CTR K

Compressor Calculator — Shaft Power, Isentropic Efficiency & Discharge Temperature (ASME PTC 10 / ISO 1217)

Governing standard: ASME PTC 10 / ISO 1217· ASME PTC 10-1997 (Performance Test Code) · ISO 1217:2009 (displacement compressor acceptance tests) · isentropic / polytropic analysis

How ASME PTC 10 works — the method explained

The MechanixCalc compressor analysis calculator sizes and verifies gas compressors to ASME PTC 10 and ISO 1217 — the governing standards for compressor performance testing and acceptance. Enter the suction and discharge conditions, the gas, the number of stages and the isentropic efficiency, and the tool returns the shaft power, actual discharge temperature, overall isentropic efficiency, volumetric flow rate and a motor drive sizing in one pass. For multi-stage configurations with intercooling the per-stage temperatures, pressures and work split are resolved automatically.

It is built for process, mechanical and refrigeration engineers who need a defensible compressor duty point — for project proposals, equipment specification, or energy audits — and who need to deliver a standards-cited calculation rather than a back-of-envelope estimate. The P-V and T-s thermodynamic diagrams, the P-V indicator loop for reciprocating machines, and the centrifugal surge/choke operating-map provide the visual context that vendors and reviewers expect.

What this calculator does

  • Shaft power and drive power sizing to ASME PTC 10 / ISO 1217
  • Isentropic efficiency and actual discharge temperature for any gas (air, nitrogen, CO₂, hydrogen, methane, argon and more)
  • Multi-stage compression with perfect or partial intercooling — per-stage P, T and work breakdown
  • P-V and T-s thermodynamic diagrams showing isentropic vs. actual path
  • Reciprocating compressor P-V indicator loop — volumetric efficiency, indicated work per cycle and indicated power
  • Centrifugal compressor surge margin and choke margin with operating-point map
  • Standard motor frame size selection from the nearest IEC/NEMA duty rating
  • Branded PDF engineering report with governing standard, formulas and results

Method & formulas

Isentropic compression work (ASME PTC 10 / ISO 1217)

The ideal (isentropic) specific work is derived from the steady-flow energy equation for a reversible adiabatic process. It depends on the inlet temperature, the pressure ratio and the ratio of specific heats γ = Cp/Cv of the gas. The actual specific work is the isentropic work divided by the isentropic efficiency, which accounts for internal irreversibilities (heat transfer through the casing, gas leakage, friction). ASME PTC 10 defines the acceptance criteria for testing these quantities; ISO 1217 applies to displacement (reciprocating and screw) compressors.

Isentropic specific work
W_is = (γ / (γ − 1)) · R · T₁ · ((P₂/P₁)^((γ−1)/γ) − 1)

where W_is = isentropic specific work (kJ/kg); γ = ratio of specific heats (Cp/Cv); R = specific gas constant (kJ/kg·K); T₁ = inlet temperature (K); P₂/P₁ = overall pressure ratio

Shaft power
P_shaft = ṁ · W_is / η_is

where P_shaft = compressor shaft power (kW); ṁ = mass flow rate (kg/s); W_is = isentropic specific work (kJ/kg); η_is = isentropic efficiency (−)

Discharge temperature and multi-stage intercooling

The actual discharge temperature follows from the isentropic temperature rise scaled by the efficiency. For a multi-stage machine with perfect intercooling the gas is cooled back to the suction temperature between stages, so each stage does equal work and operates at the same stage pressure ratio — the thermodynamically optimal split for minimum total work. Partial intercooling (effectiveness ε < 100%) is modelled by blending the stage exit temperature with the suction temperature.

Actual discharge temperature
T₂ = T₁ + (T₂ₛ − T₁) / η_is

where T₂ = actual discharge temperature (K); T₁ = inlet temperature (K); T₂ₛ = isentropic discharge temperature (K) = T₁ · (P₂/P₁)^((γ−1)/γ); η_is = isentropic efficiency (−)

Optimum stage pressure ratio (N stages, perfect intercooling)
r_stage = (P₂/P₁)^(1/N)

where r_stage = pressure ratio per stage; P₂/P₁ = overall pressure ratio; N = number of compression stages

Reciprocating P-V indicator loop and volumetric efficiency

A reciprocating compressor is analysed via its polytropic P-V indicator diagram — the closed loop of compression (1→2), discharge (2→3), re-expansion of clearance gas (3→4) and suction (4→1). The clearance volume reduces the effective swept volume: gas trapped in the clearance expands back on the suction stroke before fresh charge is admitted, reducing the volumetric efficiency. The indicated work per cycle equals the enclosed area of the P-V loop, computed on the net induced volume (BDC − end of re-expansion), which correctly excludes the shuttle work of the clearance gas.

Volumetric efficiency
η_v = 1 − c · ((P₂/P₁)^(1/n) − 1)

where η_v = volumetric efficiency (−); c = clearance ratio = V_clearance / V_displacement (−); P₂/P₁ = pressure ratio; n = polytropic index

Worked example

Estimate the shaft power and discharge temperature of a single-stage air compressor delivering 1 kg/s from 1 bar (abs) at 20 °C to 4 bar (abs), with an isentropic efficiency of 80 %.

Given

  • GasAir (γ = 1.4, R = 0.287 kJ/kg·K)
  • Inlet temperature T₁293.15 K (20 °C)
  • Pressure ratio P₂/P₁4 (1 bar → 4 bar abs)
  • Mass flow ṁ1 kg/s
  • Isentropic efficiency η_is0.80

Result

  • Isentropic discharge temperature T₂ₛ435.7 K (162.6 °C)
  • Shaft power P_shaft≈ 179 kW
  • Actual discharge temperature T₂≈ 471 K (198 °C)
  1. Compute the isentropic temperature exponent: (γ−1)/γ = 0.4/1.4 ≈ 0.2857.
  2. Isentropic discharge temperature: T₂ₛ = 293.15 × 4^0.2857 = 293.15 × 1.486 ≈ 435.7 K (162.6 °C).
  3. Isentropic specific work: W_is = (1.4/0.4) × 0.287 × 293.15 × (1.486 − 1) = 3.5 × 0.287 × 293.15 × 0.486 ≈ 143.1 kJ/kg.
  4. Actual shaft power: P_shaft = ṁ × W_is / η_is = 1 × 143.1 / 0.80 ≈ 178.9 kW.
  5. Actual discharge temperature: T₂ = 293.15 + (435.7 − 293.15) / 0.80 = 293.15 + 178.2 ≈ 471.4 K (198 °C).

Illustrative single-stage calculation using ideal-gas air properties. The calculator resolves multi-stage intercooling, real gas properties and mechanical losses; verify against your actual gas composition and operating conditions.

Frequently asked questions

Which standard does this compressor calculator use?

The main thermodynamic engine follows ASME PTC 10-1997 (Performance Test Code on Compressors and Exhausters) and ISO 1217:2009 (Displacement compressors — acceptance tests). These define the isentropic and polytropic work methods, efficiency definitions and acceptance test procedures. The governing standard and method are shown in the generated PDF report.

What gases can I analyse?

The calculator includes built-in properties for air, nitrogen, oxygen, CO₂, hydrogen, methane, argon, helium and several refrigerants. For each gas the ratio of specific heats γ, the specific gas constant R and the specific heat Cp are used in the isentropic work and discharge temperature formulas. Custom γ and R values can also be entered for any other gas.

How does multi-stage intercooling reduce power consumption?

Compression work is proportional to the inlet temperature. If the gas is cooled back to the suction temperature between stages (perfect intercooling), each stage operates from the same low inlet temperature, so the total work is less than compressing in a single stage to the same overall pressure ratio. The calculator shows the power saving and per-stage breakdown for up to four stages.

Is the surge margin analysis to a standard?

The centrifugal compressor surge and choke margin panel uses a parabolic map curve-fit to approximate the compressor characteristic. This is an engineering estimate — not a governed standard method — and is marked as such in the tool. For final design, verify against the manufacturer's actual compressor map and test data.

Is the compressor calculator free?

You can use it during a free 30-minute preview with no sign-up, and a free 14-day account trial unlocks every calculator with no credit card required. The branded PDF engineering report and saved calculations are part of a paid plan.

Related calculators

Run the Compressor Analysis on your own numbers

Free 30-minute preview — no sign-up. A free 14-day account trial unlocks every tool and the branded PDF report, no credit card required.

Start free