10.3 Specific Volume, Mass Flow, and Compression Ratio

10.3 Specific Volume, Mass Flow, and Compression Ratio

Chapter 9 turned enthalpy into pounds per hour. Compressors do not swallow pounds. They swallow cubic feet. The bridge is specific volume of the suction vapor. Pair that with compression ratio on a psia basis and you can explain why a −20°F freezer is a different machine than a +20°F dock plant at the same 154 psig head.

Specific volume from the table

Specific volume v is cubic feet per pound (ft³/lb). Its inverse is density (lb/ft³). On the saturated-properties table the vapor column is vg (saturated vapor). Superheated suction is a little larger than vg at the same pressure — more space per pound — so using vg is the minimum volume for that suction pressure. CIRO wants you to look vg up, not invent it from memory of another refrigerant.

Landmark ammonia vg values consistent with NIST-style saturation data (round the way an on-screen table will; the printed row wins on test day):

Read the story, not just the cells: colder evaporator → lower pressure → vapor takes more space per pound. From 20°F to −20°F, vg goes from 5.91 to 14.7 — about 2.5 times the volume per pound. From 0°F to −20°F it jumps 9.12 → 14.7, about 61% more volume per pound. Discharge vapor at 86°F is dense (1.77 ft³/lb); that is why discharge lines are smaller than suction lines.

Why vg kills tons at a fixed cfm

A reciprocating machine, or a screw at a given slide-valve and speed, delivers a volumetric flow of suction vapor (cfm after you include volumetric efficiency — CIRO will usually give you the volume it wants or ask for the mass implied by vg).

ṁ (lb/min) = suction cfm / v (ft³/lb)

Tons = ṁ × NRE / 200 (because 1 ton = 200 Btu/min)

If v rises and cfm is fixed, ṁ falls, so tons fall even if NRE barely changed. That is the freezer penalty. Operators who only watch 'amps look fine' miss that the machine is pumping fluff.

Worked comparison — 80 tons of displacement thinking. Keep NRE in the picture so you do not blame volume for an enthalpy change.

Case A — dock plant, 20°F saturated suction, NRE = 480 Btu/lb (teaching NRE; compute yours from the table on exam day).

ṁ = 80 × 12,000 / 480 = 2,000 lb/h = 33.3 lb/min

Suction volume = 2,000 lb/h × 5.91 ft³/lb = 11,820 ft³/h = 197 cfm

Case B — freezer, −20°F saturated suction, NRE = 456 Btu/lb (the DX-style NRE from Chapter 9's colder evaporator with hot high-side liquid).

ṁ = 80 × 12,000 / 456 = 2,105 lb/h = 35.1 lb/min

Suction volume = 2,105 × 14.7 = 30,944 ft³/h = 516 cfm

Same 80 tons, almost the same pounds, more than 2.6 times the suction cubic feet. A compressor sized for the dock plant cannot make freezer tons at the same rpm. If you fix cfm at 197 and drop to −20°F:

ṁ = 197 cfm × 60 / 14.7 ≈ 804 lb/h

Tons ≈ 804 × 456 / 12,000 ≈ 30.5 tons — you kept the motor, you lost half the plant. That is specific volume, not a mysterious 'ammonia doesn't like freezers.'

Superheat makes it slightly worse: v_superheated > vg, so the same cfm carries even fewer pounds. A starved DX coil with 30°F of suction superheat is a volume problem as well as an NRE problem.

Mass-flow formulas you must not mix

1 ton = 12,000 Btu/h = 200 Btu/min.

ṁ (lb/min) = (tons × 200) / NRE

ṁ (lb/h) = (tons × 12,000) / NRE

Same equation. Minutes versus hours is the only fork. NRE is Btu/lb from h_suction − h_liquid in (Chapter 9), not evaporator hfg on a DX cycle with hot liquid, and not condenser hfg.

Worked. 50 tons, NRE = 470 Btu/lb:

ṁ = 50 × 200 / 470 = 21.3 lb/min

ṁ = 50 × 12,000 / 470 = 1,277 lb/h (21.3 × 60 = 1,278; rounding)

If you divide by hfg = 566 Btu/lb at 5°F instead of NRE = 470, you report 50 × 12,000 / 566 = 1,060 lb/h and understate compressor mass flow by about 17%. The missing pounds are flash gas the compressor still pumps.

Suction cfm from mass flow:

cfm = ṁ (lb/min) × v (ft³/lb)

21.3 lb/min × 8.15 ft³/lb (5°F vg) = 173 cfm of saturated suction vapor.

Compression ratio — absolute pressures only

CR = P_discharge / P_suction with both in psia.

psia = psig + 14.7 unless the stem gives another barometer.

Worked — 5°F / 86°F plant (Chapter 8 landmarks).

• Suction 19.6 psig = 34.3 psia
• Discharge 154.5 psig = 169.2 psia
• CR = 169.2 / 34.3 ≈ 4.93

Gauge ratio 154.5 / 19.6 ≈ 7.9 is a different, wrong machine. Temperature ratio 86 / 5 = 17 is not a ratio of pressures at all.

Worked — −20°F freezer, same 86°F condenser.

• P_suc = 18.30 psia (3.6 psig)
• P_dis = 169.2 psia
• CR = 169.2 / 18.30 ≈ 9.25

Worked — +20°F dock, same condenser.

• P_suc = 48.21 psia
• CR = 169.2 / 48.21 ≈ 3.51

Same penthouse condenser, three different ratios, because suction psia is the denominator. Low-side vacuum makes the gauge-ratio trap even louder: 154 / 3.6 ≈ 43, which is fiction.

The ~8:1 class — hot gas and oil, not a code number

Industrial practice treats high single-stage ratios as a reliability limit. A useful order-of-magnitude picture is the ~8:1 class: not an IIAR paragraph, not a RETA passing score, not a stamped relief setting. It is the neighborhood where discharge temperature and oil breakdown get expensive on a single-stage ammonia machine.

Check the freezer: −20°F suction is 18.30 psia. An 8:1 discharge would be 8 × 18.30 = 146 psia ≈ 131 psig, which is only about 78–80°F condensing. An 80°F condenser at 153.0 psia on a −20°F freezer is already CR = 153.0 / 18.30 ≈ 8.4. The common 86°F / 154 psig teaching head is ~9.3:1. That is why two-stage (later chapter) exists for low-temperature ammonia: split the ratio, desuperheat at interstage, keep oil alive. A +20°F plant at 86°F is ~3.5:1 and is not in that fight.

What high CR does, in Heat Flow language:

• More compression work per pound (BHP/ton up, COP down).
• Higher isentropic discharge temperature; actual discharge runs hotter still when efficiency is poor or suction superheat is high (Chapter 9 charts).
• Oil that lives in that gas stream cokes, vanishes, and stops lubricating — a mechanical-integrity problem that started as a ratio problem.
• Specific volume at suction already high (freezer), so you needed two-stage for cfm as well as for temperature.

If a stem shows a single-stage freezer at 9:1 or 10:1, the correct operator comment is high ratio, expect hot discharge and oil stress, not 'illegal because 8:1 is in the code.' If the ratio is 4:1 on a cooler, do not invent an oil crisis from the number alone.

Putting vg, ṁ, and CR on one screen

A 100-ton single-stage plant, saturated suction 0°F (30.42 psia, vg = 9.12 ft³/lb), condenser 86°F (169.2 psia), NRE = 463 Btu/lb (Chapter 9's 0°F / hot-liquid order of magnitude).

• ṁ = 100 × 12,000 / 463 ≈ 2,592 lb/h = 43.2 lb/min
• Suction volume = 43.2 × 9.12 ≈ 394 cfm
• CR = 169.2 / 30.42 ≈ 5.56 — uncomfortable if dirty and superheated, not yet the freezer 9:1 class

Drop the same 100-ton cfm machine to −20°F without adding displacement: vg rises to 14.7, ṁ falls in the ratio 9.12/14.7, tons collapse even before NRE and CR get worse. Add displacement or add a booster — that is the later two-stage conversation. This section's job is to read vg, compute ṁ from tons and NRE, and compute CR in psia.

Exam traps

• vg from a liquid column, or from 86°F when the suction is 0°F.
• cfm × vg instead of cfm / v for mass flow (units scream if you watch them).
• ṁ = tons / NRE with tons not converted to Btu/h or Btu/min.
• Compression ratio in psig or as T_dis / T_suc.
• Quoting 8:1 as a numbered standard. Teach the consequence: high ratio, hot discharge, oil failure risk.
• Using hfg in the mass-flow equation when the stem gave NRE.