them with the maker’s curve separately.
Pneumatic conveying air estimate
Air mass flow = solids mass flow ÷ solids loading ratio (SLR). Free air = air mass flow ÷ free-air density, taken as 1.2 kg/m³ (air at about 1.01325 bar a and 20 °C). Actual flow at a line pressure p = free air × 1.01325 ÷ (p + 1.01325) × (T + 273.15) ÷ 293.15 (free air taken at 20 °C). Velocity = actual flow ÷ pipe area. The bore for a target pick-up velocity is √(4 × actual flow ÷ (π × velocity)). Bend, lift, feeder and filter losses are not calculated: the pressures are your inputs. For a vacuum (suction) system enter negative gauge pressures, pick-up nearest atmospheric. The velocity flags (15–25 m/s dilute pick-up, 30 m/s at the destination, 10 m/s dense phase) are screening values used by this tool, not material data.
Dryer capacity correction
Corrected capacity = rated capacity × F(pressure) × F(inlet temperature) × F(ambient) × F(dew point). Margin (%) = (corrected capacity − design flow) ÷ design flow × 100. Required rated capacity = design flow ÷ product of factors (× (1 + your margin) if you keep one); choose the next catalogue size at or above it. Use the factors for the exact model and revision from its data sheet; enter 1 for a factor the maker does not publish. If the maker publishes a combined chart instead, enter its single factor and 1 for the rest.
Compressor room cooling load
Q_room = Q_input − Q_water (leaving the room) − Q_recovered (used outside the room) − Q_other (leaving the room) + Q_dryers + Q_extra (other room loads), all in kW of heat. Cooling air: mass flow = Q ÷ (cp × ΔT), cp = 1.005 kJ/kg·K; volume = mass ÷ air density. Cooling water: mass flow = Q_water ÷ (4.19 × ΔT), volume at 1,000 kg/m³. Steady state, one operating case; enter the peak case for fan and pump sizing.
Expansion scenarios with N+1 check
Available with the largest unit out (N+1) = Σ compressor FAD − largest FAD, after any summer derating. Phase demand = previous peak + new users’ connected flow × simultaneity factor. Productive demand = baseline peak − measured leakage. Leak work subtracts the expected recovery (which cannot exceed the measured leakage). A scenario passes when its peak demand ≤ the N+1 capacity. Minimum single added unit = Phase 2 demand − (Σ existing − largest existing); if that exceeds the largest existing unit, no single machine restores N+1.
Branched network pressure drop
Trunk flow = sum of branch flows. Each segment: Darcy–Weisbach ΔP = f × (L/D) × ρv²/2, Swamee–Jain friction factor, air density at the segment’s mean pressure, flow converted from free air to actual flow at line pressure and temperature. Junction pressure = source − trunk drop; user pressure = junction − branch drop. The critical node is the one with the smallest margin over its minimum pressure. Use real internal diameters; lengths may already include fittings (then enter 0% allowance). This tool solves a single-source tree only (one trunk, one junction, up to three branches). Ring mains, loops (Hardy Cross), several sources and field calibration are NOT solved here; for those, a model is built during a pressure-drop audit. An unused branch (flow 0) is ignored.
Vacuum pump-down time and required pumping speed
Ideal pump-down: t = (V ÷ S_eff) × ln(p₀ ÷ p₁), with V the whole evacuated volume (vessel, piping, filters, condensers), absolute pressures and S_eff the average effective speed over the range. Effective speed through a line: 1/S_eff = 1/S_pump + 1/C. A continuing gas load Q (leaks, outgassing, vapour, as pressure × volume flow) sets a floor p_floor = Q ÷ S_eff; with that load the time becomes t = (V ÷ S_eff) × ln((p₀ − p_floor) ÷ (p₁ − p_floor)), and a target at or below the floor is never reached. Holding duty: the effective speed needed to hold a pressure p against Q is Q ÷ p. Required speed for a target time: S_eff = V × ln(p₀ ÷ p₁) ÷ t (solved numerically when there is a gas load), then the pump speed that gives it through the line. Units: 1 L/s = 3.6 m³/h; 1 mbar·L/s = 3.6 mbar·m³/h. Water boils when the pressure falls below its vapour pressure (Magnus formula: about 23 mbar at 20 °C, 42 mbar at 30 °C). Constant speed is assumed: real pumps lose speed towards their ultimate pressure, so treat the result as a lower bound and check the maker’s curve, or use the banded tool.
Banded pump-down time from the pump curve
For each band from pₐ down to p_b: S_eff = 1 ÷ (1/S + 1/C), floor p_f = Q ÷ S_eff, t = (V ÷ S_eff) × ln((pₐ − p_f) ÷ (p_b − p_f)) (with Q = 0 this is the ideal V/S × ln(pₐ/p_b)). The band times are added. If a band end is at or below its floor, the pump-down stops there. Smaller bands give a better answer where the curve changes quickly. Enter one conductance for all bands, or one per band (conductance falls at lower pressure in viscous flow).
Vacuum line conductance and effective speed
Long round pipe, air at about 20 °C, d and L in cm: molecular flow C ≈ 12.1 × d³ ÷ L L/s; viscous (laminar) flow C ≈ 135 × d⁴ × p̄ ÷ L L/s with p̄ the mean pressure in mbar. Regime from the Knudsen number Kn = λ ÷ d, mean free path λ ≈ 0.066 mm at 1 mbar, inversely proportional to pressure: viscous below Kn 0.01, molecular above 0.5, transitional between (this tool then adds the two, an indicative figure; use maker’s data). Series elements: 1/C_total = Σ 1/Cᵢ. Effective speed: 1/S_eff = 1/S + 1/C_total. Required effective speed for a gas load: S_eff = Q ÷ p (the mean line pressure is taken as the chamber pressure for this check). 1 L/s = 3.6 m³/h. Short pipes (L less than about 20 d) need an entrance correction; near atmospheric pressure flow may be turbulent or choked and the laminar formula is optimistic.
Vacuum rate-of-rise gas load
Q = V × Δp ÷ Δt, with V in litres, Δp in mbar and Δt in s, gives Q in mbar·L/s (× 3.6 = mbar·m³/h; × 0.1 = Pa·m³/s). Mass of air at 20 °C: 1 mbar·L/s ≈ 4.28 g/h. Curve shape (screening values used by this tool): a later interval rising at 80% or more of the first rate points to a real leak; 50% or less points to outgassing or vapour levelling off; between, a mixture. Required effective speed to hold a working pressure p: S = Q ÷ p. The isolated volume must include every pipe up to the closed valve; record temperature, because a warming vessel shows a rise of its own. A leak from atmosphere stays roughly constant only while the inside pressure is well below about half an atmosphere.
Vacuum degassing gas and vapour load
Gas released = throughput × dissolved content × share removed; add the design air leak. Specific volume of air v = R × T ÷ p = 287.05 × (t + 273.15) ÷ (p × 100) m³/kg (about 17 m³/kg at 50 mbar, 20 °C). Gas volume at the vacuum = mass × v. If the gas leaving is saturated with the liquid’s vapour, the vapour share by volume is p_v ÷ p and the total volume flow is the gas volume ÷ (1 − p_v ÷ p); water vapour carried = gas mass × (18.02 ÷ 28.97) × p_v ÷ (p − p_v). Water vapour pressure from the Magnus formula (about 23 mbar at 20 °C). The dissolved gas is taken as air. If the operating pressure is at or below the vapour pressure the liquid boils and the vapour flow is set by the heat input, which this estimate cannot give.
Vacuum dryer water removal, heat and vapour load
Wet-basis moisture: dry solids = M × (1 − w₀); final mass = dry ÷ (1 − w₁); water = M − final. Average rate = water ÷ cycle time; peak rate = water × share removed in the peak period ÷ its length. Heat (kW) = rate (kg/h) × latent heat (kJ/kg) ÷ 3,600, plus heat losses. Vapour specific volume = 461.5 × (t + 273.15) ÷ (p × 100) m³/kg (about 28 m³/kg at 50 mbar, 30 °C). Boiling temperature of water at the chamber pressure from the Magnus formula (about 33 °C at 50 mbar, 7 °C at 10 mbar). A condenser surface condenses water only if its saturation pressure is below the chamber pressure; the vapour left in the gas is about the saturation pressure at its coldest surface (over ice below 0 °C). Dry-basis or loss-on-drying figures must be converted to wet basis first.
Water vapour condensation check
Water condenses on a surface when its partial pressure is above the saturation pressure at the surface temperature. Saturation pressure (Magnus formula): over water 6.112 × exp(17.62 t ÷ (243.12 + t)) mbar; over ice, below 0 °C, 6.112 × exp(22.46 t ÷ (272.62 + t)). About 6 mbar at 0 °C, 12 at 10 °C, 23 at 20 °C, 38 at 28 °C, 42 at 30 °C; ice about 1 mbar at −20 °C. The inverse gives the dew (or frost) point: the highest surface temperature that condenses the vapour. Gas leaving a condenser carries about the saturation pressure at its coldest surface. The gauge reads total pressure: where air or other gas is present, enter the water vapour partial pressure. Water only: for solvents use their own vapour-pressure data. Range of the formula about −65 to +100 °C.
Vacuum forming reserve tank and pump recovery
Equalised pressure when the valve opens (fast, isothermal transfer): p = (p_r × V_r + p₀ × V) ÷ (V_r + V). Reserve volume needed for a target p_t: V_r = V × (p₀ − p_t) ÷ (p_t − p_r). Recovery with an ideal pump of effective speed S on the whole connected volume: t = ((V_r + V) ÷ S) × ln(p ÷ p_r). If the time available is shorter, the pressure reached is p × exp(−S t ÷ (V_r + V)); repeating that each cycle, the start pressure settles at the value where one cycle’s rise equals the pump’s recovery. Ideal pump, no leakage or line losses: check against the pump curve and measured cycle data.
Vacuum holding force
Force F = Δp × A, with Δp the pressure difference below atmosphere in Pa (1 bar = 100,000 Pa; 1 mbar = 100 Pa) and A the effective sealed area in m² (cup: π/4 × d² × number of cups; table: area × share covered). 0.2 bar acts as about 2 tonnes-force per m². Usable force = F ÷ safety factor: at least 2 is common for a straight vertical lift, 4 or more for a cup loaded in shear on a vertical face (friction carries the load). Required force = m × (g + a), with a the highest acceleration including emergency stops. Use the vacuum measured at the part, not the pump rating; the maximum possible Δp is the local atmospheric pressure (about 1.013 bar at sea level, about 0.95 bar at Hyderabad). Use the cup maker’s data for oily, dusty, textured or curved surfaces.
Vacuum ejector compressed-air consumption
Average motive air = rated consumption (Nl/min at the stated feed pressure) × on-time ÷ cycle time. Blow-off per cycle = blow-off flow × pulse ÷ 60 (litres); per minute = that × 60 ÷ cycle time. Total per gripper = motive + blow-off; line total = × number of ejectors. Peak = rated consumption × the number that can be on at once: it sizes the supply pipework, regulator and local receiver. 1 cfm = 28.317 l/min; normal litres are at reference conditions. Energy: line flow (m³/min) × specific power × hours. Air-saving (vacuum-hold) circuits reduce the on-time on sealed parts; use the measured on-time. Leaks are not included.
Liquid-ring seal-liquid flow and vapour-pressure margin
Mass flow m = Q ÷ (c_p × ΔT) (kW, kJ/kg·K, K → kg/s); volume flow = m ÷ ρ × 3,600 m³/h. In total recirculation the cooler rejects the same heat Q. The ring liquid is hottest at the outlet (supply + ΔT); the pump cannot hold a suction pressure close to the liquid’s vapour pressure there. Water vapour pressure (Magnus formula): about 17 mbar at 15 °C, 32 at 25 °C, 56 at 35 °C, 96 at 45 °C. Screening value used by this tool: suction pressure at least 1.5 × the vapour pressure at the outlet temperature; closer than that, capacity falls and cavitation is likely. Pure water only: dissolved solvent, salt or glycol changes the vapour pressure, and the maker’s performance and cavitation curves govern. Condensing process vapour adds to the liquid inventory and must leave by overflow or purge.
Central vacuum plant demand and N+1 check
Each user flow is converted to the plant set point at constant mass and temperature: q_plant = q × p_machine ÷ p_set (the same gas takes more volume at the deeper plant vacuum). Design flow = Σ(number × flow × simultaneity) + leakage + future users. Duty pumps = design flow ÷ capacity of one pump at the set point, rounded up. N+1 passes when the pumps left with one out of service still cover the design flow. The set point must be at least the header loss deeper than the most demanding machine needs; a deeper set point than that costs pump capacity. Receiver for a short peak: V = peak excess flow × duration × p_set ÷ allowed rise. All pumps are taken as the same size; use measured simultaneity and leakage where you can.
Aeration blower duty: Pressure budget, flow basis and power
Static head = depth × density × g = about 0.0981 bar per metre of fresh water (× relative density for sea water or broth). Discharge pressure (gauge) = static head + vessel back-pressure + diffuser or sparger loss + pipe, valve and meter losses + treatment losses + margin. The inlet filter and silencer loss lowers the inlet absolute pressure, so blower differential = discharge pressure + inlet loss and pressure ratio = (atmospheric + discharge) ÷ (atmospheric − inlet loss). Flow: actual inlet volume = normal volume × (T_inlet ÷ 273.15 K) × (1.01325 ÷ p_inlet absolute), dry air; vvm × working volume × vessels is taken on the normal basis (0 °C, 1.013 bar a). Power: a Roots blower has no internal compression, so its ideal air power is inlet flow × differential; a screw blower, centrifugal or compressor is taken as isentropic, P = Q₁ × p₁ × k/(k−1) × (r^((k−1)/k) − 1) with k = 1.4. Shaft or input power = ideal power ÷ overall efficiency. Ideal discharge temperature: Roots T₁ × (1 + (r − 1)(k − 1)/k); internal compression T₁ × r^((k−1)/k); real machines run hotter. Screening values; select from the maker’s curve at the hottest inlet and the fouled-diffuser pressure.
Blower duty points and hours-weighted energy
Static head = depth × relative density × 0.0981 bar per metre. Friction (diffusers, pipework, valves) is taken to rise with the square of flow: Δp_friction = Δp_design × (Q ÷ Q_design)². System pressure = static + friction + fouled-diffuser allowance. Ideal (isentropic) air power at each point = Q₁ × p₁ × k/(k−1) × (r^((k−1)/k) − 1), k = 1.4, inlet at site atmospheric pressure. Wire-to-air efficiency = ideal air power ÷ package input power (motor, VSD, bearings and cooling). Annual energy = Σ package kW × hours at that point; the hours-weighted average kW = annual energy ÷ total hours. The default kW figures are illustrative only: enter each bidder’s package input power at your duty points, under the same inlet conditions.
Blower station firm capacity, turndown and coverage
Each running blower can deliver anywhere between its minimum stable flow (maker’s minimum speed or surge limit at that pressure) and its maximum flow, so a combination covers Σ minimum to Σ maximum. The station range is the union of all combinations; any flow outside it is a gap. Firm capacity = total maximum − largest maximum. Station turndown = firm capacity ÷ smallest stable output. A demand point below the minimum air for diffuser mixing is raised to that floor. For each demand point the tool picks the combination with the fewest machines (then the smallest total capacity) and checks whether the point can still be met with the largest machine out of service. Up to 8 blowers. Pressure: use the aeration pressure budget tool; flows here must all be at the same pressure and on the same basis.
Silo and hopper aeration air estimate
Bed head (bar) = bed height × aerated bulk density × 9.81 ÷ 100,000. Supply pressure = bed head + element (pad or fabric) loss at design flow + branch, valve and hose losses. Simultaneous flow = active area per zone × maker’s flow per unit area × zones running together × (1 + start-up allowance) + coinciding pulsed devices. The all-zones figure is shown only to show how far summing every pad oversizes the supply. Header comparison: ideal isentropic power is proportional to (r^((k−1)/k) − 1), so compressing to the plant header and throttling down costs that ratio of power against compressing only to the supply pressure. Use the element maker’s pressure–flow curve and the conveying or silo designer’s figures; a trial on the actual powder is the most reliable basis.
Combustion-air blower duty
Dry-air density ρ = P ÷ (R × T), with P absolute in Pa, R = 287 J/(kg·K) and T in kelvin. Actual inlet volume = mass flow ÷ ρ. The reference volume uses 101.325 kPa and 20 °C. Required blower pressure = Σ the element losses for the case being checked (intake and filter, duct, silencer, damper or register, burner internal loss, chamber back-pressure). Enter a separate list for low, normal and peak fire, because damper losses fall as the damper opens while the others rise roughly with the square of flow. Ideal air power = (Q ÷ 3,600) × Δp; shaft power = air power ÷ blower efficiency. Turndown gap = stable minimum flow − low-fire flow. Air proving, purge and safety settings come only from the burner supplier.
Blower pulsation frequency and pipe resonance check
Excitation f = shaft rpm ÷ 60 × discharge pulses per revolution × harmonic number (2-lobe Roots 4 pulses, 3-lobe 6, or as the maker states), taken from minimum to maximum speed. Speed of sound c = √(k × R × T), T in kelvin. Half-wave (both ends open, or both closed): f_m = m × c ÷ (2L). Quarter-wave (one end open, one closed): f_m = (2m − 1) × c ÷ (4L). A mode within a band (widened by the separation margin) is flagged with the shaft speed that would excite it; with a VFD, the drive frequency is pro-rata to speed from the frequency at maximum speed. Screening only: the acoustic and pipe-stress design for a large installation stays with the blower maker, the silencer supplier and the piping engineer.
Gas compression stage screening
P(abs) = P(gauge) + site atmospheric pressure. Overall ratio r = P₂(abs) ÷ P₁(abs); dividing gauge figures gives a wrong ratio, worst at low suction pressure. Equal split: stage ratio = r^(1/n); interstage pressure after stage i = P₁ × (stage ratio)^i. Ideal (isentropic) discharge temperature T₂ = T₁ × (stage ratio)^((k−1)/k), kelvin, assuming intercooling back to the suction temperature before every stage; with an isentropic efficiency η, T₂ = T₁ + (T₂ideal − T₁) ÷ η. Gas constant R = 8,314.46 ÷ molecular weight. Actual suction volume = ṁ × Z × R × T₁ ÷ P₁; normal volume uses 0 °C and 1.01325 bar a with Z = 1. Transferred mass = mass flow × running hours. Rounded textbook k values near ambient; real-gas Z and the maker’s calculation for the actual composition govern. These are screening values, not equipment ratings or settings.
Pressure ratio for a blower or compressor duty
p(abs) = p(gauge) + local atmospheric pressure (about 1.013 bar a at sea level, lower at altitude). Differential = outlet − inlet (absolute). Pressure ratio = absolute outlet ÷ absolute inlet. Ideal discharge temperature: with internal compression (screw, centrifugal, compressor) T₂ = T₁ × r^((k−1)/k); a Roots blower has no internal compression, so ideally T₂ = T₁ × (1 + (r − 1)(k − 1)/k), which is hotter. Vocabulary bands used here: up to about 1.1 fan range; up to about 2 the duty is sold as a blower (Roots, screw, side-channel, centrifugal); about 2 to 4.5 (roughly 1–3.5 bar g from atmosphere) is the grey area where screw blowers, low-pressure oil-free screw compressors and multistage centrifugals compete; plant-air compressors work at about 8–11. Select from the maker’s envelope, not a label.
Drilling booster: Pressure ratio, water head and air volume
Ratio = (P₂ gauge + atmospheric) ÷ (P₁ gauge + atmospheric). Water head = ρ × g × h with g = 9.81 m/s² and h the vertical water column above the hammer (not drilled depth): about 1 bar per 10 m. Free air (mass) is set by the primary compressor and is unchanged through the booster. Actual volume entering the booster = FAD × (P_atm ÷ P₁ abs) × (T₁ ÷ T_ambient); leaving it, Q₂ = Q₁ × (P₁ ÷ P₂) × (T₂ ÷ T₁), absolute pressures and kelvin. Ideal single-stage discharge temperature T = T₁ × ratio^0.286 (air). Pressure needed at the booster outlet = hammer working pressure + string losses + annular back-pressure + water head + margin. Static planning estimates: aeration of the water column, inflow and cuttings change the real figure, and the booster’s capacity comes from its maker’s data at the stated inlet conditions.
Blow-tank batch air budget
Pressurisation air (free air) = free gas space × conveying pressure (gauge) ÷ atmospheric pressure. Conveying air = conveying flow × conveying time; clearing air = clearing flow × clearing time; fluidising and booster air is added per batch. Batches per hour = 3,600 ÷ cycle time in seconds; theoretical throughput = usable batch mass × batches per hour (a schedule check only). Average demand = air per batch × batches per hour ÷ 60. Peak rates: pressurisation air ÷ pressurisation time, and the conveying and clearing flows. Receiver: the free air the compressor cannot supply during pressurisation, conveying and clearing, Σ max(0, phase rate − compressor delivery) × phase time, is drawn from storage; V = shortfall × P_atm ÷ usable pressure band (isothermal, as in the receiver tool). The conveying pressure and air flow come from the conveying designer.
Vessel filling: Free air and fill time
Free air to add = V × (p₂ − p₁) ÷ p₀, with p₁ and p₂ the start and end pressures (a gauge difference equals an absolute difference) and p₀ the atmospheric pressure, about 1.013 bar a. The “absolute pressure ratio” basis, V × (p₂ − p₁ + p₀) ÷ p₀, adds one volume of free air: for a volume that starts at atmospheric pressure it equals V × p₂(abs) ÷ p₀. It counts the air already inside, so it overstates what must be pumped in by one vessel volume; some procedures use it as a conservative figure. Fill time = free air ÷ supply flow (the supply flow is compressor FAD at the final pressure, or regulator flow capacity, as free air). Flow for a required time = free air ÷ time. Average demand = free air per fill × fills per hour + make-up flow. Receiver able to give one whole fill on its own = free air per fill × p₀ ÷ (receiver charge pressure − lowest pressure the user accepts). Isothermal and ideal gas: a fast fill heats the air, which then cools and loses pressure, so allow extra; real fill time through a regulator is longer than the minimum shown because flow falls as the pressure difference shrinks near the set point.
Pipeline pigging: Air volume, run time and driving pressure
Line volume V = π × D² ÷ 4 × L (internal diameter). The space behind the pig starts empty and ends full of air at the driving pressure, so free air = V × (p_g + p₀) ÷ p₀, plus your allowance for hose and launcher volume, leakage and bypass past the pig. Run time = free air ÷ total FAD (1 m³/min = 35.31 cfm). Pig speed ≈ actual air flow at driving pressure ÷ pipe area = FAD × p₀ ÷ (p_g + p₀) ÷ area. Driving pressure needed ≈ pig friction + liquid head (ρ g h: 0.0981 bar per metre of water lifted × specific gravity) + back-pressure at the receiver. Temperature and pressure gradient along the line are ignored. The maximum permitted driving pressure and any speed limit come from the pipeline owner’s procedure, never from the compressor rating.
Tyre top-up air, forecourt peak and receiver reserve
Free air per tyre = tyre volume × (target − start pressure) ÷ atmospheric pressure (same pressure unit; constant tyre volume and temperature). Idealised time = free air ÷ effective transfer rate × 60; real time is longer as the pressures equalise, and handling time is extra. Average demand = free air per vehicle × vehicles per hour. Coincident demand = points × transfer rate; deficit = coincident demand − compressor delivery; reserve needed = deficit × overlap duration. Usable receiver reserve = receiver volume × usable band ÷ 1.013 (isothermal). Receiver needed = reserve × 1.013 ÷ band. Recovery time = reserve ÷ (compressor delivery − air still being used). Illustrative screening figures, not promised service times. 1 cfm = 28.3168 L/min.
Valve actuator air per stroke, peak flow and reserve receiver
Free air per stroke = (swept volume + tubing volume + other volume filled each stroke) × (p + p₀) ÷ p₀, with p the supply pressure in bar g and p₀ ≈ 1.013 bar a. Cylinder swept volume: extend = π/4 × D² × stroke; retract = π/4 × (D² − d²) × stroke. Tubing volume = π/4 × (inside diameter)² × length, filled once per stroke on the side being pressurised. Double-acting: a full cycle is two strokes (both directions). Spring-return or single-acting: one air stroke per cycle. Average flow needed during a stroke = free air per stroke ÷ stroke time; this is the flow the solenoid valve, tubing and regulator must pass, before allowing for pressure build-up time and margin (valve Kv ≈ 0.86 × Cv; select from the maker’s flow charts at an acceptable pressure drop). Average demand = free air per cycle × cycle rate × number of actuators + steady positioner bleed. Reserve receiver for the worst case = free air for the actuators that move together × p₀ ÷ (normal pressure − lowest pressure the actuators accept); isothermal, add margin.
Rotary actuator torque margin check
Required torque = valve torque × (1 + margin ÷ 100), with the margin the valve maker recommends for the service (often 20–50%). Double-acting: air start torque must exceed breakaway, the lower of air start and air end must exceed running, and air end must exceed seating (closing by air). Spring-return (air opens, spring closes): air start ≥ breakaway, air end ≥ running, spring start ≥ running, spring end ≥ seating, so the spring can close the valve on loss of air. Read the actuator torques from the maker’s table at the lowest pressure the actuator reliably receives, not at header pressure. Energy at end of travel = ½ × J × ω²; with ω = angle ÷ swing time this is the mean-speed value; a load that accelerates uniformly arrives at twice the mean speed and four times this energy.
Robot cell air per cycle
Actuator free air per stroke = (swept volume + hose and valve dead volume) × (p + 1.013) ÷ 1.013; per cycle × strokes per cycle. Ejector and nozzle air per cycle = rated consumption (L/min free air) × on-time per cycle ÷ 60. Average flow = air per cycle ÷ cycle time × (1 + re-pick allowance) + tool-change air per hour ÷ 60. Indicative peak = all ejectors and nozzles on together + the largest actuator stroke filled in the gripper close time. Illustrative defaults (the page gives no figures): replace them with your gripper and ejector data.
Machine air per cycle and per accepted item
Air per cycle = total free air ÷ completed cycles. Air per accepted item = total ÷ good items. Average flow = total ÷ window duration (1 m³/min = 35.31 cfm). Peak-to-average = peak short-interval flow (state the averaging interval) ÷ average. Reject share = 1 − good ÷ cycles. Repeatability = (highest − lowest) ÷ mean of the repeat-window results; if it exceeds the meter uncertainty, the machine is not yet stable. State the flow basis (FAD, Nm³ or scfm) and convert to the compressor’s FAD basis before sizing.
Pneumatic cylinder force and bore selection
Push area A = π × D² ÷ 4; pull (annulus) area = π × (D² − d²) ÷ 4. Force (N) = pressure (bar g) × area (cm²) × 10, since 1 bar on 1 cm² ≈ 10 N. Net force = driving pressure × driving area − exhaust back-pressure × exhausting area (friction and load still to come off). Theoretical force needed = load ÷ load ratio (about 0.5 for dynamic duties, up to about 0.7 for slow, near-static duties). The smallest standard bore is the first in the series 12–320 mm (typical rods as in the table on the page; check the data sheet) whose net force in that direction reaches the force needed. Mean speed = stroke ÷ travel time; free-air flow during the stroke = area × speed × (p + 1.013) ÷ 1.013; kinetic energy = ½ m v² at mean speed (the real end speed can be higher; a descending vertical load adds gravitational energy).
Actuator pressure for a web tension or force
Web tension = tension per unit width × width (or enter the actuator force directly). Actuator force = tension × dancer geometry factor ÷ number of actuators sharing it (a dancer roll with a 180° wrap carries about twice the web tension; use the machine builder’s geometry). Effective area = π × D² ÷ 4. Pressure (Pa) = force ÷ area; 1 bar = 100,000 Pa. Working pressure = pressure × (1 + friction allowance ÷ 100). Brake torque = web tension × roll radius; it falls as the roll diameter falls. The regulator needs its inlet a margin above the set pressure.
Tool air demand: Connected, average and credible peak
Connected = Σ(number × rating) + background. Average = Σ(number × rating × duty cycle) + background. Credible peak = Σ(number running in the largest credible overlap × rating) + background. Ratings are free air at the tool’s rated pressure (usually 6.2 bar g, 90 psig); consumption rises roughly in proportion to absolute inlet pressure. Suggested capacity = peak × (1 + margin). If a compressor FAD below the peak is entered, the receiver to carry the peak for its duration = (peak − FAD) × duration × 1.013 ÷ allowed pressure fall. 1 m³/min = 35.31 cfm = 16.67 L/s.
How many breakers or rock drills a compressor can run
Air per tool with margin = rated consumption × (1 + margin ÷ 100); the page suggests 15–25%. Tools supported = whole number of FAD ÷ air per tool with margin. FAD needed for n tools = n × consumption × (1 + margin). Portable classes: 185–250 cfm, 250–400 cfm, 400–600 cfm (5.2–7.1, 7.1–11.3, 11.3–17 m³/min). Use the maker’s consumption at the pressure the tool really receives; consumption rises with inlet pressure. Hose guide: 19 mm (3/4 in) for one tool up to about 15–20 m; a 25 mm (1 in) or larger main hose to a manifold with short 19 mm whips for longer runs or two or more tools.
Cooling heat balance and compressed-air cooling energy
Cooling duty (W) = internal heat + wall gain + solar/radiant gain + product heat, with product heat = mass flow (kg/h) ÷ 3,600 × specific heat (kJ/kg·K) × 1,000 × temperature drop (K). Sensible cooling by air: air mass flow = duty ÷ (1,005 J/kg·K × air temperature rise); free-air flow = mass flow ÷ 1.204 kg/m³ (20 °C, 1.013 bar a). Compressor power attributable to a device = its air consumption (free air, m³/min) × station specific power (kW per m³/min). Annual energy = kW × running hours (use thermostat-controlled hours where fitted). Illustrative defaults (the page gives no numbers): enter your own heat loads, device rating and station specific power.
Pressure-decay leak rate and thermal sensitivity
Leak rate Q = V × ΔP ÷ (t × P_ref) in cm³/s at the reference pressure (sccm = cm³/s × 60). V must be the total test volume: part, fixture cavities, seal spaces, tubing, valves and transducer. Thermal effect in a fixed volume: ΔP = P_abs × ΔT ÷ T_abs, with P_abs = (test pressure + atmospheric) × 100,000 Pa and T_abs = T + 273.15 K. Pressure drop at the leak limit = limit (sccm) ÷ 60 × t × P_ref ÷ V. Station air per cycle = V × (p + p₀) ÷ p₀ (filled then vented). Illustrative method only: stabilisation and test times come from trials on known good and leaking masters.
Artificial demand after a pressure change
Pressure-sensitive users behave like a fixed opening: at choked conditions free-air flow is proportional to absolute upstream pressure, so Q_new = Q_old × (p_new + p₀) ÷ (p_old + p₀). The gauge ratio p_new ÷ p_old overstates the change and is shown only as the pitfall. Compressor saving from the lower set point = input kW × Δp × saving per bar (about 7% per bar is typical; edit it). Energy of the air no longer used = air saved (m³/min) × specific power × hours. The two overlap; the combined estimate = kW − (kW − air saved × specific power) × (1 − saving per bar × Δp). Regulated users and process users with a fixed mass flow do not respond. Teaching estimate: prove the saving by a stepped trial with logged flow and power.
System leakage test: Load/unload timing, residual flow or pressure decay
Load/unload timing (fixed-speed load/unload compressor, production stopped, timed over several cycles): leakage ≈ FAD × T ÷ (T + t), with T the loaded and t the unloaded time per cycle. Residual flow (flow meter, production stopped): unexplained residual = measured residual flow − verified legitimate users (dryer purge, instrument air, drains); it is the figure to investigate, not automatically all leakage. Pressure decay (compressors stopped and isolated, no users): leakage in free air ≈ V × (p_start − p_end) ÷ (p_atm × time), with V the receiver plus pipework volume in m³, pressures in bar and time in minutes; the pressure difference is the same in gauge or absolute terms. Leak flow through an orifice rises roughly in proportion to upstream absolute pressure, so a result taken at one pressure is restated at the normal operating pressure by × (p_op + p_atm) ÷ (p_test + p_atm). Leak power = leakage × station specific power (kW per m³/min); annual energy = power × pressurised hours. The after-repair figure must come from the same method at the same pressure. The measured-power option gives (kW before − kW after) × idle hours, which is a measured saving, not an estimate. Money is shown only when you enter your own tariff.
Receiver volume to limit load/unload cycling
V = 0.25 × q × p_atm ÷ (f × Δp), with V in litres, q the compressor free air delivery in L/s, f the maximum load cycles per second the maker allows (1 cycle per 30 s = 0.033 per s) and Δp the load/unload band in bar. The worst case is demand equal to half the compressor output, which is where 0.25 comes from. Rearranged, the shortest cycle with an existing receiver = V × Δp ÷ (0.25 × q × p_atm). Unit factors: 1 cfm = 0.472 L/s, 1 m³/min = 16.67 L/s. Pipework adds a little storage. The 6–12 litres per cfm range is the page’s rough guide for a single load/unload screw compressor; peak and standby-bridging duties are sized with the receiver storage tool, and the largest of the volumes is used.
Receiver pump-up test: Estimated free air delivery
FAD ≈ V × (p_end − p_start) ÷ p_atm ÷ t × (T_intake ÷ T_receiver), with V in m³ (receiver plus connected pipe), pressures in bar, t in minutes and temperatures in kelvin. With equal temperatures the correction is 1 (isothermal). Expected time at the rated FAD = V × Δp ÷ (p_atm × FAD_rated) × (T_intake ÷ T_receiver). It is a screening test: warm air in the receiver, an unknown pipe volume and a 1 s timing error all move the result, so a machine is judged far off its rating only with a clear margin. For a definitive figure use a flow meter or an air audit.
Nitrogen generator feed-air compressor sizing
Feed air per generator = nitrogen flow × air factor (same reference basis), or the feed-air flow from the data sheet. Total = per generator × number running together. Losses outside the air factor (for example heatless desiccant dryer purge, as a share of compressor delivery): total ÷ (1 − loss). Margin: × (1 + margin). Conversion to FAD at site inlet: Q_FAD = Q_ref × (p_ref ÷ p_inlet) × (T_inlet ÷ T_ref), absolute values; Nm³/h is 0 °C and 1.01325 bar a; for scfm enter the reference temperature its quoter uses (at 1.01325 bar a). Minimum compressor discharge pressure = generator minimum inlet pressure + filter, dryer and pipe losses. The air factor must come from the selected generator’s data at your purity, pressure and temperature; it rises steeply with purity.
Electric vs diesel compressor running cost
Electric energy = package input kW at the duty × running hours. On grid power: cost = kWh × tariff + demand or fixed charges. On a DG set: DG diesel = kWh × the DG’s litres per kWh at its expected load (from the DG data; light loading raises it), cost = litres × diesel price + fixed charges. Diesel portable: fuel = litres per hour at the expected load × hours; cost = litres × diesel price + engine servicing per hour × hours. Break-even tariff = (diesel L/h × price + servicing per hour) ÷ electric kW: below it, grid electric is cheaper to run. No prices are assumed; enter your own.
Heat recovery: Compressor supply vs hot-water demand
Supply per day = recoverable heat (kW) × overlapping hours. Demand per day = litres × temperature rise × 4.186 kJ/(kg·K) ÷ 3,600, about 1.16 kWh per 1,000 litres per °C. Useful recovery = the lower of the two. Fuel energy displaced = useful heat ÷ efficiency of the heater it replaces; fuel quantity = that energy ÷ the fuel’s calorific value (net values used here: diesel about 9.9 kWh per litre, furnace oil about 10.7 kWh per litre, LPG about 12.8 kWh per kg). Recoverable heat = compressor input power × the share the maker states is recoverable for the model and recovery method (see the heat recovery tool).
Combined savings of interacting energy measures
Each measure’s stand-alone saving is turned into a fraction of the baseline. Applied in sequence, each measure saves its fraction of the energy left by the measures before it: saving_i = residual_(i−1) × fraction_i, residual_i = residual_(i−1) − saving_i. Combined saving = baseline − final residual. The combined total does not depend on the order, but the saving credited to each measure does, so list the measures in the order they will be done (usually leaks and demand first, then pressure, then supply matching, then replacement and heat recovery). This is a multiplicative screening model; verify each stage by measurement against the adjusted baseline.
VSD trim control-gap check
VSD minimum flow = maximum × minimum %. Usable range = maximum − minimum. A control gap exists when the largest fixed-speed step is larger than the usable range. When demand rises just above the VSD maximum, the fixed machine starts and the VSD must fall to demand − step; below its minimum it cannot, so demand between the VSD maximum and (fixed step + VSD minimum) cannot be followed smoothly. Gap width = step − usable range. Minimum VSD maximum flow to close the gap = step × (1 + margin) ÷ (1 − minimum %), at the same turndown. Use the maker’s minimum flow; many VSD screws turn down to about 20–40%.
FMEA risk priority number with severity review
Enter one score per failure mode in each list, in the same order (Item 1, Item 2 …), on the site’s own 1–10 scales. Detection: 10 = will not be detected before it acts. RPN = S × O × D (maximum 1,000). Items are ranked by RPN; equal RPNs are ordered by severity. Any item with severity at or above the review threshold is listed separately, because multiplying ordinal scores can hide a rare but serious failure behind a frequent nuisance. The RPN sorts work; it is not a probability.
Compressor motor overload setting and supply unbalance
Overload setting = motor nameplate full-load current (at the actual supply voltage) × the service factor or ambient correction from the relay and motor makers. On a star-delta starter with the relay in the winding (phase) circuit, the winding current is line current ÷ √3, so the setting is FLC ÷ √3 (about 58% of FLC); in the line circuit it is FLC. Typical starting current (page table, typical values only): DOL 6–8 × FLC; star-delta about one third of DOL (2–2.7 × FLC); soft starter 2–4 × FLC; VFD about 1 × FLC. Unbalance (%) = largest deviation from the average ÷ average × 100 (the common definition used in motor standards); voltages phase to phase, currents in the three lines, all under load. A small voltage unbalance produces a much larger current unbalance and extra winding heating.
Drilling fuel and cost per metre: Two air packages
Productive hours = hours in the period − downtime. Accepted metres = productive hours × average penetration rate. Fuel: either the litres used in the period, or litres per drilling hour × productive hours. Fuel per metre = litres ÷ metres. Time per metre = 60 ÷ penetration rate (minutes). Effective rate = metres ÷ all hours in the period (penetration × availability). Cost per metre = (fuel × diesel price + other period costs such as crew, hire or ownership, bits, hammer, servicing) ÷ accepted metres. Project: drilling hours = metres ÷ penetration rate; scheduled hours = metres ÷ effective rate; fuel = metres × fuel per metre. Availability from records = MTBF ÷ (MTBF + MTTR). Use several holes or a month, not one day; the comparison works in litres, metres and hours whatever your prices.
Pumping test: Drawdown, specific capacity and pumped volume
Drawdown s = pumping water level − static water level (both as depths below the same datum, e.g. top of casing). Specific capacity = discharge Q ÷ s, quoted with the rate and the pumping duration, because it usually falls as the rate rises and as pumping continues. Pumped volume V = Q × t, valid only while the discharge is constant; for a varying discharge add the measured interval volumes. 1 L/s = 3.6 m³/h = 60 L/min.
Borewell air-lift start pressure and submergence
Start pressure ≈ submerged length of the air line × 0.0981 bar per metre of fresh water (10 m ≈ 0.98 bar ≈ 14.2 psi) + hose and fitting losses. The submerged length is measured from the water level at the time of starting to the air-line foot; once lifting begins the working pressure usually falls. Submergence ratio = submerged length ÷ (submerged length + lift from the water level to the discharge point); about 60% is commonly quoted as a target, and lower submergence lifts water poorly. Free air delivery is a volume at inlet conditions, so hot intake air carries less mass: mass ratio = (20 + 273.15) ÷ (intake °C + 273.15).
Borewell production forecast
Scheduled hours H = hours per day × days − planned maintenance hours removed from the schedule. Forecast wellhead volume V = Q × H × A, with A the availability factor for unplanned stops only (power cuts, faults, trips); maintenance already removed from H is not deducted again through A. For a second interval with a different rate or schedule, V = Σ(Q × H × A). Water entering the tank = V × (1 − transfer loss). Shortfall or surplus = tank volume − demand. The result is arithmetic on assumptions, not evidence that the well can sustain the rate: that comes from testing and monitoring.
Borewell production variance: Rate and hours effects
Forecast volume Vf = Qf × Hf; actual Va = Qa × Ha. Absolute variance = Va − Vf; percentage = 100 × (Va − Vf) ÷ Vf. Sign convention: negative = less than forecast (not necessarily bad, if demand fell). Rate effect = (Qa − Qf) × Hf; hours effect = Qa × (Ha − Hf); the two add up exactly to the total. Other conventions place the interaction term differently, so keep one convention month to month. Compare forecast and actual at the same boundary (wellhead, tank inflow or usable water) and period.
Borewell derating options: Rate factor, daily volume and shortfall
Enter one rate and one run time per option, in the same order. Daily volume = rate × run hours. Rate factor fQ = Q_restricted ÷ Q_reference (0.75 means 75% of the reference rate; it is not a 25% groundwater, energy or impact saving). Volume factor = option daily volume ÷ reference daily volume. Shortfall = demand − option daily volume. “Reduce pumping by 25%” is ambiguous: it can mean rate, hours or volume, so decide which the restriction must control.
Technical content reviewed by D. Srinivas Reddy, Managing Partner and service engineer, Reddy Compressors. Last updated 17 October 2026. How our engineering content is reviewed.