Single-Stage Air Compressor Overloading Its 75 kW Motor
A garment unit at Ranchi runs a single-stage reciprocating air compressor at 0.30 m³/s free air delivery, drawing air at 1.0 bar absolute and 32 °C and delivering at 7.0 bar absolute. The compression index is n = 1.30 and the overall efficiency (indicated power to electrical input) is 0.88. The compressor is coupled to a 75 kW induction motor and runs 6,000 hours a year; energy is billed at ₹7.50 per kWh. The unit engineer proposes either a two-stage machine with perfect intercooling back to 32 °C across the same overall pressure ratio, or an improved aftercooler on the existing set. Separately, the measured free air delivery of the existing machine is only 0.27 m³/s, the discharge pipe is too hot to touch, and the aftercooler outlet is barely cooler than its inlet. Management wants a decision this week, and the electrician reports the 75 kW motor running at about 104% of rated current.
1. Estimate the indicated and input power of the existing single-stage machine and state whether the 75 kW motor is adequate.
Read the worked answer
Formula. W = (n/(n−1))·p1V1·[(p2/p1)^((n−1)/n) − 1]
n/(n−1) = 1.3/0.3 = 4.333; p1V1 = 100 kPa × 0.30 m³/s = 30 kJ; pressure ratio = 7.
7^0.2308 = e^(0.2308 × 1.9459) = e^0.4491 = 1.567, so the bracket = 0.567.
W = 4.333 × 30 × 0.567 = 73.7 kW indicated.
Input power = 73.7/0.88 = 83.8 kW.
Verdict. The 75 kW motor is loaded to 83.8/75 = 112%, which matches the reported 104% current (current is not exactly proportional to power, and the motor is probably running a little below rated voltage). The motor is undersized and will trip on overload or fail thermally; the machine also consumes 83.8/0.30 = 279 kW per m³/s of free air, which is high for 7 bar.
So the answer to 'is 75 kW enough' is no - and this is a selection error, not a fault that can be tuned out.
2. Evaluate the two-stage option with perfect intercooling: compute the power, the annual saving and the practical caveat.
Read the worked answer
Per-stage ratio = √7 = 2.646. With intercooling back to 32 °C, stage 2 suction volume = 0.30/2.646 = 0.1134 m³/s, so p1V1 per stage = 100 × 0.30 = 30 kJ (and 264.6 × 0.1134 = 30 kJ).
Work per stage = 4.333 × 30 × (2.646^0.2308 − 1) = 4.333 × 30 × (1.252 − 1) = 32.7 kW.
Total indicated = 65.5 kW; input = 65.5/0.88 = 74.4 kW.
Saving = 83.8 − 74.4 = 9.4 kW → 9.4 × 6,000 = 56,400 kWh/year → 56,400 × 7.50 = ₹4.23 lakh per year. Against the capital cost of a two-stage set this is a good return.
Caveat - the motor. 74.4 kW on a 75 kW motor is 99% loading, with no margin for fouling, high ambient temperature or voltage dip. Order the two-stage set with a 90 kW motor, and also specify intercooler outlet temperature, a moisture separator and the pressure drop allowed across the intercooler (that pressure drop is what turns 'perfect' intercooling into a real 8–10% saving rather than 12%).
Conclusion: two-stage is justified technically and economically - but not on the existing 75 kW motor.
3. Explain the measured 0.27 m³/s delivery, the very hot discharge pipe and the ineffective aftercooler, and rank the actions.
Read the worked answer
Delivery shortfall. 0.30 → 0.27 m³/s is roughly a 10% loss of volumetric efficiency. Likely causes: excessive clearance volume, leaking or carbonised suction/delivery valves, worn piston rings, or a choked suction filter dropping suction pressure. A drop of this size is not normal for a healthy machine; confirm by an indicator card or a clearance (bumping) test.
Hot discharge pipe. Ideal delivery temperature = T1(p2/p1)^((n−1)/n) = 305 × 1.567 ≈ 478 K ≈ 205 °C. A single-stage machine to 7 bar is expected to run a very hot discharge; the hot pipe is not itself a fault. It is the reason an aftercooler and lagging/guarding are required.
Barely-cooled aftercooler outlet. This is the actual defect: scaled or fouled tubes, a bypass left open, or no/low cooling water flow. Repairing it will not reduce compression power (the work is done in the cylinder) but it protects the downstream dryer, pipework and tools.
Ranking. (1) Repair the aftercooler and check valves/clearance - no capital cost. (2) Re-rate or replace the motor. (3) Only then commit capital to a two-stage machine.